

<p>$X_0(N)/F_5$</p>

{{{id=4|
B = BrandtModule(5, 37); B
///
Brandt module of dimension 14 of level 5*37 of weight 2 over Rational Field
}}}

{{{id=3|
dimension_new_cusp_forms(37*5,2,5) + 1
///
14
}}}

{{{id=2|
time RI = B.right_ideals()
///
Time: CPU 0.22 s, Wall: 0.22 s
}}}

{{{id=1|
time R_0 = RI[0].left_order()
///
Time: CPU 0.01 s, Wall: 0.01 s
}}}

{{{id=6|
q_0 = R_0.ternary_quadratic_form()
///
}}}

{{{id=7|
show(q_0.theta_series(200))
///
<html><div class="math">1 + 2q^{3} + 2q^{12} + 2q^{27} + 2q^{48} + 2q^{75} + 2q^{108} + 2q^{147} + 2q^{192} + O(q^{200})</div></html>
}}}

{{{id=8|
time quadforms = [I.left_order().ternary_quadratic_form() for I in RI]
///
Time: CPU 0.49 s, Wall: 0.50 s
}}}

{{{id=10|
time theta_series = [q.theta_series(1000) for q in quadforms]
///
Time: CPU 0.09 s, Wall: 0.09 s
}}}

{{{id=9|
for q in theta_series:
    print q
///
1 + 2*q^3 + 2*q^12 + 2*q^27 + 2*q^48 + 2*q^75 + 2*q^108 + 2*q^147 + 2*q^192 + 2*q^243 + 6*q^247 + 6*q^248 + 6*q^252 + 6*q^255 + 6*q^263 + 6*q^268 + 6*q^280 + 6*q^287 + 2*q^300 + 6*q^303 + 6*q^312 + 6*q^332 + 6*q^343 + 2*q^363 + 6*q^367 + 6*q^380 + 6*q^408 + 6*q^423 + 2*q^432 + 6*q^455 + 6*q^472 + 2*q^507 + 6*q^508 + 6*q^527 + 6*q^567 + 8*q^588 + 6*q^632 + 6*q^655 + 2*q^675 + 6*q^703 + 6*q^728 + 6*q^740 + 12*q^743 + 12*q^752 + 12*q^767 + 2*q^768 + 6*q^780 + 12*q^788 + 6*q^807 + 12*q^815 + 12*q^848 + 6*q^863 + 2*q^867 + 12*q^887 + 6*q^892 + 12*q^932 + 6*q^952 + 2*q^972 + 18*q^983 + 6*q^987 + 6*q^988 + 6*q^992 + 6*q^995 + O(q^1000)
1 + 2*q^12 + 2*q^48 + 2*q^63 + 2*q^67 + 2*q^83 + 2*q^95 + 2*q^108 + 2*q^127 + 2*q^147 + 4*q^188 + 2*q^192 + 2*q^195 + 4*q^212 + 2*q^223 + 4*q^247 + 2*q^248 + 2*q^252 + 4*q^255 + 4*q^260 + 4*q^263 + 2*q^268 + 2*q^280 + 6*q^287 + 2*q^300 + 4*q^303 + 2*q^312 + 2*q^323 + 6*q^332 + 4*q^343 + 4*q^367 + 2*q^380 + 2*q^403 + 2*q^408 + 4*q^423 + 4*q^428 + 6*q^432 + 4*q^440 + 2*q^447 + 4*q^448 + 4*q^455 + 6*q^472 + 4*q^488 + 2*q^508 + 4*q^527 + 4*q^528 + 2*q^543 + 4*q^548 + 4*q^552 + 2*q^555 + 8*q^567 + 4*q^588 + 2*q^595 + 4*q^603 + 4*q^608 + 2*q^632 + 4*q^640 + 4*q^655 + 4*q^663 + 4*q^692 + 4*q^703 + 2*q^707 + 4*q^712 + 2*q^728 + 2*q^740 + 8*q^743 + 4*q^747 + 8*q^752 + 10*q^767 + 2*q^768 + 2*q^780 + 4*q^788 + 4*q^803 + 8*q^807 + 8*q^815 + 4*q^823 + 4*q^835 + 4*q^840 + 4*q^848 + 4*q^855 + 4*q^860 + 4*q^863 + 4*q^867 + 12*q^887 + 4*q^888 + 2*q^892 + 2*q^895 + 4*q^932 + 4*q^935 + 2*q^952 + 6*q^963 + 2*q^972 + 12*q^983 + 4*q^987 + 6*q^988 + 10*q^992 + O(q^1000)
1 + 2*q^47 + 2*q^48 + 2*q^63 + 2*q^83 + 2*q^95 + 2*q^107 + 2*q^108 + 2*q^112 + 2*q^127 + 2*q^132 + 2*q^152 + 2*q^160 + 4*q^188 + 2*q^192 + 2*q^212 + 2*q^215 + 2*q^223 + 2*q^247 + 2*q^248 + 2*q^252 + 2*q^255 + 2*q^260 + 4*q^263 + 2*q^268 + 4*q^287 + 2*q^292 + 2*q^295 + 4*q^303 + 2*q^307 + 2*q^308 + 2*q^323 + 4*q^332 + 2*q^343 + 2*q^360 + 2*q^363 + 2*q^367 + 2*q^380 + 2*q^395 + 2*q^407 + 4*q^423 + 2*q^428 + 4*q^432 + 2*q^435 + 2*q^440 + 2*q^443 + 4*q^447 + 2*q^448 + 2*q^455 + 2*q^460 + 2*q^472 + 2*q^480 + 4*q^488 + 2*q^492 + 2*q^507 + 4*q^508 + 2*q^515 + 4*q^527 + 4*q^528 + 4*q^543 + 4*q^548 + 4*q^552 + 6*q^567 + 2*q^580 + 2*q^583 + 2*q^588 + 2*q^592 + 2*q^603 + 6*q^608 + 4*q^620 + 2*q^628 + 2*q^632 + 2*q^640 + 2*q^655 + 6*q^663 + 4*q^667 + 4*q^687 + 6*q^692 + 2*q^703 + 2*q^707 + 4*q^712 + 2*q^715 + 4*q^728 + 6*q^743 + 2*q^747 + 6*q^752 + 8*q^767 + 6*q^768 + 2*q^780 + 2*q^787 + 2*q^788 + 2*q^803 + 6*q^807 + 4*q^815 + 4*q^823 + 2*q^840 + 2*q^847 + 4*q^848 + 2*q^852 + 4*q^855 + 4*q^860 + 6*q^863 + 2*q^867 + 4*q^872 + 8*q^887 + 2*q^888 + 4*q^892 + 4*q^895 + 2*q^915 + 4*q^932 + 4*q^935 + 2*q^963 + 6*q^972 + 8*q^983 + 4*q^988 + 6*q^992 + O(q^1000)
1 + 2*q^27 + 2*q^28 + 2*q^47 + 2*q^63 + 2*q^108 + 2*q^112 + 2*q^120 + 2*q^123 + 2*q^152 + 2*q^155 + 2*q^188 + 4*q^192 + 4*q^215 + 4*q^223 + 2*q^243 + 2*q^247 + 4*q^248 + 4*q^252 + 2*q^255 + 4*q^263 + 4*q^287 + 4*q^292 + 2*q^295 + 2*q^303 + 2*q^307 + 4*q^308 + 2*q^312 + 4*q^332 + 4*q^360 + 4*q^367 + 4*q^380 + 2*q^403 + 4*q^407 + 2*q^408 + 6*q^423 + 6*q^428 + 2*q^432 + 2*q^443 + 4*q^447 + 2*q^448 + 4*q^455 + 2*q^480 + 4*q^492 + 2*q^507 + 4*q^508 + 8*q^527 + 4*q^528 + 4*q^543 + 2*q^567 + 4*q^580 + 4*q^583 + 2*q^588 + 2*q^595 + 6*q^608 + 2*q^620 + 4*q^632 + 4*q^640 + 6*q^663 + 2*q^675 + 6*q^687 + 4*q^692 + 2*q^700 + 2*q^707 + 4*q^712 + 6*q^728 + 2*q^740 + 6*q^743 + 6*q^752 + 6*q^767 + 4*q^768 + 2*q^780 + 6*q^787 + 4*q^788 + 4*q^803 + 2*q^807 + 4*q^815 + 2*q^823 + 4*q^847 + 8*q^848 + 4*q^852 + 4*q^855 + 4*q^860 + 8*q^863 + 2*q^867 + 4*q^872 + 8*q^887 + 2*q^888 + 4*q^892 + 4*q^895 + 4*q^928 + 4*q^932 + 4*q^935 + 2*q^952 + 2*q^963 + 4*q^972 + 8*q^983 + 6*q^987 + 2*q^988 + 8*q^992 + 4*q^995 + O(q^1000)
1 + 2*q^47 + 2*q^48 + 2*q^63 + 2*q^83 + 2*q^95 + 2*q^107 + 2*q^108 + 2*q^112 + 2*q^127 + 2*q^132 + 2*q^152 + 2*q^160 + 4*q^188 + 2*q^192 + 2*q^212 + 2*q^215 + 2*q^223 + 2*q^247 + 2*q^248 + 2*q^252 + 2*q^255 + 2*q^260 + 4*q^263 + 2*q^268 + 4*q^287 + 2*q^292 + 2*q^295 + 4*q^303 + 2*q^307 + 2*q^308 + 2*q^323 + 4*q^332 + 2*q^343 + 2*q^360 + 2*q^363 + 2*q^367 + 2*q^380 + 2*q^395 + 2*q^407 + 4*q^423 + 2*q^428 + 4*q^432 + 2*q^435 + 2*q^440 + 2*q^443 + 4*q^447 + 2*q^448 + 2*q^455 + 2*q^460 + 2*q^472 + 2*q^480 + 4*q^488 + 2*q^492 + 2*q^507 + 4*q^508 + 2*q^515 + 4*q^527 + 4*q^528 + 4*q^543 + 4*q^548 + 4*q^552 + 6*q^567 + 2*q^580 + 2*q^583 + 2*q^588 + 2*q^592 + 2*q^603 + 6*q^608 + 4*q^620 + 2*q^628 + 2*q^632 + 2*q^640 + 2*q^655 + 6*q^663 + 4*q^667 + 4*q^687 + 6*q^692 + 2*q^703 + 2*q^707 + 4*q^712 + 2*q^715 + 4*q^728 + 6*q^743 + 2*q^747 + 6*q^752 + 8*q^767 + 6*q^768 + 2*q^780 + 2*q^787 + 2*q^788 + 2*q^803 + 6*q^807 + 4*q^815 + 4*q^823 + 2*q^840 + 2*q^847 + 4*q^848 + 2*q^852 + 4*q^855 + 4*q^860 + 6*q^863 + 2*q^867 + 4*q^872 + 8*q^887 + 2*q^888 + 4*q^892 + 4*q^895 + 2*q^915 + 4*q^932 + 4*q^935 + 2*q^963 + 6*q^972 + 8*q^983 + 4*q^988 + 6*q^992 + O(q^1000)
1 + 2*q^40 + 4*q^47 + 2*q^95 + 2*q^115 + 4*q^127 + 4*q^132 + 2*q^148 + 4*q^152 + 2*q^155 + 2*q^160 + 4*q^188 + 4*q^192 + 2*q^215 + 4*q^243 + 4*q^252 + 4*q^263 + 4*q^287 + 2*q^295 + 4*q^303 + 4*q^308 + 4*q^332 + 4*q^343 + 2*q^360 + 4*q^363 + 4*q^380 + 2*q^395 + 4*q^407 + 4*q^423 + 4*q^428 + 4*q^432 + 4*q^443 + 8*q^447 + 4*q^448 + 4*q^460 + 4*q^488 + 4*q^508 + 2*q^515 + 4*q^527 + 8*q^528 + 4*q^543 + 4*q^548 + 4*q^552 + 8*q^567 + 4*q^583 + 2*q^592 + 8*q^608 + 4*q^620 + 4*q^628 + 4*q^632 + 2*q^640 + 2*q^655 + 4*q^663 + 4*q^687 + 4*q^692 + 4*q^703 + 4*q^707 + 4*q^728 + 8*q^743 + 4*q^747 + 4*q^752 + 8*q^767 + 8*q^768 + 4*q^788 + 4*q^803 + 4*q^807 + 2*q^815 + 4*q^823 + 2*q^835 + 4*q^847 + 4*q^848 + 4*q^852 + 2*q^855 + 4*q^860 + 8*q^863 + 4*q^872 + 4*q^887 + 4*q^892 + 2*q^895 + 4*q^932 + 4*q^935 + 4*q^952 + 2*q^955 + 4*q^963 + 8*q^972 + 4*q^983 + 4*q^987 + 4*q^988 + 4*q^992 + 2*q^995 + O(q^1000)
1 + 2*q^40 + 4*q^47 + 2*q^95 + 2*q^115 + 4*q^127 + 4*q^132 + 2*q^148 + 4*q^152 + 2*q^155 + 2*q^160 + 4*q^188 + 4*q^192 + 2*q^215 + 4*q^243 + 4*q^252 + 4*q^263 + 4*q^287 + 2*q^295 + 4*q^303 + 4*q^308 + 4*q^332 + 4*q^343 + 2*q^360 + 4*q^363 + 4*q^380 + 2*q^395 + 4*q^407 + 4*q^423 + 4*q^428 + 4*q^432 + 4*q^443 + 8*q^447 + 4*q^448 + 4*q^460 + 4*q^488 + 4*q^508 + 2*q^515 + 4*q^527 + 8*q^528 + 4*q^543 + 4*q^548 + 4*q^552 + 8*q^567 + 4*q^583 + 2*q^592 + 8*q^608 + 4*q^620 + 4*q^628 + 4*q^632 + 2*q^640 + 2*q^655 + 4*q^663 + 4*q^687 + 4*q^692 + 4*q^703 + 4*q^707 + 4*q^728 + 8*q^743 + 4*q^747 + 4*q^752 + 8*q^767 + 8*q^768 + 4*q^788 + 4*q^803 + 4*q^807 + 2*q^815 + 4*q^823 + 2*q^835 + 4*q^847 + 4*q^848 + 4*q^852 + 2*q^855 + 4*q^860 + 8*q^863 + 4*q^872 + 4*q^887 + 4*q^892 + 2*q^895 + 4*q^932 + 4*q^935 + 4*q^952 + 2*q^955 + 4*q^963 + 8*q^972 + 4*q^983 + 4*q^987 + 4*q^988 + 4*q^992 + 2*q^995 + O(q^1000)
1 + 2*q^7 + 2*q^28 + 2*q^63 + 2*q^107 + 2*q^108 + 2*q^112 + 2*q^120 + 2*q^123 + 2*q^147 + 2*q^152 + 2*q^175 + 2*q^188 + 2*q^195 + 4*q^212 + 4*q^215 + 4*q^223 + 4*q^232 + 2*q^243 + 4*q^248 + 4*q^252 + 4*q^263 + 4*q^287 + 4*q^308 + 2*q^312 + 2*q^323 + 4*q^340 + 2*q^343 + 4*q^367 + 2*q^395 + 4*q^407 + 2*q^408 + 6*q^423 + 6*q^428 + 6*q^432 + 4*q^440 + 6*q^447 + 2*q^448 + 6*q^455 + 6*q^480 + 4*q^488 + 8*q^492 + 2*q^507 + 10*q^527 + 6*q^543 + 2*q^567 + 4*q^583 + 6*q^588 + 2*q^603 + 6*q^608 + 2*q^620 + 4*q^628 + 6*q^663 + 6*q^687 + 4*q^692 + 2*q^700 + 2*q^728 + 2*q^740 + 4*q^743 + 6*q^747 + 6*q^752 + 4*q^768 + 6*q^780 + 4*q^803 + 4*q^815 + 10*q^847 + 8*q^848 + 4*q^852 + 6*q^855 + 8*q^860 + 8*q^863 + 2*q^867 + 4*q^872 + 14*q^887 + 2*q^888 + 8*q^892 + 4*q^915 + 8*q^928 + 8*q^935 + 6*q^952 + 2*q^955 + 2*q^963 + 8*q^972 + 8*q^983 + 2*q^988 + 12*q^992 + O(q^1000)
1 + 2*q^47 + 2*q^48 + 2*q^63 + 2*q^83 + 2*q^95 + 2*q^107 + 2*q^108 + 2*q^112 + 2*q^127 + 2*q^132 + 2*q^152 + 2*q^160 + 4*q^188 + 2*q^192 + 2*q^212 + 2*q^215 + 2*q^223 + 2*q^247 + 2*q^248 + 2*q^252 + 2*q^255 + 2*q^260 + 4*q^263 + 2*q^268 + 4*q^287 + 2*q^292 + 2*q^295 + 4*q^303 + 2*q^307 + 2*q^308 + 2*q^323 + 4*q^332 + 2*q^343 + 2*q^360 + 2*q^363 + 2*q^367 + 2*q^380 + 2*q^395 + 2*q^407 + 4*q^423 + 2*q^428 + 4*q^432 + 2*q^435 + 2*q^440 + 2*q^443 + 4*q^447 + 2*q^448 + 2*q^455 + 2*q^460 + 2*q^472 + 2*q^480 + 4*q^488 + 2*q^492 + 2*q^507 + 4*q^508 + 2*q^515 + 4*q^527 + 4*q^528 + 4*q^543 + 4*q^548 + 4*q^552 + 6*q^567 + 2*q^580 + 2*q^583 + 2*q^588 + 2*q^592 + 2*q^603 + 6*q^608 + 4*q^620 + 2*q^628 + 2*q^632 + 2*q^640 + 2*q^655 + 6*q^663 + 4*q^667 + 4*q^687 + 6*q^692 + 2*q^703 + 2*q^707 + 4*q^712 + 2*q^715 + 4*q^728 + 6*q^743 + 2*q^747 + 6*q^752 + 8*q^767 + 6*q^768 + 2*q^780 + 2*q^787 + 2*q^788 + 2*q^803 + 6*q^807 + 4*q^815 + 4*q^823 + 2*q^840 + 2*q^847 + 4*q^848 + 2*q^852 + 4*q^855 + 4*q^860 + 6*q^863 + 2*q^867 + 4*q^872 + 8*q^887 + 2*q^888 + 4*q^892 + 4*q^895 + 2*q^915 + 4*q^932 + 4*q^935 + 2*q^963 + 6*q^972 + 8*q^983 + 4*q^988 + 6*q^992 + O(q^1000)
1 + 2*q^47 + 2*q^48 + 2*q^63 + 2*q^83 + 2*q^95 + 2*q^107 + 2*q^108 + 2*q^112 + 2*q^127 + 2*q^132 + 2*q^152 + 2*q^160 + 4*q^188 + 2*q^192 + 2*q^212 + 2*q^215 + 2*q^223 + 2*q^247 + 2*q^248 + 2*q^252 + 2*q^255 + 2*q^260 + 4*q^263 + 2*q^268 + 4*q^287 + 2*q^292 + 2*q^295 + 4*q^303 + 2*q^307 + 2*q^308 + 2*q^323 + 4*q^332 + 2*q^343 + 2*q^360 + 2*q^363 + 2*q^367 + 2*q^380 + 2*q^395 + 2*q^407 + 4*q^423 + 2*q^428 + 4*q^432 + 2*q^435 + 2*q^440 + 2*q^443 + 4*q^447 + 2*q^448 + 2*q^455 + 2*q^460 + 2*q^472 + 2*q^480 + 4*q^488 + 2*q^492 + 2*q^507 + 4*q^508 + 2*q^515 + 4*q^527 + 4*q^528 + 4*q^543 + 4*q^548 + 4*q^552 + 6*q^567 + 2*q^580 + 2*q^583 + 2*q^588 + 2*q^592 + 2*q^603 + 6*q^608 + 4*q^620 + 2*q^628 + 2*q^632 + 2*q^640 + 2*q^655 + 6*q^663 + 4*q^667 + 4*q^687 + 6*q^692 + 2*q^703 + 2*q^707 + 4*q^712 + 2*q^715 + 4*q^728 + 6*q^743 + 2*q^747 + 6*q^752 + 8*q^767 + 6*q^768 + 2*q^780 + 2*q^787 + 2*q^788 + 2*q^803 + 6*q^807 + 4*q^815 + 4*q^823 + 2*q^840 + 2*q^847 + 4*q^848 + 2*q^852 + 4*q^855 + 4*q^860 + 6*q^863 + 2*q^867 + 4*q^872 + 8*q^887 + 2*q^888 + 4*q^892 + 4*q^895 + 2*q^915 + 4*q^932 + 4*q^935 + 2*q^963 + 6*q^972 + 8*q^983 + 4*q^988 + 6*q^992 + O(q^1000)
1 + 2*q^12 + 2*q^48 + 2*q^63 + 2*q^67 + 2*q^83 + 2*q^95 + 2*q^108 + 2*q^127 + 2*q^147 + 4*q^188 + 2*q^192 + 2*q^195 + 4*q^212 + 2*q^223 + 4*q^247 + 2*q^248 + 2*q^252 + 4*q^255 + 4*q^260 + 4*q^263 + 2*q^268 + 2*q^280 + 6*q^287 + 2*q^300 + 4*q^303 + 2*q^312 + 2*q^323 + 6*q^332 + 4*q^343 + 4*q^367 + 2*q^380 + 2*q^403 + 2*q^408 + 4*q^423 + 4*q^428 + 6*q^432 + 4*q^440 + 2*q^447 + 4*q^448 + 4*q^455 + 6*q^472 + 4*q^488 + 2*q^508 + 4*q^527 + 4*q^528 + 2*q^543 + 4*q^548 + 4*q^552 + 2*q^555 + 8*q^567 + 4*q^588 + 2*q^595 + 4*q^603 + 4*q^608 + 2*q^632 + 4*q^640 + 4*q^655 + 4*q^663 + 4*q^692 + 4*q^703 + 2*q^707 + 4*q^712 + 2*q^728 + 2*q^740 + 8*q^743 + 4*q^747 + 8*q^752 + 10*q^767 + 2*q^768 + 2*q^780 + 4*q^788 + 4*q^803 + 8*q^807 + 8*q^815 + 4*q^823 + 4*q^835 + 4*q^840 + 4*q^848 + 4*q^855 + 4*q^860 + 4*q^863 + 4*q^867 + 12*q^887 + 4*q^888 + 2*q^892 + 2*q^895 + 4*q^932 + 4*q^935 + 2*q^952 + 6*q^963 + 2*q^972 + 12*q^983 + 4*q^987 + 6*q^988 + 10*q^992 + O(q^1000)
1 + 2*q^3 + 2*q^12 + 2*q^27 + 2*q^48 + 2*q^75 + 2*q^108 + 2*q^147 + 2*q^192 + 2*q^243 + 6*q^247 + 6*q^248 + 6*q^252 + 6*q^255 + 6*q^263 + 6*q^268 + 6*q^280 + 6*q^287 + 2*q^300 + 6*q^303 + 6*q^312 + 6*q^332 + 6*q^343 + 2*q^363 + 6*q^367 + 6*q^380 + 6*q^408 + 6*q^423 + 2*q^432 + 6*q^455 + 6*q^472 + 2*q^507 + 6*q^508 + 6*q^527 + 6*q^567 + 8*q^588 + 6*q^632 + 6*q^655 + 2*q^675 + 6*q^703 + 6*q^728 + 6*q^740 + 12*q^743 + 12*q^752 + 12*q^767 + 2*q^768 + 6*q^780 + 12*q^788 + 6*q^807 + 12*q^815 + 12*q^848 + 6*q^863 + 2*q^867 + 12*q^887 + 6*q^892 + 12*q^932 + 6*q^952 + 2*q^972 + 18*q^983 + 6*q^987 + 6*q^988 + 6*q^992 + 6*q^995 + O(q^1000)
1 + 2*q^27 + 2*q^28 + 2*q^47 + 2*q^63 + 2*q^108 + 2*q^112 + 2*q^120 + 2*q^123 + 2*q^152 + 2*q^155 + 2*q^188 + 4*q^192 + 4*q^215 + 4*q^223 + 2*q^243 + 2*q^247 + 4*q^248 + 4*q^252 + 2*q^255 + 4*q^263 + 4*q^287 + 4*q^292 + 2*q^295 + 2*q^303 + 2*q^307 + 4*q^308 + 2*q^312 + 4*q^332 + 4*q^360 + 4*q^367 + 4*q^380 + 2*q^403 + 4*q^407 + 2*q^408 + 6*q^423 + 6*q^428 + 2*q^432 + 2*q^443 + 4*q^447 + 2*q^448 + 4*q^455 + 2*q^480 + 4*q^492 + 2*q^507 + 4*q^508 + 8*q^527 + 4*q^528 + 4*q^543 + 2*q^567 + 4*q^580 + 4*q^583 + 2*q^588 + 2*q^595 + 6*q^608 + 2*q^620 + 4*q^632 + 4*q^640 + 6*q^663 + 2*q^675 + 6*q^687 + 4*q^692 + 2*q^700 + 2*q^707 + 4*q^712 + 6*q^728 + 2*q^740 + 6*q^743 + 6*q^752 + 6*q^767 + 4*q^768 + 2*q^780 + 6*q^787 + 4*q^788 + 4*q^803 + 2*q^807 + 4*q^815 + 2*q^823 + 4*q^847 + 8*q^848 + 4*q^852 + 4*q^855 + 4*q^860 + 8*q^863 + 2*q^867 + 4*q^872 + 8*q^887 + 2*q^888 + 4*q^892 + 4*q^895 + 4*q^928 + 4*q^932 + 4*q^935 + 2*q^952 + 2*q^963 + 4*q^972 + 8*q^983 + 6*q^987 + 2*q^988 + 8*q^992 + 4*q^995 + O(q^1000)
1 + 2*q^7 + 2*q^28 + 2*q^63 + 2*q^107 + 2*q^108 + 2*q^112 + 2*q^120 + 2*q^123 + 2*q^147 + 2*q^152 + 2*q^175 + 2*q^188 + 2*q^195 + 4*q^212 + 4*q^215 + 4*q^223 + 4*q^232 + 2*q^243 + 4*q^248 + 4*q^252 + 4*q^263 + 4*q^287 + 4*q^308 + 2*q^312 + 2*q^323 + 4*q^340 + 2*q^343 + 4*q^367 + 2*q^395 + 4*q^407 + 2*q^408 + 6*q^423 + 6*q^428 + 6*q^432 + 4*q^440 + 6*q^447 + 2*q^448 + 6*q^455 + 6*q^480 + 4*q^488 + 8*q^492 + 2*q^507 + 10*q^527 + 6*q^543 + 2*q^567 + 4*q^583 + 6*q^588 + 2*q^603 + 6*q^608 + 2*q^620 + 4*q^628 + 6*q^663 + 6*q^687 + 4*q^692 + 2*q^700 + 2*q^728 + 2*q^740 + 4*q^743 + 6*q^747 + 6*q^752 + 4*q^768 + 6*q^780 + 4*q^803 + 4*q^815 + 10*q^847 + 8*q^848 + 4*q^852 + 6*q^855 + 8*q^860 + 8*q^863 + 2*q^867 + 4*q^872 + 14*q^887 + 2*q^888 + 8*q^892 + 4*q^915 + 8*q^928 + 8*q^935 + 6*q^952 + 2*q^955 + 2*q^963 + 8*q^972 + 8*q^983 + 2*q^988 + 12*q^992 + O(q^1000)
}}}

{{{id=12|
for n in range(1,1000):
    k = len([i for i in range(len(theta_series)) if theta_series[i][n]])
    if k == len(theta_series):
        print n, k, factor(n)
///
252 14 2^2 * 3^2 * 7
263 14 263
287 14 7 * 41
423 14 3^2 * 47
432 14 2^4 * 3^3
527 14 17 * 31
567 14 3^4 * 7
728 14 2^3 * 7 * 13
743 14 743
752 14 2^4 * 47
768 14 2^8 * 3
815 14 5 * 163
848 14 2^4 * 53
863 14 863
887 14 887
892 14 2^2 * 223
972 14 2^2 * 3^5
983 14 983
988 14 2^2 * 13 * 19
992 14 2^5 * 31
}}}

{{{id=11|
QuadraticField(-263,'a').factor(37)
///
(Fractional ideal (37, a - 12)) * (Fractional ideal (37, a + 12))
}}}

{{{id=13|
QuadraticField(-743,'a').factor(37)
///
(Fractional ideal (37, a - 16)) * (Fractional ideal (37, a + 16))
}}}

{{{id=14|
QuadraticField(-863,'a').factor(37)
///
(Fractional ideal (37, a + 5)) * (Fractional ideal (37, a - 5))
}}}

{{{id=15|
for n in range(1,1000):
    k = len([i for i in range(len(theta_series)) if theta_series[i][n]])
    if k == len(theta_series):
        print n, k, factor(n)
///
252 14 2^2 * 3^2 * 7
263 14 263
287 14 7 * 41
423 14 3^2 * 47
432 14 2^4 * 3^3
527 14 17 * 31
567 14 3^4 * 7
728 14 2^3 * 7 * 13
743 14 743
752 14 2^4 * 47
768 14 2^8 * 3
815 14 5 * 163
848 14 2^4 * 53
863 14 863
887 14 887
892 14 2^2 * 223
972 14 2^2 * 3^5
983 14 983
988 14 2^2 * 13 * 19
992 14 2^5 * 31
}}}

{{{id=19|
squarefree_part(20)
///
5
}}}

{{{id=18|
def conductor_part(n):
    n = ZZ(n)
    D = squarefree_part(n)
    if D%4 != 0 or is_fundamental_discriminant(-D):
        return n//D
    else:
        return n//(4*D)
///
}}}

{{{id=17|
%time
primreps = []
for t in theta_series:
    v = [0] + [sum(moebius(d)*t[n//d^2] for d in divisors(conductor_part(n))) for 
           n in range(1,t.degree())]
    primreps.append(v)
///
CPU time: 5.06 s,  Wall time: 5.15 s
}}}

{{{id=20|
for n in range(len(primreps[0])-10):
    k = len([i for i in range(len(primreps)) if primreps[i][n] != 0])
    if k == len(primreps):
        print n, factor(n)
///
263 263
287 7 * 41
527 17 * 31
728 2^3 * 7 * 13
743 743
815 5 * 163
863 863
887 887
983 983
}}}

{{{id=21|
def conductor_part(n):
    n = ZZ(n)
    D = squarefree_part(n)
    if D%4 != 0 or is_fundamental_discriminant(-D):
        return n//D
    else:
        return n//(4*D)

def my_moebius(n) : return ZZ(pari(n).moebius())

def surjective_discriminant(N, p, bound=500):
    N,p,bound = ZZ(N), ZZ(p), ZZ(bound)
    if not is_prime(p): raise ValueError, "p must be prime"
    B = BrandtModule(p, N)
    RI = B.right_ideals()
    quadforms = [I.left_order().ternary_quadratic_form() for I in RI]
    theta_series = [q.theta_series(bound) for q in quadforms]
    for n in range(1,bound):
        k = len([i for i in range(len(theta_series)) if theta_series[i][n]])
        if k == len(theta_series):
            # Every single ternary quadratic form represent n.
            # Now, check to see if all representations are primitive.
            primreps = []
            for t in theta_series:
                v = [0] + [sum(my_moebius(d)*t[dc//d^2] for d in divisors(conductor_part(dc))) for dc in range(1,t.degree())]
                primreps.append(v)
            if n <= len(primreps[0])-10: 
                k = len([i for i in range(len(primreps)) if primreps[i][n] != 0])
                if k == len(primreps):
                    print n, factor(n)
///
}}}

{{{id=23|
surjective_discriminant(37, 5, 1000)
///
WARNING: Output truncated!  
<html><a target='_new' href='/home/admin/1/cells/23/full_output.txt' class='file_link'>full_output.txt</a></html>


moebius took 0.288894
moebius took 0.287628
moebius took 0.28545
moebius took 0.281376
moebius took 0.280608
moebius took 0.281467
moebius took 0.281152
moebius took 0.281554
moebius took 0.280034
moebius took 0.28047
moebius took 0.366339
moebius took 0.281077
moebius took 0.281069
moebius took 0.280694
moebius took 0.282651
moebius took 0.281076
moebius took 0.280517
moebius took 0.280226
moebius took 0.2803
moebius took 0.279897
moebius took 0.280707
moebius took 0.280256
moebius took 0.362126
moebius took 0.280008
moebius took 0.282082
moebius took 0.282512
moebius took 0.280101
moebius took 0.281939
263 263
moebius took 0.281591
moebius took 0.291407
moebius took 0.280915
moebius took 0.280552
moebius took 0.281182
moebius took 0.28014
moebius took 0.365432
moebius took 0.280347
moebius took 0.279153
moebius took 0.280163
moebius took 0.279384
moebius took 0.281608
moebius took 0.281079
moebius took 0.280439
287 7 * 41
moebius took 0.281347
moebius took 0.2799
moebius took 0.281246
moebius took 0.280991
moebius took 0.280948
moebius took 0.364194
moebius took 0.281523
moebius took 0.285815
moebius took 0.285542
moebius took 0.28071
moebius took 0.279378
moebius took 0.280873
moebius took 0.28067
moebius took 0.280272
moebius took 0.279662
moebius took 0.279297

...

moebius took 0.280654
moebius took 0.279856
moebius took 0.278795
moebius took 0.280227
moebius took 0.279465
moebius took 0.279672
moebius took 0.280275
moebius took 0.280257
moebius took 0.27954
moebius took 0.279674
moebius took 0.278762
moebius took 0.36152
moebius took 0.278775
moebius took 0.279146
moebius took 0.280962
moebius took 0.279575
moebius took 0.285083
moebius took 0.280016
moebius took 0.278965
moebius took 0.279403
moebius took 0.279805
moebius took 0.279316
moebius took 0.279402
moebius took 0.361757
moebius took 0.278609
moebius took 0.279955
moebius took 0.279289
moebius took 0.278564
moebius took 0.280498
moebius took 0.279251
moebius took 0.278675
983 983
moebius took 0.289725
moebius took 0.281156
moebius took 0.279221
moebius took 0.280146
moebius took 0.279447
moebius took 0.362119
moebius took 0.279458
moebius took 0.278735
moebius took 0.278787
moebius took 0.278917
moebius took 0.2789
moebius took 0.280784
moebius took 0.279431
moebius took 0.278638
moebius took 0.279573
moebius took 0.279548
moebius took 0.279922
moebius took 0.364836
moebius took 0.283811
moebius took 0.279647
moebius took 0.279662
moebius took 0.279067
moebius took 0.279302
moebius took 0.288751
moebius took 0.279557
moebius took 0.289598
moebius took 0.282484
moebius took 0.287889
}}}

{{{id=24|
moebius??
///
}}}

{{{id=25|

///
}}}