Differences between revisions 3 and 4
 ⇤ ← Revision 3 as of 2009-09-08 21:16:19 → Size: 1201 Editor: was Comment: ← Revision 4 as of 2009-09-08 21:16:49 → ⇥ Size: 1200 Editor: was Comment: Deletions are marked like this. Additions are marked like this. Line 31: Line 31: == Cuspidal Subgroup == == Cuspidal Subgroup ==

# Specific Tables

## Component Groups of J0(N)(R) and J1(N)(R)

• New Code:

This function computes the J_0(N) real component groups.

```def f(N):
M = ModularSymbols(N).cuspidal_subspace()
d = M.dimension()//2
S = matrix(GF(2),2*d,2*d, M.star_involution().matrix().list()) - 1
return 2^(S.nullity()-d)```

For J_1(N) it is:

```def f(N):
M = ModularSymbols(Gamma1(N)).cuspidal_subspace()
d = M.dimension()//2
S = matrix(GF(2),2*d,2*d, M.star_involution().matrix().list()) - 1
return 2^(S.nullity()-d)```

Future extension: one could replace Gamma1(N) by GammaH(N,...). One could also do the new subspace.

## Cuspidal Subgroup

Computing the structure of the cuspidal subgroup of J0(N) and J1(N) (say).

• New Sage code:

```def cuspidal_subgroup_J0(N):
J = J0(N)
I = C.cuspidal_subgroup().invariants()
# maybe pickle J
return I```

```def cuspidal_subgroup_J0(N):
J = J1(N)
I = C.cuspidal_subgroup().invariants()
# maybe pickle J
return I```

days17/projects/presagedays/discussion (last edited 2010-07-12 07:39:51 by was)