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

Specific Tables

Contents

  1. Specific Tables
    1. Component Groups of J0(N)(R) and J1(N)(R)

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

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.

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