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,...).