the integral of modular forms

asked 2024-11-19 10:07:10 +0100

Lee gravatar image

updated 2024-11-20 08:12:03 +0100

FrédéricC gravatar image

I compute the integral of modular forms using the PARI command in SageMath as follows.

def phi(s, t):
    mf = pari.mfinit([27, 2], 0)
    f = pari.mfeigenbasis(mf)[0]
    symb = pari.mfsymbol(mf, f)
    F = pari.mfsymboleval(symb, [s,t]) * 2 * pi * I
    return F

but the results show that phi(oo,0)+phi(0,a)=-phi(oo,a) where a is the cubic root of unity in the upper half plane.

Should it be phi(oo,0)+phi(0,a)=phi(oo,a)? What is the reason?

edit retag flag offensive close merge delete

Comments

This is more suitable for pari-users maillist: https://pari.math.u-bordeaux.fr/lists...

Max Alekseyev gravatar imageMax Alekseyev ( 2024-11-19 18:10:05 +0100 )edit