Computing Classical Modular Forms for Arbitrary Congruence Subgroups

Abstract

In this paper, we prove the existence of an efficient algorithm for the computation of $q$-expansions of modular forms of weight $k$ and level $\hat{I}“$, where $\hat{I}“\subseteq S{L}_2(\mathbb{Z})$ is an arbitrary congruence subgroup. We also discuss some practical aspects and provide the necessary theoretical background.

for associated code, see https://github.com/assaferan/ModFrmGL2