Computing Classical Modular Forms for Arbitrary Congruence Subgroups

Eran Assaf

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arXiv · 2002.07212

Computing Classical Modular Forms for Arbitrary Congruence Subgroups

Eran Assaf

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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 $\Gamma$, where $\Gamma \subseteq SL_{2}({\mathbb{Z}})$ is an arbitrary congruence subgroup. We also discuss some practical aspects and provide the necessary theoretical background.

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Eran Assaf. 2020-02-17. Computing Classical Modular Forms for Arbitrary Congruence Subgroups. https://arxiv.org/abs/2002.07212

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