Computing Classical Modular Forms for Arbitrary Congruence Subgroups

Eran Assaf

Computing Classical Modular Forms for Arbitrary Congruence Subgroups

Number Theory 2026-03-10 v3

Authors: Eran Assaf

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.

Keywords

modular forms siegel modular forms highest weight modules

Cite

@article{arxiv.2002.07212,
  title  = {Computing Classical Modular Forms for Arbitrary Congruence Subgroups},
  author = {Eran Assaf},
  journal= {arXiv preprint arXiv:2002.07212},
  year   = {2026}
}

Comments

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

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