Computing bases of modular forms using the graded algebra structure

Michael Lam; Noah McClelland; Matthew Petty; John Webb

Computing bases of modular forms using the graded algebra structure

Number Theory 2017-09-25 v1

Authors: Michael Lam , Noah McClelland , Matthew Petty , John Webb

Abstract

We develop a new algorithm to compute a basis for $M_k(\Gamma_0(N))$ , the space of weight $k$ holomorphic modular forms on $\Gamma_0(N)$ , in the case when the graded algebra of modular forms over $\Gamma_0(N)$ is generated at weight two. Our tests show that this algorithm significantly outperforms a commonly used algorithm which relies more heavily on modular symbols.

Keywords

modular forms matrix algorithms highest weight modules

Cite

@article{arxiv.1709.07475,
  title  = {Computing bases of modular forms using the graded algebra structure},
  author = {Michael Lam and Noah McClelland and Matthew Petty and John Webb},
  journal= {arXiv preprint arXiv:1709.07475},
  year   = {2017}
}

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