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arXiv · 1709.07475

Computing bases of modular forms using the graded algebra structure

Michael Lam·Noah McClelland·Matthew Petty·John Webb
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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.

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Michael Lam, Noah McClelland, Matthew Petty, John Webb. 2017-09-21. Computing bases of modular forms using the graded algebra structure. https://arxiv.org/abs/1709.07475

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