Expressions for weight 2 cusp forms in holomorphic eta quotients

Elisabeth Chan; Lewis Combes

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arXiv · 2407.05748

Expressions for weight 2 cusp forms in holomorphic eta quotients

Elisabeth Chan·Lewis Combes

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Abstract

We attempt to compute expressions in terms of the Dedekind eta function for all weight 2 new cusp forms with level up to 100, using methods of Allen et. al. In cases where no expression exists, we raise the level instead of the weight, meaning our eta quotients are always holomorphic. Of the forms we examine, we find expressions for all but 4. We also present methods to find expressions with relatively few terms, and how these expressions can be used to demonstrate zeroes of modular forms.

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Elisabeth Chan, Lewis Combes. 2024-07-08. Expressions for weight 2 cusp forms in holomorphic eta quotients. https://arxiv.org/abs/2407.05748

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