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arXiv · 1404.0699

Congruences for coefficients of modular functions

Paul Jenkins·DJ Thornton
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Abstract

We examine canonical bases for weakly holomorphic modular forms of weight $0$ and level $p = 2, 3, 5, 7, 13$ with poles only at the cusp at $\infty$. We show that many of the Fourier coefficients for elements of these canonical bases are divisible by high powers of $p$, extending results of the first author and Andersen. Additionally, we prove similar congruences for elements of a canonical basis for the space of modular functions of level $4$, and give congruences modulo arbitrary primes for coefficients of such modular functions in levels 1, 2, 3, 4, 5, 7, and 13.

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Paul Jenkins, DJ Thornton. 2014-04-02. Congruences for coefficients of modular functions. https://arxiv.org/abs/1404.0699

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