%0 Journal Article
%T Congruences for coefficients of modular functions
%A Paul Jenkins
%A DJ Thornton
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1404.0699v1