$p$-adic properties of coefficients of basis for the space of weakly holomorphic modular forms of weight 2

Abstract

We observe properties of coefficients of certain basis elements for the space of weakly holomorphic modular forms of weight 2 for $SL_{2}(\mathbf{Z})$. Moreover we show that these coefficients are often highly divisible by the primes 2, 3, 5, 7, 11.