Congruences for the Coefficients of Modular forms and Some New Congruences for the Partition Function

Abstract

If n is a non-negative integer, define pr(n) as the coefficient of xn in;otherwise define pr(n) as 0. In a recent paper (2) the author established the following congruence:Let r = 4, 6, 8, 10, 14, 26. Let p be a prime greater than 3 such that r(p + l) / 24 is an integer, and set Δ = r(p2 − l)/24.