Abstract
We obtain new lower bounds for the number of Fourier coefficients of a weakly holomorphic modular form of half-integral weight not divisible by some prime l. Among the applications of this we show that there are >> root X/log log X integers n <= X for which the partition function p( n) is not divisible by l, and that there are >> root X/log log X values of n <= X for which c(n), the nth Fourier coefficient of the j-invariant, is odd.