$p$-adic properties of Maass forms arising from theta series

We investigate arithmetic properties of the Fourier coefficients of certain harmonic weak Maass forms of weight 1/2 and 3/2. Each of the forms in question is the sum of a holomorphic function and a period integral of a theta series. In particular, for any positive integer M coprime to 6 we prove that the coefficients of the holomorphic function satisfy Ramanujan-type congruences modulo M, and establish sufficient conditions under which they are well-distributed modulo l(j) for primes l >= 5. As an example we show that our results apply to Ramanujan's mock theta function w(q).