Recently, Bruinier and Ono classified cusp forms $f(z) := \sum_{ n=0}^{ \infty} a_f(n)q ^n \in S_{ \lambda+1/2}(\Gamma_0(N),\chi)\cap \mathbb{ Z}[[q]]$ that does not satisfy a certain distribution property for modulo odd primes $p$. In this paper, using Rankin-Cohen Bracket, we extend this result to modular forms of half integral weight for primes $p \geq 5$. As applications of our main theorem we derive distribution properties, for modulo primes $p\geq5$, of traces of singular moduli and Hurwitz class number. We also study an analogue of Newman's conjecture for overpartitions.
Categories: math.NT