Abstract. Bruinier and Ono classified cusp forms of half-integral weight F (z): = a(n)q n=0 n ∈ Sλ+ 1 (Γ0(N),χ) ∩ Z[[q]] 2 whose Fourier coefficients are not well distributed for modulo odd primes ℓ. Ahlgren and Boylan established bounds for the weight of such a cusp form and used these bounds to prove Newman’s conjecture for the partition function for prime-power moduli. In this note, we give a simple proof of Ahlgren and Boylan’s result on bounds of cusp forms of half-integral weight. 1. Introduction an
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