  Let $f$ be a half-integral weight cusp form of level $4N$ for odd and
squarefree $N$ and let $a(n)$ denote its $n^{\rm th}$ normalized Fourier
coefficient. Assuming that all the coefficients $a(n)$ are real, we study the
sign of $a(n)$ when $n$ runs through an arithmetic progression. As a
consequence, we establish a lower bound for the number of integers $n\le x$
such that $a(n)>n^{-\alpha}$ where $x$ and $\alpha$ are positive and $f$ is not
necessarily a Hecke eigenform.
