  For a half integral weight modular form $f$ we study the signs of the Fourier
coefficients $a(n)$. If $f$ is a Hecke eigenform of level $ N$ with real
Nebentypus character, and $t$ is a fixed square-free positive integer with
$a(t)\neq 0$, we show that for all but finitely many primes $p$ the sequence
$(a(tp^{2m}))_{m}$ has infinitely many signs changes. Moreover, we prove
similar (partly conditional) results for arbitrary cusp forms $f$ which are not
necessarily Hecke eigenforms.
