  In this paper we prove a theorem about the coefficients in a block of a half
integral weight modular form. We show that the result of Serre and Stark for
weight 1/2 forms does not generalize to higher higher weights.
  Let f be a half integral weight cusp form of weight at leat 3/2. We consider
blocks of coefficients of f and prove that, under some weak assumptions on f,
if such a coefficient block is periodic when considered as a function of in the
square root of its index, then it must vanish completely. The proof is analytic
in nature and uses Shimura's lifting theorem together with estimates on the
order of growth of Fourier coefficients of modular forms.
