  We develop geometric methods to study the generating weights of free modules
of vector valued modular forms of half-integral weight, taking values in a
complex representation of the metaplectic group. We then compute the generating
weights for modular forms taking values in the Weil representation attached to
cyclic quadratic modules of order 2p^r, where p is a prime greater than three.
We also show that the generating weights approach a simple limiting
distribution as p grows, or as r grows and p remains fixed.
