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

Generating weights for the Weil representation attached to an even order cyclic quadratic module