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

TextWe 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 2pr, where p≥5 is a prime. We also show that the generating weights approach a simple limiting distribution as p grows, or as r grows and p remains fixed.VideoFor a video summary of this paper, please visit https://youtu.be/QNbPSXXKot4.