Computing Invariants of the Weil representation

Abstract

We propose an algorithm for computing bases and dimensions of spaces of invariants of Weil representations of ${\mathrm{SL}}_2(\mathbb{Z})$ associated to finite quadratic modules. We prove that these spaces are defined over $\mathbb{Z}$, and that their dimension remains stable if we replace the base field by suitable finite prime fields.

15 pages, submitted