Paramodular forms of level 16 and supercuspidal representations

Abstract

This work bridges the abstract representation theory of $GSp\left(4\right)$ with recent computational techniques. We construct four examples of paramodular newforms whose associated automorphic representations have local representations at $p=2$ that are supercuspidal. We classify all relevant irreducible, admissible, supercuspidal representations of $GSp\left(4,{\mathbb{Q}}_2\right)$, and show that our examples occur at the lowest possible paramodular level, 16. The required theoretical and computational techniques include paramodular newform theory, Jacobi restriction, bootstrapping and Borcherds products.