Paramodular forms of level 16 and supercuspidal representations

This work bridges the abstract representation theory of GSp(4) 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(4,ℚ2), 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.