Vol. 8, No. 4, 2019

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Paramodular forms of level 16 and supercuspidal representations

Cris Poor, Ralf Schmidt and David S. Yuen

Vol. 8 (2019), No. 4, 289–324
Abstract

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, 2), 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.

Keywords
Siegel modular forms, paramodular forms
Mathematical Subject Classification 2010
Primary: 11F46, 11F70
Milestones
Received: 27 October 2018
Revised: 3 May 2019
Accepted: 30 June 2019
Published: 11 October 2019
Authors
Cris Poor
Department of Mathematics
Fordham University
Bronx, NY
United States
Ralf Schmidt
Department of Mathematics
University of North Texas
Denton, TX
United States
David S. Yuen
Department of Mathematics
University of Hawaii
Honolulu, HI
United States