Packet structure and paramodular forms

Abstract

We explore the consequences of the structure of the discrete automorphic spectrum of the split orthogonal groupSO⁡(5)\operatorname {SO}(5)for holomorphic Siegel modular forms of degree22. In particular, the combination of the local and global packet structure with the local paramodular newform theory forGSp⁡(4)\operatorname {GSp}(4)leads to a strong multiplicity one theorem for paramodular cusp forms.