Packet structure and paramodular forms

Abstract

We explore the consequences of the structure of the discrete automorphic spectrum of the split orthogonal group SO ⁡ ( 5 ) \operatorname {SO}(5) for holomorphic Siegel modular forms of degree 2 2 . In particular, the combination of the local and global packet structure with the local paramodular newform theory for GSp ⁡ ( 4 ) \operatorname {GSp}(4) leads to a strong multiplicity one theorem for paramodular cusp forms.