Invariant Vectors for Weak Endoscopic and Saito-Kurokawa Lifts to GSp(4)

Abstract

Let A be the adele ring over a totally real number field F. For cohomological cuspidal automorphic irreducible representations of GSp(4,A) coming from weak endoscopic or Saito-Kurokawa Lifts we determine the local invariant spaces under the first principal congruence subgroup at the non-archimedean places. For F=Q this gives rise to dimension formulas regarding certain subspaces of the inner cohomology of the genus two Shimura variety corresponding to the principal congruence subgroup level N=2. We prove the conjectures made by Bergström, Faber and van der Geer in a recent paper.

arXiv commentUpdate: Shinoda's GSp(4,q)-characters included

References in corpus (2)

• Yoshida lifts and simultaneous non-vanishing of dihedral twists of modular L-functions
• The trace of Hecke operators on the space of classical holomorphic Siegel modular forms of genus two