Invariant vectors for weak endoscopic and Saito-Kurokawa lifts to GSp(4) - Rösner, Mirko (Arxiv, 2013)
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 Bergstrøm, Faber and van der Geer in a recent paper.