Companion forms for GSp4

We believe that the role played by CM forms in Coleman’s conjecture should be replaced by Yoshida lifts in the setting of Siegel cuspidal Hecke eigenforms of genus 2. In particular, the purpose of our project is to show that the Yoshida lifts lie in the image of a certain theta operator. Although companion forms and theta operators of in this setting of Siegel modular forms have studied in characteristic p by numerous authors, the characteristic 0 story remains unexplored.