Arithmetic behaviour of Hecke eigenvalues of Siegel cusp forms of degree two

Abstract

Let F and G be Siegel cusp forms for \({\mathrm{Sp}}_4({{\mathbb {Z}}})\) and weights \(k_1, k_2\), respectively. Also let F and G be Hecke eigenforms lying in distinct eigen spaces. Further suppose that neither F nor G is a Saito–Kurokawa lift. In this article, we study simultaneous arithmetic behaviour of Hecke eigenvalues of these Hecke eigenforms.