  Let $F$ and $G$ be Siegel cusp forms for $\Sp_4(\Z)$ 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.
