Congruences among Siegel and hermitian modular forms and the Bloch-Kato conjecture

Let $f$ and $g$ be two cusp forms of weights $k$ and $2$ respectively. Let $\rho_f$ (resp. $\rho_g$) be the $p$-adic Galois representations attached to $f$ (resp. $g$). We will present two theorems (one of them work in progress with M. Agarwal) towards the Bloch-Kato conjecture for the motives $ad^0 \rho_f(-1)$ and $\rho_f \otimes \rho_g(-k/2-1)$. The method of the proof involves constructing congruences among either modular forms on the symplectic group of genus 2 or modular forms on the unitary group $U(2,2)$.