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Let $k > 3$ be an integer and $p$ a prime with $p > 2k-2$. Let $f$ be anewform of weight $2k-2$ and level 1 so that $f$ is ordinary at $p$ and$\bar{\rho}_{f}$ is irreducible. Under some additional hypotheses we prove that$ord_{p}(L_{alg}(k,f)) \leq ord_{p}(# S)$ where $S$ is the Pontryagin dual ofthe Selmer group associated to $\rho_{f} \otimes \epsilon^{1-k}$ with$\epsilon$ the $p$-adic cyclotomic character. We accomplish this by firstconstructing a congruence between the Saito-Kurokawa lift of $f$ and a non-CAPSiegel cusp form. Once this congruence is established, we use Galoisrepresentations to obtain the lower bound on the Selmer group.

On the cuspidality of pullbacks of Siegel Eisenstein series and applications to the Bloch-Kato conjecture