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Let k > 9 be an even integer and p a prime with p > 2k −2. Let f be a newform of weight 2k −2 and level so that f is ordinary at p and is irreducible. Under some additional hypotheses, we prove that , where S is the Pontryagin dual of the Selmer group associated to with ϵ the p-adic cyclotomic character. We accomplish this by first constructing a congruence between the Saito–Kurokawa lift of f and a non-CAP Siegel cusp form. Once this congruence is established, we use Galois representations 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