Yoshida lifts and the Bloch-Kato conjecture for the convolution L-function

Let f(1) (resp. f(2)) denote two (elliptic) newforms of prime level N, trivial character and weight 2 (resp. k + 2, where k is an element of {8,12}). We provide evidence for the Bloch-Kato conjecture for the motive M = rho(f1) circle times rho(f2)(-k/2 - 1) by proving that under some assumptions the l-valuation of the order of the Bloch-Kato Selmer group of M is bounded from below by the l-valuation of the relevant L-value (a special value of the convolution L-function of f(1) and f(2)). We achieve this by constructing congruences between the Yoshida lift Y(f(1) circle times f(2)) of f(1) and f(2) and Siegel modular forms whose l-adic Galois representations are irreducible. Our result is conditional upon a conjectural formula for the Petersson norm of Y(f(1) circle times f(2)). (C) 2013 Elsevier Inc. All rights reserved.