Siegel modular forms of degree two attached to Hilbert modular forms

Let E/Q be a real quadratic field and π0 a cuspidal, irreducible, automorphic representation of GL(2,AE) with trivial central character and infinity type (2,2n+2) for some non-negative integer n. We show that there exists a non-zero Siegel paramodular newform F:H2→C with weight, level, Hecke eigenvalues, epsilon factor and L-function determined explicitly by π0. We tabulate these invariants in terms of those of π0 for every prime p of Q.