Siegel modular forms of degree two attached to Hilbert modular forms

Abstract

Let E / Q be a real quadratic field and π 0 a cuspidal, irreducible, automorphic representation of GL ( 2 , A E ) with trivial central character and infinity type ( 2 , 2 n + 2 ) for some non-negative integer n . We show that there exists a non-zero Siegel paramodular newform F : H 2 → C with weight, level, Hecke eigenvalues, epsilon factor and L -function determined explicitly by π 0 . We tabulate these invariants in terms of those of π 0 for every prime p of Q .