Abstract
Let E/L be a real quadratic extension of number fields. We construct an explicit map from an irreducible cuspidal automorphic representation of \mathop \mathrm{GL}(2,E)
which contains a Hilbert modular form with T0 level to an irreducible automorphic representation of \mathop \mathrm{GSp}(4,L) which contains a Siegel paramodular form and exhibit local data which produces a paramodular invariant vector for the local theta lift at every finite place, except when the local extension has wild ramification.