Siegel modular forms of degree two attached to Hilbert modular forms

TL;DR

This paper constructs explicit Siegel paramodular newforms of degree two linked to Hilbert modular forms over real quadratic fields, detailing their invariants and L-functions.

Contribution

It explicitly relates Siegel modular forms to Hilbert modular forms over real quadratic fields, providing formulas for invariants and L-functions.

Findings

Existence of non-zero Siegel paramodular newforms associated with given Hilbert modular forms.

Explicit formulas for invariants and L-functions in terms of the Hilbert modular form data.

Tabulation of invariants for all rational primes p.

Abstract

Let E/Q be a real quadratic field and pi_0 a cuspidal, irreducible, automorphic representation of GL(2,A_E) 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 with weight, level, Hecke eigenvalues, epsilon factor and L-function determined explicitly by pi_0. We tabulate these invariants in terms of those of pi_0 for every rational prime p.