Explicit Computations of Hilbert Modular Forms on $\Q(\sqrt{5})$

Abstract

This article presents an algorithm to compute Hilbert modular forms on the quadratic field $\Q(\sqrt{5})$. It also provides a list of all modular abelian varieties defined over $\Q(\sqrt{5})$ with prime level of norm less than 100 (up to $\Q$-isogeny).