Explicit computations of Hilbert modular forms on Q(square root 5)

We compute the eigenvalues of the first few Hecke operators Tp (N( p ) ≤ 100) for all Hilbert modular forms on Q5 of parallel weight 2 and level of norm less than 500. This is done by exploiting the Jacquet-Langlands correspondence which allows us to transfer such computations to forms on the (totally definite) Hamilton quaternion algebra over Q5 . We use these computations to test numerically a conjecture of Oda on periods of Hilbert modular forms