  Let $p$ be an unramified prime in a totally real field $L$ such that
$h^+(L)=1$. Our main result shows that Hilbert modular newforms of parallel
weight two for $\Gamma_0(p)$ can be constructed naturally, via classical theta
series, from modules of isogenies of superspecial abelian varieties with real
multiplication on a Hilbert moduli space. This can be viewed as a geometric
reinterpretation of the Eichler Basis Problem for Hilbert modular forms.

Number Theory;Algebraic Geometry