%0 Journal Article
%T Superspecial Abelian Varieties and the Eichler Basis Problem for Hilbert Modular Forms
%A Marc-Hubert Nicole
%J Mathematics
%D 2007
%I arXiv
%R 10.1016/j.jnt.2008.01.006
%X 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.
%U http://arxiv.org/abs/0711.0239v2