Superspecial Abelian Varieties and the Eichler Basis Problem for Hilbert Modular Forms

Details Superspecial Abelian Varieties and the Eichler Basis Problem for Hilbert Modular Forms Superspecial Abelian Varieties and the Eichler Basis Problem for Hilbert Modular Forms

2007-11-02

arxiv.org/abs/0711.0239v2

Journal of Number Theory, 128, 2008, 2874-2889

Mathematics

Number Theory

to appear in J.N.T

Scientific paper

10.1016/j.jnt.2008.01.006

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.

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