Mark Gross and Sorin Popescu
We prove that the moduli space $\A_{11}^{lev}$ of $(1,11)$-polarized abelian surfaces with level structure of canonical type is birational to Klein's cubic hypersurface in $\Pfour$. Therefore, $\A_{11}^{lev}$ is unirational but not rational, and there are no $\Gamma_{11}$-cusp forms of weight 3. The same methods also provide an easy proof of the rationality of $\A_{9}^{lev}$.