THE MODULI SPACE OF (1,11)-POLARIZED ABELIAN SURFACES IS UNIRATIONAL

MARK GROSS AND SORIN POPESCU

Abstract. 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 P^{4}. Therefore, A_{11}^{lev} is unirational but not rational, and there are no Γ_{11}-cusp forms of weight 3. The same methods also provide an easy proof of the rationality of A_{9}^{lev}.