On Elliptic Curves with Complex Multiplication as Factors of the Jacobians of Modular Function Fields

Abstract

1. As Hecke showed, every L -function of an imaginary quadratic field K with a Grössen-character γ is the Mellin transform of a cusp form f(z) belonging to a certain congruence subgroup Γ of SL 2 (Z). We can normalize γ so that