Hermitian Maass lift for general level

Abstract

For an imaginary quadratic field K of discriminant −D, let χ=χK be the associated quadratic character. We will show that the space of special hermitian Jacobi forms of level N is isomorphic to the space of plus forms of level DN and nebentypus χ (the hermitian analogue of Kohnen's plus space) for any integer N prime to D. This generalizes the results of Krieg from N=1 to arbitrary level. Combining this isomorphism with the recent work of Berger and Klosin and a modification of Ikeda's construction we prove the existence of a lift from the space of elliptic modular forms to the space of hermitian modular forms of level N which can be viewed as a generalization of the classical hermitian Maaß lift to arbitrary level.