On the lifting of hermitian modular forms

Abstract

Let K be an imaginary quadratic field with discriminant -D. We denote by o the ring of integers of K. Let x be the primitive Dirichlet character corresponding to K/ℚ. Let Γ(m)K={U} (m,m)({ℚ})∩ {GL}{2m}({O}) be the hermitian modular group of degree m. We construct a lifting from S2k(SL2(ℤ)) to S 2k+2n(ΓK(2n+1),det -k-n) and a lifting from S2k+2n(Γ0(D),x) to 2k+2n(Γ K(2n),det -k-n). We give an explicit Fourier coefficient formula of the lifting. This is a generalization of the Maass lift considered by Kojima, Krieg and Sugano. We also discuss its extension to the adele group of U(m,m). © 2008 Foundation Compositio Mathematica.