Congruence Between Duke-Imamoglu-Ikeda Lifts and Non-Duke-Imamoglu-Ikeda Lifts

摘要

Let k and n be positive even integers. For a Hecke eigenform g in the Kohnen plus subspace of weight k - n/2 + 1/2 for Γ_0(4), let f be the primitive form of weight 2k --n for SL_2 (Z) corresponding to g under the Shimura correspondence, and I_n (g) the Duke-Imamoglu-Ikeda lift of g to the space of cusp forms of weight k for Sp_n(Z). Then we characterize prime ideals giving congruence between I_n (g) and another cuspidal Hecke eigenform not coming from the Duke-Imamoglu-Ikeda lift in terms of the special values of the Hecke L-function and the adjoint L-function of f.