Shimura lifting of modular forms of weight 3/2

Abstract

We show that there is the Shimura lifting map of \(\mathbf {M}_{3/2}(N,\chi _{0})\) to \(\mathbf {M}_{2}(N/2,\chi _{0}^{2})\) for any natural number N divisible by 4 and for any odd Dirichlet character \(\chi _{0}\), which was already proved in the case of higher weight (Tsuyumine, Tsukuba J Math 23:465–483, 1999). As the application, we show that the lift of the weighted average of theta series of quadratic forms of an odd number of variables in a class, is an Eisenstein series of integral weight.