On the Kohnen-Zagier formula in the case of `$4 \times$ general odd' level

Abstract

We study the Fourier coefficients of cusp forms of half integral weight and generalize the Kohnen-Zagier formula to the case of `$4 \times$ general odd$' level by using results of Ueda. As an application, we obtain a generalization of the result of Luo-Ramakrishnan [11] to the case of arbitrary odd level.