Abstract
Let $S(k + 1/2, N, \chi)$ denote the space of cusp forms of weight $k+1/2$, level $N$, and character $\chi$. Let $R_{\psi}$ be a twisting operator for a quadratic primitive character $\psi$ of even conductor and $\tilde{T}(n^2)$ the $n^2$-th Hecke operator. We give an explicit trace formula of $R_{\psi} \tilde{T}(n^2)$ on $S(k + 1/2, N, \chi)$.
Citation
Masaru Ueda. "Trace formula of twisting operators of half-integral weight in the case of even conductors." Proc. Japan Acad. Ser. A Math. Sci. 79 (4) 85 - 88, April 2003. https://doi.org/10.3792/pjaa.79.85
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