Let $R_{\psi}$ be a twisting operator for a quadratic primitive
character $\psi$ and $\tilde{T}(n^2)$ the $n^2$-th Hecke operator
of half-integral weight. When $\psi$ has an odd conductor,
we already found trace identities between twisted Hecke operators
$R_{\psi} \tilde{T}(n^2)$ of half-integral weight and certain
Hecke operators of integral weight for almost all cases (cf.
[U1--3]). In this paper, the restriction is removed and we
give similar trace identities for every quadratic primitive
character $\psi$, including the case that $\psi$ has an even
conductor.
@article{1116442330,
author = {Ueda, Masaru},
title = {Trace identities of twisted Hecke operators on the spaces of cusp forms of half-integral weight},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {80},
number = {6},
year = {2004},
pages = { 131-135},
language = {en},
url = {http://dml.mathdoc.fr/item/1116442330}
}
Ueda, Masaru. Trace identities of twisted Hecke operators on the spaces of cusp forms of half-integral weight. Proc. Japan Acad. Ser. A Math. Sci., Tome 80 (2004) no. 6, pp. 131-135. http://gdmltest.u-ga.fr/item/1116442330/