## Journal of Mathematics of Kyoto University

### Supplement to the decomposition of the spaces of cusp forms of half-integral weight and trace formula of Hecke operators

Masaru Ueda

#### Abstract

In the previous paper [U], we calculated the trace of the Hecke operator $\tilde{T}_{k+1/2,N,\chi }(n^{2})$ on the space of cusp forms $S(k + 1/2, N, \chi )$ of half-integral weight under the assumption $\chi ^{2} = 1$. The purpose of this calculation is to find a relation between these traces and those of the Hecke operators of integral weight $2k$. When the 2-order of the level $N$ ($= \mathrm{ord}_{2}(N))$ is small, we found certain relations between the traces, in [U].

In this paper, we report relations for the remaining cases.

#### Article information

Source
J. Math. Kyoto Univ., Volume 31, Number 1 (1991), 307-309.

Dates
First available in Project Euclid: 17 August 2009

https://projecteuclid.org/euclid.kjm/1250519907

Digital Object Identifier
doi:10.1215/kjm/1250519907

Mathematical Reviews number (MathSciNet)
MR1093343

Zentralblatt MATH identifier
0726.11029

#### Citation

Ueda, Masaru. Supplement to the decomposition of the spaces of cusp forms of half-integral weight and trace formula of Hecke operators. J. Math. Kyoto Univ. 31 (1991), no. 1, 307--309. doi:10.1215/kjm/1250519907. https://projecteuclid.org/euclid.kjm/1250519907