## Journal of Mathematics of Kyoto University

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

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

#### 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

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1215/kjm/1250519907

**Mathematical Reviews number (MathSciNet)**

MR1093343

**Zentralblatt MATH identifier**

0726.11029

**Subjects**

Primary: 11F37: Forms of half-integer weight; nonholomorphic modular forms

Secondary: 11F25: Hecke-Petersson operators, differential operators (one variable)

#### 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