Proceedings of the Japan Academy, Series A, Mathematical Sciences

Trace formula and trace identity of twisted Hecke operators on the spaces of cusp forms of weight $k+1/2$ and level $32M$

Masaru Ueda

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Abstract

Let $M$ be an odd positive integer, $\chi$ an even quadratic character defined modulo $32 M$, and $\psi$ a quadratic primitive character of conductor divisible by 8. Then, we can define twisted Hecke operators $R_{\psi} \tilde{T}(n^{2})$ on the space of cusp forms of weight $k+1/2$, level $32M$, and character $\chi$, under certain conditions on the conductors of $\chi$ and $\psi$. This is a specific feature of the case of half-integral weight. We give explicit trace formulas of the twisted Hecke operators and their trace identities.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 85, Number 2 (2009), 11-15.

Dates
First available in Project Euclid: 2 February 2009

Permanent link to this document
https://projecteuclid.org/euclid.pja/1233584550

Digital Object Identifier
doi:10.3792/pjaa.85.11

Mathematical Reviews number (MathSciNet)
MR2494590

Zentralblatt MATH identifier
1238.11054

Subjects
Primary: 11F37: Forms of half-integer weight; nonholomorphic modular forms
Secondary: 11F25: Hecke-Petersson operators, differential operators (one variable)

Keywords
Trace formula twisting operator half-integral weight trace identity Hecke operator cusp form

Citation

Ueda, Masaru. Trace formula and trace identity of twisted Hecke operators on the spaces of cusp forms of weight $k+1/2$ and level $32M$. Proc. Japan Acad. Ser. A Math. Sci. 85 (2009), no. 2, 11--15. doi:10.3792/pjaa.85.11. https://projecteuclid.org/euclid.pja/1233584550


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References

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