Let $S_{2m}(Γ(\frak p))$ be the space of Hilbert modular cusp forms for the principal congruence subgroup with level $\frak p$ of $SL_2(O_K)$ (here $O_K$ is the ring of integers of $K$, and $\frak p$ is a prime ideal of $O_K$). Then we have the action of $SL_2(\Bbb F_q)$ on $S_{2m}(Γ(\frak p))$, where $q=N\frak p$. When $q$ is a power of an odd prime, for each $SL_2(\Bbb F_q)$ we have two irreducible characters which have conjugate values mutually. In the case where $K$ is the field of rationals, M. Eichler gives a formula for the difference of multiplicites of these characters in the trace of the representation of $SL_2(\Bbb F_q)$ on $S_{2m}(Γ(\frak p))$. In the case where $K$ is a real quadratic field, H. Saito gives a formula analogous to that of Eichler for the difference. The purpose of this paper is to give a formula analogous to that of Eichler in the case where $K$ is a totally real cubic field.
雑誌名
Journal of mathematical sciences, the University of Tokyo
巻
5
号
2
ページ
367 - 399
発行年
1998
ISSN
13405705
書誌レコードID
AA11021653
フォーマット
application/pdf
日本十進分類法
415
Mathematical Reviews Number
MR1633870
Mathmatical Subject Classification
11F41(MSC1991)
10D21(MSC1991)
12A50(MSC1991)
出版者
Graduate School of Mathematical Sciences, The University of Tokyo
The Spaces of Hilbert Cusp Forms for Totally Real Cubic Fields and Representations of $SL_2(\Bbb F_q)$
jms050207.pdf
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