The Spaces of Hilbert Cusp Forms for Totally Real Cubic Fields and Representations of $SL_2(\Bbb F_q)$

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概要

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• 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.

著者

• Hamahata Yoshinori

  Department Of Mathematics Faculty Of Science And Technology Science University Of Tokyo

関連論文

• The Spaces of Hilbert Cusp Forms for Totally Real Cubic Fields and Representations of $SL_2(\Bbb F_q)$

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