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 タイトル: The Spaces of Hilbert Cusp Forms for Totally Real Cubic Fields and Representations of \$SL_2(\Bbb F_q)\$ 著者: Hamahata, Yoshinori 発行日: 1998年 出版者: Graduate School of Mathematical Sciences, The University of Tokyo 掲載誌情報: Journal of Mathematical Sciences, The University of Tokyo. Vol. 5 (1998), No. 2, Page 367-399 抄録: 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. URI: http://hdl.handle.net/2261/1342 ISSN: 13405705 出現カテゴリ: Journal of Mathematical Sciences, the University of TokyoJournal of Mathematical Sciences, the University of Tokyo

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