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On a decomposition of spaces of cusp forms and trace formula of Hecke operators

Published online by Cambridge University Press:  22 January 2016

Hiroshi Saito
Hiroshi Saito*
Affiliation:
Department of Mathematics, College of General Education, Kyoto University
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For a positive integer N, put

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 80 , December 1980 , pp. 129 - 165
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1980

References

[ 1 ] Atkin, A. O. L. and Li, W., Twists of newforms and pseudo-eigenvalues of W-operators, Inv. math. 48 (1978), 221–243.Google Scholar
[ 2 ] Deligne, P. and Serre, J. P., Formes modulaires de poids 1, Ann. scient. Ee. Norm. Sup. 4e serie 7 (1974), 507–530.Google Scholar
[ 3 ] Doi, K. and Yamauchi, M., On the Hecke operators for ΓQ(N) and class fields over quadratic fields, J. Math. Soc. Japan 25 (1973), 629–643.Google Scholar
[ 4 ] Doi, K. and Ohta, M., On some congruence between cusp forms for Γ0(N), Modular functions of one variable V, Lecture Notes in Math., vol. 601, Springer, 1977.Google Scholar
[ 5 ] Doi, K. and Hida, H., On a congruence of cusp forms and the special values of their Dirichlet series (to appear).Google Scholar
[ 6 ] Eichler, M., Eine Verallgemeinerung der Abelschen Integrale, Math. Z. 67 (1957), 267–298.CrossRefGoogle Scholar
[ 7 ] Eichler, M., Quadratische Formen und Modulfunktionen, Acta Arith. 4 (1958), 217–239.CrossRefGoogle Scholar
[ 8 ] Hijikata, H., Explicit formula of the traces of Hecke operators for Γ0(N), J. Math. Soc. Japan 26 (1974), 56–82.Google Scholar
[ 9 ] Ishikawa, H., On the trace formula for Hecke operators, J. Fac. Sci. Univ. Tokyo 21 (1974), 357–376.Google Scholar
[10] Saito, H., On Eichler’s trace formula, J. Math. Soc. Japan 24 (1972), 333–340.Google Scholar
[11] Saito, H. and Yamauchi, M., Trace formula of certain Hecke operators for Γ0(qv ), Nagoya Math. J. 76 (1979), 1–33.CrossRefGoogle Scholar
[12] Shimizu, H., On traces of Hecke operators, J. Fac. Sci. Univ. Tokyo 10 (1963), 1–19.Google Scholar
[13] Shimura, G., Introduction to the arithmetic theory of automorphic functions, Publ. Math. Soc. Japan, No. 11, Iwanami Shoten and Princeton University press, 1971.Google Scholar
[14] Shimura, G., On elliptic curves with complex multiplication as factors of the Jacobians of modular function fields, Nagoya Math. J. 43 (1971), 199–208.Google Scholar
[15] Shimura, G., Class fields over real quadratic fields and Hecke operators, Ann. of Math. 95 (1972), 130–190.Google Scholar
[16] Shimura, G., The special values of the zeta functions associated with cusp forms, Comm. pure appl. Math. 29 (1978), 333–340.Google Scholar
[17] Shimura, G., The special values of the zeta functions associated with Hilbert modular forms, Duke Math. J. 45 (1978), 637–679.CrossRefGoogle Scholar
[18] Yamauchi, M., On the traces of Hecke operators for a normalizer of Γ0(N), J. Math. Kyoto Univ. 13 (1973), 403–411.Google Scholar