Hostname: page-component-84b7d79bbc-dwq4g Total loading time: 0 Render date: 2024-07-31T21:16:38.406Z Has data issue: false hasContentIssue false
  • English
  • Français

On certain abelian varieties obtained from new forms of weight 2 on Γ0(34) and Γ0(35)

Published online by Cambridge University Press:  22 January 2016

Masao Koike
Masao Koike*
Affiliation:
Nagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let N be a positive integer and let Γ0(N) be the subgroup of SL(2, Z) defined by all matrices with c ≡ 0 (mod N). Let S2(Γ0(N)) be the space of holomorphic cusp forms of weight 2 with respect to Γ0(N) and let be the “essential part” of S2(Γ0(N)), which is defined in [1].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 62 , September 1976 , pp. 29 - 39
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

[1] Atkin, A. O. L. and Lehner, J.: Hecke operators on Γ 0(m), Math. Ann., 185 (1970),134–160.Google Scholar
[2] Doi, K., and Yamauchi, M.: On the Hecke operators for 0(N) and class fields over real quadratic number fields, J. Math. Soc. Japan, 25 (1973), 629–643.CrossRefGoogle Scholar
[3] Honda, T. and Miyawaki, I.: Zeta-f unctions of elliptic curves of 2-power conductor, J. Math. Soc. Japan, 26 (1974), 362–373.CrossRefGoogle Scholar
[4] Koike, M.: On the congruences between Eisenstein series and cusp forms, in preparation.Google Scholar
[5] Kolberg, O.: Congruences for Ramanujan’s function τ(n), Univ. Bergen Årbok Naturvit Rekke 1962.Google Scholar
[6] Ligozat, G.: A letter to Mr. T. Hadano.Google Scholar
[7] Shimura, G.: On analytic families of polarized abelian varieties and automorphic functions, Ann. of Math., 78 (1963), 149–192.CrossRefGoogle Scholar
[8] 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
[9] Shimura, G.: Class fields over real quadratic fields and Hecke operators, Ann. Of Math., 95 (1972), 130–190.Google Scholar
[10] Shimura, G.: On the factors of the jacobian variety of a modular function field, J. Math. Soc. Japan, 25 (1973), 523–544.Google Scholar
[11] Shimura, G. and Taniyama, Y.: Complex multiplication of abelian varieties and its applications to number theory, Publ. Math. Soc. Japan, No. 6, 1961.Google Scholar
[12] Yamauchi, M.: On the fields generated by certain points of finite order on Shimura’s elliptic curve, J. Math. Kyoto Univ., 14 (1974), 243–255.Google Scholar