Proceedings of the Japan Academy, Series A, Mathematical Sciences

Trigonal Modular Curves $X_0^{+d}(N)$

Yuji Hasegawa and Mahoro Shimura

Full-text: Open access

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 75, Number 9 (1999), 172-175.

First available in Project Euclid: 23 May 2006

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F11: Holomorphic modular forms of integral weight
Secondary: 11F03: Modular and automorphic functions 11G30: Curves of arbitrary genus or genus = 1 over global fields [See also 14H25] 14E20: Coverings [See also 14H30] 14H25: Arithmetic ground fields [See also 11Dxx, 11G05, 14Gxx]


Hasegawa, Yuji; Shimura, Mahoro. Trigonal Modular Curves $X_0^{+d}(N)$. Proc. Japan Acad. Ser. A Math. Sci. 75 (1999), no. 9, 172--175. doi:10.3792/pjaa.75.172.

Export citation


  • E. Arbarello, M. Cornalba, P. A. Griffis, and J. Harris: Geometry of Algebraic Curves, Vol.I. Grundlehren Math. Wiss., 267, Springer-Verlag, Berlin-Heidelberg-New York, pp. 1–386 (1985).
  • A. O. L. Atkin and J. Lehner: Hecke operators on $\Gamma_0(m)$. Math. Ann., 185, 134–160 (1970).
  • A. O. L. Atkin and D. J. Tingley: Numerical tables on elliptic curves. Modular Functions of One Variable IV (eds. B. Birch and W. Kuyk). Lecture Notes in Math., 476, Springer-Verlag, Berlin-Heidelberg-New York, pp. 74–144 (1975).
  • M. Furumoto and Y. Hasegawa: Hyperelliptic quotients of modular curves $X_0(N)$. Tokyo J. Math., 22, 105–125 (1999).
  • R. Hartshorne: Algebraic Geometry. Graduate Text in Math., 52, Springer-Verlag, Berlin-Heidelberg-New York, pp. 1–496 (1977).
  • Y. Hasegawa: Table of quotient curves of modular curves $X_0(N)$ with genus 2. Proc. Japan Acad., 71A, 235–239 (1995).
  • Y. Hasegawa: Hyperelliptic modular curves $X_0^*(N)$. Acta Arith., 81, 369–385 (1997).
  • Y. Hasegawa and M. Shimura: Trigonal modular curves. Acta Arith., 88, 129–140 (1999).
  • H. Hijikata:\penalty-9999 Explicit formula of the traces of Hecke operators for $\Gamma_0(N)$. J. Math. Soc. Japan, 26, 56–82 (1974).
  • M. Newman: Conjugacy, genus, and class number. Math. Ann., 196, 198–217 (1972).
  • K.V. Nguyen and M.-H. Saito: D-gonality of modular curves and bounding torsions (preprint).
  • A. P. Ogg: Hyperelliptic modular curves. Bull. Soc. Math. France, 449–462 (1974).
  • A. P. Ogg: Modular functions. The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979) (eds. B. Cooperstein and G. Mason), Proc. Sympos. Pure Math., 37, Amer. Math. Soc., pp. 521–532 (1980).
  • B. Saint-Donat: On Petri's analysis of the linear system of quadrics through a canonical curve. Math. Ann., 206, 157–175 (1973).
  • M. Shimura: Defining equations of modular curves $X_0(N)$. Tokyo J. Math., 18, 443–456 (1995).
  • M. Yamauchi: On the traces of Hecke operators for a normalizer of $\Gamma_0(N)$. J. Math. Kyoto Univ., 13, 403–411 (1973).
  • P. G. Zograf: Small eigenvalues of automorphic Laplacians in spaces of cusp forms. Automorphic functions and number theory, II, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI), 134, 157–168 (1984) (Russian).