On Representations of Gl2 and The Arithmetic of Modular Curves

  • W. Casselman
Part of the Lecture Notes in Mathematics book series (LNM, volume 349)


Let H be the upper half-plane and Γ a subgroup of SL2(Z) containing some principal congruence subgroup Γ(N). Then the Riemann surface Γ\H, compactified by the cusps of Γ, is the set of C-valued points of a complete algebraic curve MC (Γ) defined over Q(e2πi/N) (and often over a smaller field). One knows that MC(Γ) has good reduction at primes not dividing N, but it is only recently that anything general has been known about the reduction at other primes. Suppose that N = q · Q, where q is a prime not dividing Q. Recall that
and let


Elliptic Curve Elliptic Curf Abelian Variety Cusp Form Cuspidal Representation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1973

Authors and Affiliations

  • W. Casselman
    • 1
  1. 1.Department of MathematicsUniversity of British ColumbiaCanada

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