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The Basis Problem for Modular Forms and the Traces of the Hecke Operators

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Part of the Lecture Notes in Mathematics book series (LNM,volume 320)

Abstract

In the following article we consider holomorphic modular forms with respect to the congruence subgroup \( \Gamma _0 (N) = \{ (\begin{array}{*{20}c} a & b \\ c & d \\ \end{array} ) \in \Gamma :c \equiv 0\bmod N\} \) of the modular group Γ. Of course the holomorphy condition includes the cusps. By Sk0(N),χ) we denote the space of these forms of weight k and character χ, i.e. those satisfying

$$ f(\frac{{az + b}} {{cz + d}})(cz + d)^{ - k} = \chi (a)f(z) $$

for all substitutions of Γ0(N), which vanish in the cusps.

Keywords

  • Zeta Function
  • Modular Form
  • Theta Function
  • Cusp Form
  • Trace Formula

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Eichler, M. (1973). The Basis Problem for Modular Forms and the Traces of the Hecke Operators. In: Kuijk, W. (eds) Modular Functions of One Variable I. Lecture Notes in Mathematics, vol 320. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-38509-7_4

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  • DOI: https://doi.org/10.1007/978-3-540-38509-7_4

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