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The Hecke Operators on Sk(Γ1(N))

✍ Scribed by Xiangdong Wang

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
283 KB
Volume
18
Category
Article
ISSN
0747-7171

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✦ Synopsis

In this paper we describe the space of the cusp forms with the weight (k) for the congruence subgroup (\Gamma_{1}(N), S_{k}\left(\Gamma_{1}(N)\right)), using Eichler-Shimura isomorphism, Shapiro lemma and the theory of group cohomology. An algorithm computing an integral basis of (S_{k}\left(\Gamma_{1}(N)\right)) is developed. Applying the Hecke operators on the basis we can determine newforms in (S_{k}\left(\Gamma_{1}(N)\right)).

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