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The Hecke Algebra T_k has Large Index

Frank Calegari·Matthew Emerton
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Abstract

Let T_k denote the Hecke algebra acting on newforms of weight k and level N. We prove that the power of p dividing the index of T_k inside its normalisation grows at least linearly with k (for fixed N), answering a question of Serre. We also apply our method to give heuristic evidence towards recent conjectures of Buzzard and Mazur.

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Frank Calegari, Matthew Emerton. 2003-11-21. The Hecke Algebra T_k has Large Index. https://arxiv.org/abs/math/0311367

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