The Hecke Algebra T_k has Large Index

Details The Hecke Algebra T_k has Large Index The Hecke Algebra T_k has Large Index

2003-11-21

arxiv.org/abs/math/0311367v1

Mathematics

Number Theory

13 pages, to appear in Math Research Letters

Scientific paper

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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