English

The Hecke Algebra T_k has Large Index

Number Theory 2007-05-23 v1

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.

Keywords

Cite

@article{arxiv.math/0311367,
  title  = {The Hecke Algebra T_k has Large Index},
  author = {Frank Calegari and Matthew Emerton},
  journal= {arXiv preprint arXiv:math/0311367},
  year   = {2007}
}

Comments

13 pages, to appear in Math Research Letters

R2 v1 2026-07-22T16:59:53.871Z