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