The Hecke Algebra T_k has Large Index

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.

13 pages, to appear in Math Research Letters

References in corpus (1)

• Limites de représentations cristallines

Cited by in corpus (2)

• On certain finiteness questions in the arithmetic of modular forms
• Filtrations of dc-weak eigenforms