The Hecke Algebra T k has Large Index

@inproceedings{Calegari2004TheHA,
  title={The Hecke Algebra T k has Large Index},
  author={Frank Calegari and Matthew Emerton},
  year={2004}
}
Let Tk(N) denote the Hecke algebra acting on newforms of weight k and level N . We prove that the power of p dividing the index of Tk(N) 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. 

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-9 of 9 references

The Index of the Hecke Ring, Tk, in the Ring of Integers

  • N. Jochnowitz
  • Tk ⊗Q. Duke,
  • 1979
Highly Influential
5 Excerpts

Families of modular eigenforms

  • F. Gouvêa, B. Mazur
  • Math. Comp
  • 1992
Highly Influential
2 Excerpts

Overconvergent modular forms and the Fontaine-Mazur conjecture

  • M. Kisin
  • Invent. Math
  • 2003

Approximation of Infinite Slope Modular Eigenforms By Finite Slope Eigenforms

  • W. Stein
  • Dwork Proceedings
  • 2002
1 Excerpt

The eigencurve, Galois representations in algebraic geometry (Durham

  • B. Mazur
  • London Math Soc. Lecture Note Ser
  • 1996
2 Excerpts

Représentations p-adiques semi-stables, Périodes p-adique, Astérisque 223

  • J.-M. Fontaine
  • Soc. Math. de France,
  • 1994
1 Excerpt

Geometric Galois representations, Conference on Elliptic curves and modular forms

  • B. Mazur
  • (Hong Kong,
  • 1993
1 Excerpt

Eigenvalues of Hecke Operators on SL ( 2 , Z )

  • N. Jochnowitz
  • Math . Ann .
  • 1979

Similar Papers

Loading similar papers…