English

Derived Hecke algebra for weight one forms

Number Theory 2017-06-13 v1

Abstract

We study the action of the derived Hecke algebra on the space of weight one forms. By analogy with the topological case, we formulate a conjecture relating this to a certain Stark unit. We verify the truth of the conjecture numerically, for the weight one forms of level 2323 and 3131, and many derived Hecke operators at primes less than 200200. Our computation depends in an essential way on Merel's evaluation of the pairing between the Shimura and cuspidal subgroups of J0(q)J_0(q).

Keywords

Cite

@article{arxiv.1706.03417,
  title  = {Derived Hecke algebra for weight one forms},
  author = {Michael Harris and Akshay Venkatesh},
  journal= {arXiv preprint arXiv:1706.03417},
  year   = {2017}
}
R2 v1 2026-06-22T20:15:28.291Z