Derived Hecke Algebra for Weight One Forms. Issue 3 (3rd July 2019)

• Record Type: Journal Article
• Authors: Harris, Michael; Venkatesh, Akshay
• Is Part Of: Experimental mathematics. Volume 28:Issue 3(2019)
• Page Start: 342
• Page End: 361
• Publication Date: 2019-07-03
• Subjects: Modular forms -- number theory; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: 10.1080/10586458.2017.1409144
• Languages: English
• ISSNs: 1058-6458

Abstract

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 23 and 31, and many derived Hecke operators at primes less than 200. Our computation depends in an essential way on Merel's evaluation of the pairing between the Shimura and cuspidal subgroups of J 0 ( q ).