Hecke eigenforms for meromorphic cusp forms

2023/05/02 by Bringmann, Kathrin, Kane, Ben, Mertens, Michael H.
#11F11 #11F25 #11F37 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2305.01235

Abstract

In this paper, we construct Hecke eigenforms for two families of quotient spaces of meromorphic cusp forms on SL₂(ℤ). We show that each quotient space in the first (resp. second family) is isomorphic as a Hecke module to the space S_2k (resp. M_2k) of cusp forms (resp. holomorphic modular forms) of the same weight on SL₂(ℤ).

Related

• Eigenspaces of Newforms with Nontrivial Character
• Relations between cusp forms sharing Hecke eigenvalues
• All Siegel Hecke eigensystems (mod p) are cuspidal
• Multiplicative Hecke operators and their application II
• Explicit Computation of Cusp forms via Hecke Action on Cohomology and its Complexity