Hecke eigenforms for meromorphic cusp forms

Mathematische Zeitschrift, vol. 313

Abstract

Abstract In this paper, we construct Hecke eigenforms for two families of quotient spaces of meromorphic cusp forms on $$\operatorname {SL}_2(\mathbb {Z})$$ SL 2 ( Z ) . We show that each quotient space in the first (resp. second family) is isomorphic as a Hecke module to the space $$S_{2k}$$ S 2 k (resp. $$M_{2k}$$ M 2 k ) of cusp forms (resp. holomorphic modular forms) of the same weight on $$\operatorname {SL}_2(\mathbb {Z})$$ SL 2 ( Z ) .

Authors 3

1. Kathrin Bringmann

   University of Cologne

   Affiliation as printed

   Department of Mathematics and Computer Science, University of Cologne, Weyertal 86-90, 50931, Cologne, Germany

2. Ben Kane

   University of Hong Kong

   Affiliation as printed

   Department of Mathematics, University of Hong Kong, Pokfulam, Hong Kong

3. Michael H. Mertens corresponding Aachen Lehrstuhl für Algebra und Zahlentheorie

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl für Algebra und Zahlentheorie, RWTH Aachen University, Pontdriesch 14/16, 52062, Aachen, Germany