Products of vector valued Eisenstein series
Artikel i vetenskaplig tidskrift, 2017

We prove that products of at most two vector valued Eisenstein series that originate in level 1 span all spaces of cusp forms for congruence subgroups. This can be viewed as an analogue in the level aspect to a result that goes back to Rankin, and Kohnen and Zagier, which focuses on the weight aspect. The main feature of the proof are vector valued Hecke operators. We recover several classical constructions from them, including classical Hecke operators, Atkin-Lehner involutions, and oldforms. As a corollary to our main theorem, we obtain a vanishing condition for modular forms reminiscent of period relations deduced by Kohnen and Zagier in the context their previously mentioned result.

cusp expansions of modular forms

toric modular-forms

period relations

weight

identities

Vector valued Hecke operators

Mathematics

Författare

Martin Raum

Chalmers, Matematiska vetenskaper, Algebra och geometri

Göteborgs universitet

Forum Mathematicum

0933-7741 (ISSN) 1435-5337 (eISSN)

Vol. 29 157-186

Ämneskategorier

Matematik

Fundament

Grundläggande vetenskaper

DOI

10.1515/forum-2014-0198