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Glasgow Mathematical Journal Glasgow Mathematical Journal

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A TRACE FORMULA FOR HECKE OPERATORS ON VECTOR-VALUED MODULAR FORMS

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  10 June 2016

NICOLE RAULF  and
OLIVER STEIN
NICOLE RAULF
Affiliation:
Université de Lille 1, U.M.R. CNRS 8524, U.F.R. de Mathématiques, Cité Scientifique, F-59655 Villeneuve d'Ascq Cédex e-mail: nicole.raulf@math.univ-lille1.fr
OLIVER STEIN
Affiliation:
Ostbayerische Technische Hochschule Regensburg, Fakultät für Informatik und Mathematik, Universitätsstraße 31, 93053 Regensburg, Germany e-mail: oliver.stein@hs-regensburg.de
Corresponding
E-mail address:
nicole.raulf@math.univ-lille1.fr
oliver.stein@hs-regensburg.de
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Abstract

We present a ready to compute trace formula for Hecke operators on vector-valued modular forms of integral weight for SL2(ℤ) transforming under the Weil representation. As a corollary, we obtain a ready to compute dimension formula for the corresponding space of vector-valued cusp forms, which is more general than the dimension formulae previously published in the vector-valued setting.

MSC classification

Primary: 11F27: Theta series; Weil representation; theta correspondences
Secondary: 11F25: Hecke-Petersson operators, differential operators (one variable) 11F72: Spectral theory; Selberg trace formula
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 59 , Issue 1 , January 2017 , pp. 143 - 165
Copyright
Copyright © Glasgow Mathematical Journal Trust 2016 

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A TRACE FORMULA FOR HECKE OPERATORS ON VECTOR-VALUED MODULAR FORMS
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