Twisted component sums of vector-valued modular forms

We construct isomorphisms between spaces of vector-valued modular forms for the dual Weil representation and certain spaces of scalar-valued modular forms in the case that the underlying finite quadratic module A has order p or 2 p , where p is an odd prime. The isomorphisms are given by twisted sum...

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Bibliographic Details
Published in:Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2019-10, Vol.89 (2), p.151-168
Main Authors: Schwagenscheidt, Markus, Williams, Brandon
Format: Article
Language:English
Subjects:
Algebra
Analytic functions
Differential Geometry
Geometry
Isomorphism
Mathematics
Mathematics and Statistics
Modular construction
Number Theory
Sums
Topology
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Summary:We construct isomorphisms between spaces of vector-valued modular forms for the dual Weil representation and certain spaces of scalar-valued modular forms in the case that the underlying finite quadratic module A has order p or 2 p , where p is an odd prime. The isomorphisms are given by twisted sums of the components of vector-valued modular forms. Our results generalize work of Bruinier and Bundschuh to the case that the components F γ of the vector-valued modular form are antisymmetric in the sense that F γ = - F - γ for all γ ∈ A . As an application, we compute restrictions of Doi–Naganuma lifts of odd weight to components of Hirzebruch–Zagier curves.
ISSN:0025-5858
1865-8784
DOI:10.1007/s12188-019-00209-4