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A construction of antisymmetric modular forms for Weil representations

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Abstract

We give coefficient formulas for antisymmetric vector-valued cusp forms with rational Fourier coefficients for the Weil representation associated to a finite quadratic module. The forms we construct always span all cusp forms in weight at least three. These formulas are useful for computing explicitly with theta lifts.

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Acknowledgements

I am grateful to Richard Borcherds for supervising the dissertation this note is based on, and for many discussions when I was a graduate student to which I owe my interest in vector-valued modular forms. I also thank Jan Hendrik Bruinier and Martin Raum for helpful discussions, and I thank the reviewer for suggestions which improved the structure of this note. This work was supported by the LOEWE research unit Uniformized Structures in Arithmetic and Geometry.

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  1. Fachbereich Mathematik, Technische Universität Darmstadt, 64289, Darmstadt, Germany

    Brandon Williams

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Correspondence to Brandon Williams.

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Williams, B. A construction of antisymmetric modular forms for Weil representations. Math. Z. 296, 391–408 (2020). https://doi.org/10.1007/s00209-019-02443-1

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