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Mathematics of Computation

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Covariants of binary sextics and modular forms of degree 2 with character

Authors: Fabien Cléry, Carel Faber and Gerard van der Geer
Journal: Math. Comp. 88 (2019), 2423-2441
MSC (2010): Primary 11F11, 16W22; Secondary 14H45
Published electronically: January 30, 2019
MathSciNet review: 3957899
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Abstract: We use covariants of binary sextics to describe the structure of modules of scalar-valued or vector-valued Siegel modular forms of degree $2$ with character, over the ring of scalar-valued Siegel modular forms of even weight. For a modular form defined by a covariant we express the order of vanishing along the locus of products of elliptic curves in terms of the covariant.

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Additional Information

Fabien Cléry
Affiliation: Department of Mathematical Sciences, Loughborough University, United Kingdom

Carel Faber
Affiliation: Mathematisch Instituut, Universiteit Utrecht, Postbus 80010, 3508 TA Utrecht, The Netherlands
MR Author ID: 64735

Gerard van der Geer
Affiliation: Korteweg-de Vries Instituut, Universiteit van Amsterdam, Postbus 94248, 1090 GE Amsterdam, The Netherlands
MR Author ID: 194375

Received by editor(s): March 29, 2018
Received by editor(s) in revised form: September 12, 2018, and November 1, 2018
Published electronically: January 30, 2019
Additional Notes: The research of the first author was supported by the EPSRC grant EP/N031369/1.
Article copyright: © Copyright 2019 American Mathematical Society