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

Cléry, Fabien; Faber, Carel; van der Geer, Gerard

doi:10.1090/mcom/3412

Covariants of binary sextics and modular forms of degree 2 with character
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by Fabien Cléry, Carel Faber and Gerard van der Geer HTML | PDF

Math. Comp. 88 (2019), 2423-2441 Request permission

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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