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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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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


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
  • Email:
  • Carel Faber
  • Affiliation: Mathematisch Instituut, Universiteit Utrecht, Postbus 80010, 3508 TA Utrecht, The Netherlands
  • MR Author ID: 64735
  • Email:
  • Gerard van der Geer
  • Affiliation: Korteweg-de Vries Instituut, Universiteit van Amsterdam, Postbus 94248, 1090 GE Amsterdam, The Netherlands
  • MR Author ID: 194375
  • Email:
  • 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.
  • © Copyright 2019 American Mathematical Society
  • Journal: Math. Comp. 88 (2019), 2423-2441
  • MSC (2010): Primary 11F11, 16W22; Secondary 14H45
  • DOI:
  • MathSciNet review: 3957899