Transformation Groups

, Volume 9, Issue 1, pp 25–45

The Burkhardt Group and Modular Forms


DOI: 10.1007/s00031-004-7002-6

Cite this article as:
Freitag, E. & Manni, R. Transformation Groups (2004) 9: 25. doi:10.1007/s00031-004-7002-6


In this paper we investigate the ring of Siegel modular forms of genus two and level 3. We determine the structure of this ring. It is generated by 10 modular forms (5 of weight 1 and 5 of weight 3) and there are 20 relations (5 in weight 5 and 15 in weight 6). The proof consists of two steps. In a first step we prove that the Satake compactification of the modular variety of genus 2 and level 3 is the normalization of the dual of the Burkhardt quartic. The second part consists in the normalization of the Burkhardt dual. Our basic tool is the representation theory of the Burkhardt group G = G25 920, which acts on our varieties.

Copyright information

© Birkhauser Boston 2004

Authors and Affiliations

  1. 1.Mathematisches Institut, Im Neuenheimer Feld 288, D69120 HeidelbergGermany
  2. 2.Dipartimento di Matematica, Piazzale Aldo Moro, 2, I-00185 RomaItaly

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