Siegel Modular Forms of Degree 2 and 3

This website aims at providing an open access source for information on traces of Hecke operators on Siegel modular forms of degree 2, level 1 and level 2, and of degree 3, level 1. This is based on the data obtained by counting curves over finite fields and their interpretation by Bergström, Faber and van der Geer. For degree 2, this provides the traces of Hecke operators via results of Weissauer, Petersen and Rösner, while for degree 3, this rests on the conjectures made in [3].

This website is an initiative of Jonas Bergström, Carel Faber, and Gerard van der Geer.

The website also provides Fourier expansions for modular forms of degree 2 of level 1 and of level 1 with character. The pages with the Fourier expansions were taken care of by Fabien Cléry and Gerard van der Geer. We intend to add pages with Fourier expansions of modular forms of degree 3.

This website is supported by the Foundation Compositio Mathematica.

We intend to add pages giving Fourier series of forms of degree 2 and 3 and level 1.

The preferred way to cite this website is (in BibTeX format):

AUTHOR = {Bergström, Jonas and Cléry, Fabien and Faber, Carel and van der Geer, Gerard},
TITLE = {Siegel Modular Forms of Degree Two and Three},
YEAR = {2017},
URL = {},
NOTE = {Retrieved [insert date here]}