Tables of traces of Hecke operators on spaces of Siegel modular forms of degree 2 (levels 1 and 2) and degree 3 (level 1), obtained from counting curves over finite fields.

Jonas Bergström, Fabien Cléry, Carel Faber, Gerard van der Geer

Provides traces of Hecke operators on spaces of scalar- and vector-valued Siegel modular forms of degree 2 (levels 1 and 2) and degree 3 (level 1), derived from counts of curves over finite fields and their cohomological interpretation by Bergström, Faber and van der Geer, together with dimension tables, data on forms related to G2, congruences, and Fourier expansions of degree 2 forms of level 1. For degree 2 the traces are unconditional; the degree 3 data rests on conjectures of Bergström-Faber-van der Geer.

References

  • J. Bergström, C. Faber, G. van der Geer, Siegel modular forms of degree three and the cohomology of local systems, Selecta Math. (N.S.) 20 (2014), no. 1, 83-124
  • arXiv:0909.1744
  • F. Cléry, C. Faber, G. van der Geer, Covariants of binary sextics and vector-valued Siegel modular forms of genus two, Math. Ann. 369 (2017), 1649-1669