Eigenforms on Sp(2,Z)
Contents
- A short introduction
- Fourier coefficients and eigenvalues of the first non-Maass, non-Eisenstein eigenforms
| Table 1: Dimensions of subspaces | |||||
|---|---|---|---|---|---|
| k | All Forms |
Klingen- Eisenst. Series |
Maass Cusp Forms |
Interest. Forms |
Names of interesting forms |
| 20 | 5 | 2 | 2 | 1 | Upsilon_20 |
| 22 | 6 | 2 | 3 | 1 | Upsilon_22 |
| 24 | 8 | 3 | 3 | 2 | Upsilon_24a, Upsilon_24b |
| 26 | 7 | 2 | 3 | 2 | Upsilon_26a, Upsilon_26b |
| 28 | 10 | 3 | 4 | 3 | Upsilon_28 |
| 30 | 11 | 3 | 4 | 4 | Upsilon_30 |
| 32 | 12 | 3 | 4 | 5 | Upsilon_32 |
A short introduction
For a detailed description of the method applied to compute the tables underlying this page, see [Sko 1].
The first weight where we have an interesting eigenform is k=20. The table gives the dimensions of various subspaces in weight 20 up to weight 28. The naming of the interesting eigenforms, more precisely, of the classes of Galois equivalent eigenforms, is chosen as in [Sko 1]. Why are the spaces of interesting forms in weight 24 and 26 not irreducible under Galois ?
Currently the Modi data base contains all the Fourier coefficients C(a,b,c) of the listed forms Upsilon_XY with |b2-4ac| < 1000, and, for weights 20 to 26, all n-th Hecke eigenvalues for n=p prime with p < 1000 and n=p2 with a prime p < 80.