Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of M10(Γ0(39)).
|
Total |
New |
Old |
Modular forms
| 44 |
18 |
26 |
Cusp forms
| 40 |
18 |
22 |
Eisenstein series
| 4 |
0 |
4 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
3 | 13 | Fricke | | Total | | Cusp | | Eisenstein |
---|
All | New | Old | All | New | Old | All | New | Old |
---|
+ | + | + | | 10 | 4 | 6 | | 9 | 4 | 5 | | 1 | 0 | 1 |
+ | − | − | | 12 | 5 | 7 | | 11 | 5 | 6 | | 1 | 0 | 1 |
− | + | − | | 12 | 6 | 6 | | 11 | 6 | 5 | | 1 | 0 | 1 |
− | − | + | | 10 | 3 | 7 | | 9 | 3 | 6 | | 1 | 0 | 1 |
Plus space | + | | 20 | 7 | 13 | | 18 | 7 | 11 | | 2 | 0 | 2 |
Minus space | − | | 24 | 11 | 13 | | 22 | 11 | 11 | | 2 | 0 | 2 |
Decomposition of S10new(Γ0(39)) into newform subspaces
Decomposition of S10old(Γ0(39)) into lower level spaces