Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of M2(Γ0(30)).
|
Total |
New |
Old |
Modular forms
| 10 |
1 |
9 |
Cusp forms
| 3 |
1 |
2 |
Eisenstein series
| 7 |
0 |
7 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
2 | 3 | 5 | Fricke | | Total | | Cusp | | Eisenstein |
---|
All | New | Old | All | New | Old | All | New | Old |
---|
+ | + | − | − | | 2 | 0 | 2 | | 1 | 0 | 1 | | 1 | 0 | 1 |
+ | − | + | − | | 2 | 1 | 1 | | 1 | 1 | 0 | | 1 | 0 | 1 |
+ | − | − | + | | 1 | 0 | 1 | | 0 | 0 | 0 | | 1 | 0 | 1 |
− | + | + | − | | 1 | 0 | 1 | | 0 | 0 | 0 | | 1 | 0 | 1 |
− | + | − | + | | 2 | 0 | 2 | | 1 | 0 | 1 | | 1 | 0 | 1 |
− | − | + | + | | 1 | 0 | 1 | | 0 | 0 | 0 | | 1 | 0 | 1 |
− | − | − | − | | 1 | 0 | 1 | | 0 | 0 | 0 | | 1 | 0 | 1 |
Plus space | + | | 4 | 0 | 4 | | 1 | 0 | 1 | | 3 | 0 | 3 |
Minus space | − | | 6 | 1 | 5 | | 2 | 1 | 1 | | 4 | 0 | 4 |
Decomposition of S2new(Γ0(30)) into newform subspaces
Decomposition of S2old(Γ0(30)) into lower level spaces