Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of M4(Γ0(72)).
|
Total |
New |
Old |
Modular forms
| 44 |
4 |
40 |
Cusp forms
| 28 |
4 |
24 |
Eisenstein series
| 16 |
0 |
16 |
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 | Fricke | | Total | | Cusp | | Eisenstein |
---|
All | New | Old | All | New | Old | All | New | Old |
---|
+ | + | + | | 12 | 1 | 11 | | 8 | 1 | 7 | | 4 | 0 | 4 |
+ | − | − | | 11 | 1 | 10 | | 7 | 1 | 6 | | 4 | 0 | 4 |
− | + | − | | 10 | 1 | 9 | | 6 | 1 | 5 | | 4 | 0 | 4 |
− | − | + | | 11 | 1 | 10 | | 7 | 1 | 6 | | 4 | 0 | 4 |
Plus space | + | | 23 | 2 | 21 | | 15 | 2 | 13 | | 8 | 0 | 8 |
Minus space | − | | 21 | 2 | 19 | | 13 | 2 | 11 | | 8 | 0 | 8 |
Decomposition of S4new(Γ0(72)) into newform subspaces
Decomposition of S4old(Γ0(72)) into lower level spaces