Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of M2(Γ0(725)).
|
Total |
New |
Old |
Modular forms
| 80 |
45 |
35 |
Cusp forms
| 69 |
45 |
24 |
Eisenstein series
| 11 |
0 |
11 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
5 | 29 | Fricke | | Total | | Cusp | | Eisenstein |
---|
All | New | Old | All | New | Old | All | New | Old |
---|
+ | + | + | | 15 | 9 | 6 | | 13 | 9 | 4 | | 2 | 0 | 2 |
+ | − | − | | 24 | 12 | 12 | | 21 | 12 | 9 | | 3 | 0 | 3 |
− | + | − | | 22 | 15 | 7 | | 19 | 15 | 4 | | 3 | 0 | 3 |
− | − | + | | 19 | 9 | 10 | | 16 | 9 | 7 | | 3 | 0 | 3 |
Plus space | + | | 34 | 18 | 16 | | 29 | 18 | 11 | | 5 | 0 | 5 |
Minus space | − | | 46 | 27 | 19 | | 40 | 27 | 13 | | 6 | 0 | 6 |
Decomposition of S2new(Γ0(725)) into newform subspaces
Decomposition of S2old(Γ0(725)) into lower level spaces