Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of M2(Γ0(1170)).
|
Total |
New |
Old |
Modular forms
| 268 |
20 |
248 |
Cusp forms
| 237 |
20 |
217 |
Eisenstein series
| 31 |
0 |
31 |
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 | 13 | Fricke | | Total | | Cusp | | Eisenstein |
---|
All | New | Old | All | New | Old | All | New | Old |
---|
+ | + | + | + | + | | 13 | 0 | 13 | | 12 | 0 | 12 | | 1 | 0 | 1 |
+ | + | + | − | − | | 19 | 2 | 17 | | 17 | 2 | 15 | | 2 | 0 | 2 |
+ | + | − | + | − | | 17 | 1 | 16 | | 15 | 1 | 14 | | 2 | 0 | 2 |
+ | + | − | − | + | | 17 | 1 | 16 | | 15 | 1 | 14 | | 2 | 0 | 2 |
+ | − | + | + | − | | 18 | 2 | 16 | | 16 | 2 | 14 | | 2 | 0 | 2 |
+ | − | + | − | + | | 17 | 2 | 15 | | 15 | 2 | 13 | | 2 | 0 | 2 |
+ | − | − | + | + | | 16 | 2 | 14 | | 14 | 2 | 12 | | 2 | 0 | 2 |
+ | − | − | − | − | | 17 | 1 | 16 | | 15 | 1 | 14 | | 2 | 0 | 2 |
− | + | + | + | − | | 18 | 1 | 17 | | 16 | 1 | 15 | | 2 | 0 | 2 |
− | + | + | − | + | | 16 | 1 | 15 | | 14 | 1 | 13 | | 2 | 0 | 2 |
− | + | − | + | + | | 18 | 0 | 18 | | 16 | 0 | 16 | | 2 | 0 | 2 |
− | + | − | − | − | | 14 | 2 | 12 | | 12 | 2 | 10 | | 2 | 0 | 2 |
− | − | + | + | + | | 16 | 1 | 15 | | 14 | 1 | 13 | | 2 | 0 | 2 |
− | − | + | − | − | | 17 | 2 | 15 | | 15 | 2 | 13 | | 2 | 0 | 2 |
− | − | − | + | − | | 18 | 2 | 16 | | 16 | 2 | 14 | | 2 | 0 | 2 |
− | − | − | − | + | | 17 | 0 | 17 | | 15 | 0 | 15 | | 2 | 0 | 2 |
Plus space | + | | 130 | 7 | 123 | | 115 | 7 | 108 | | 15 | 0 | 15 |
Minus space | − | | 138 | 13 | 125 | | 122 | 13 | 109 | | 16 | 0 | 16 |
Decomposition of S2new(Γ0(1170)) into newform subspaces
Decomposition of S2old(Γ0(1170)) into lower level spaces