Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of M2(Γ0(2070)).
|
Total |
New |
Old |
Modular forms
| 448 |
34 |
414 |
Cusp forms
| 417 |
34 |
383 |
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 | 23 | Fricke | | Total | | Cusp | | Eisenstein |
---|
All | New | Old | All | New | Old | All | New | Old |
---|
+ | + | + | + | + | | 22 | 2 | 20 | | 21 | 2 | 19 | | 1 | 0 | 1 |
+ | + | + | − | − | | 32 | 1 | 31 | | 30 | 1 | 29 | | 2 | 0 | 2 |
+ | + | − | + | − | | 32 | 1 | 31 | | 30 | 1 | 29 | | 2 | 0 | 2 |
+ | + | − | − | + | | 26 | 2 | 24 | | 24 | 2 | 22 | | 2 | 0 | 2 |
+ | − | + | + | − | | 31 | 4 | 27 | | 29 | 4 | 25 | | 2 | 0 | 2 |
+ | − | + | − | + | | 26 | 2 | 24 | | 24 | 2 | 22 | | 2 | 0 | 2 |
+ | − | − | + | + | | 27 | 2 | 25 | | 25 | 2 | 23 | | 2 | 0 | 2 |
+ | − | − | − | − | | 28 | 4 | 24 | | 26 | 4 | 22 | | 2 | 0 | 2 |
− | + | + | + | − | | 30 | 2 | 28 | | 28 | 2 | 26 | | 2 | 0 | 2 |
− | + | + | − | + | | 26 | 1 | 25 | | 24 | 1 | 23 | | 2 | 0 | 2 |
− | + | − | + | + | | 28 | 1 | 27 | | 26 | 1 | 25 | | 2 | 0 | 2 |
− | + | − | − | − | | 28 | 2 | 26 | | 26 | 2 | 24 | | 2 | 0 | 2 |
− | − | + | + | + | | 28 | 1 | 27 | | 26 | 1 | 25 | | 2 | 0 | 2 |
− | − | + | − | − | | 27 | 4 | 23 | | 25 | 4 | 21 | | 2 | 0 | 2 |
− | − | − | + | − | | 26 | 4 | 22 | | 24 | 4 | 20 | | 2 | 0 | 2 |
− | − | − | − | + | | 31 | 1 | 30 | | 29 | 1 | 28 | | 2 | 0 | 2 |
Plus space | + | | 214 | 12 | 202 | | 199 | 12 | 187 | | 15 | 0 | 15 |
Minus space | − | | 234 | 22 | 212 | | 218 | 22 | 196 | | 16 | 0 | 16 |
Decomposition of S2new(Γ0(2070)) into newform subspaces
Decomposition of S2old(Γ0(2070)) into lower level spaces