Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of M10(Γ0(63)).
|
Total |
New |
Old |
Modular forms
| 76 |
23 |
53 |
Cusp forms
| 68 |
23 |
45 |
Eisenstein series
| 8 |
0 |
8 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
3 | 7 | Fricke | | Total | | Cusp | | Eisenstein |
---|
All | New | Old | All | New | Old | All | New | Old |
---|
+ | + | + | | 18 | 4 | 14 | | 16 | 4 | 12 | | 2 | 0 | 2 |
+ | − | − | | 20 | 6 | 14 | | 18 | 6 | 12 | | 2 | 0 | 2 |
− | + | − | | 20 | 7 | 13 | | 18 | 7 | 11 | | 2 | 0 | 2 |
− | − | + | | 18 | 6 | 12 | | 16 | 6 | 10 | | 2 | 0 | 2 |
Plus space | + | | 36 | 10 | 26 | | 32 | 10 | 22 | | 4 | 0 | 4 |
Minus space | − | | 40 | 13 | 27 | | 36 | 13 | 23 | | 4 | 0 | 4 |
Decomposition of S10new(Γ0(63)) into newform subspaces
Decomposition of S10old(Γ0(63)) into lower level spaces