Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(24))\).
|
Total |
New |
Old |
Modular forms
| 8 |
1 |
7 |
Cusp forms
| 1 |
1 |
0 |
Eisenstein series
| 7 |
0 |
7 |
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 |
---|
\(+\) | \(+\) | \(+\) | | \(1\) | \(0\) | \(1\) | | \(0\) | \(0\) | \(0\) | | \(1\) | \(0\) | \(1\) |
\(+\) | \(-\) | \(-\) | | \(2\) | \(0\) | \(2\) | | \(0\) | \(0\) | \(0\) | | \(2\) | \(0\) | \(2\) |
\(-\) | \(+\) | \(-\) | | \(3\) | \(1\) | \(2\) | | \(1\) | \(1\) | \(0\) | | \(2\) | \(0\) | \(2\) |
\(-\) | \(-\) | \(+\) | | \(2\) | \(0\) | \(2\) | | \(0\) | \(0\) | \(0\) | | \(2\) | \(0\) | \(2\) |
Plus space | \(+\) | | \(3\) | \(0\) | \(3\) | | \(0\) | \(0\) | \(0\) | | \(3\) | \(0\) | \(3\) |
Minus space | \(-\) | | \(5\) | \(1\) | \(4\) | | \(1\) | \(1\) | \(0\) | | \(4\) | \(0\) | \(4\) |