Defining parameters
| Level: | \( N \) | \(=\) | \( 13 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 13.a (trivial) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(2\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(13))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1 | 1 | 0 |
| Cusp forms | 0 | 0 | 0 |
| Eisenstein series | 1 | 1 | 0 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
| \(13\) | Total | Cusp | Eisenstein | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| All | New | Old | All | New | Old | All | New | Old | ||||
| \(-\) | \(1\) | \(1\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) | \(1\) | \(0\) | |||