Defining parameters
| Level: | \( N \) | = | \( 4 = 2^{2} \) |
| Weight: | \( k \) | = | \( 13 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(13\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{13}(\Gamma_1(4))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 7 | 7 | 0 |
| Cusp forms | 5 | 5 | 0 |
| Eisenstein series | 2 | 2 | 0 |
Trace form
Decomposition of \(S_{13}^{\mathrm{new}}(\Gamma_1(4))\)
We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.
| Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
|---|---|---|---|---|
| 4.13.b | \(\chi_{4}(3, \cdot)\) | 4.13.b.a | 1 | 1 |
| 4.13.b.b | 4 |