Defining parameters
| Level: | \( N \) | = | \( 15 = 3 \cdot 5 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(32\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(15))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 16 | 9 | 7 |
| Cusp forms | 1 | 1 | 0 |
| Eisenstein series | 15 | 8 | 7 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)
We only show spaces with even 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 |
|---|---|---|---|---|
| 15.2.a | \(\chi_{15}(1, \cdot)\) | 15.2.a.a | 1 | 1 |
| 15.2.b | \(\chi_{15}(4, \cdot)\) | None | 0 | 1 |
| 15.2.e | \(\chi_{15}(2, \cdot)\) | None | 0 | 2 |