Defining parameters
| Level: | \( N \) | = | \( 1999 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(333000\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1999))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1012 | 1012 | 0 |
| Cusp forms | 13 | 13 | 0 |
| Eisenstein series | 999 | 999 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 13 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1999))\)
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 |
|---|---|---|---|---|
| 1999.1.b | \(\chi_{1999}(1998, \cdot)\) | 1999.1.b.a | 1 | 1 |
| 1999.1.b.b | 3 | |||
| 1999.1.b.c | 9 | |||
| 1999.1.d | \(\chi_{1999}(809, \cdot)\) | None | 0 | 2 |
| 1999.1.f | \(\chi_{1999}(461, \cdot)\) | None | 0 | 6 |
| 1999.1.i | \(\chi_{1999}(120, \cdot)\) | None | 0 | 18 |
| 1999.1.j | \(\chi_{1999}(54, \cdot)\) | None | 0 | 36 |
| 1999.1.l | \(\chi_{1999}(28, \cdot)\) | None | 0 | 72 |
| 1999.1.n | \(\chi_{1999}(7, \cdot)\) | None | 0 | 216 |
| 1999.1.p | \(\chi_{1999}(3, \cdot)\) | None | 0 | 648 |