Defining parameters
| Level: | \( N \) | = | \( 2003 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(334334\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2003))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1005 | 1005 | 0 |
| Cusp forms | 4 | 4 | 0 |
| Eisenstein series | 1001 | 1001 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2003))\)
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 |
|---|---|---|---|---|
| 2003.1.b | \(\chi_{2003}(2002, \cdot)\) | 2003.1.b.a | 1 | 1 |
| 2003.1.b.b | 3 | |||
| 2003.1.f | \(\chi_{2003}(318, \cdot)\) | None | 0 | 6 |
| 2003.1.g | \(\chi_{2003}(180, \cdot)\) | None | 0 | 10 |
| 2003.1.h | \(\chi_{2003}(45, \cdot)\) | None | 0 | 12 |
| 2003.1.l | \(\chi_{2003}(50, \cdot)\) | None | 0 | 60 |
| 2003.1.m | \(\chi_{2003}(6, \cdot)\) | None | 0 | 72 |
| 2003.1.n | \(\chi_{2003}(2, \cdot)\) | None | 0 | 120 |
| 2003.1.p | \(\chi_{2003}(5, \cdot)\) | None | 0 | 720 |