Defining parameters
| Level: | \( N \) | = | \( 2004 = 2^{2} \cdot 3 \cdot 167 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 6 \) | ||
| Sturm bound: | \(223104\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2004))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1716 | 358 | 1358 |
| Cusp forms | 56 | 26 | 30 |
| Eisenstein series | 1660 | 332 | 1328 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 26 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2004))\)
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 |
|---|---|---|---|---|
| 2004.1.d | \(\chi_{2004}(1337, \cdot)\) | None | 0 | 1 |
| 2004.1.e | \(\chi_{2004}(1669, \cdot)\) | None | 0 | 1 |
| 2004.1.f | \(\chi_{2004}(1003, \cdot)\) | None | 0 | 1 |
| 2004.1.g | \(\chi_{2004}(2003, \cdot)\) | 2004.1.g.a | 1 | 1 |
| 2004.1.g.b | 1 | |||
| 2004.1.g.c | 2 | |||
| 2004.1.g.d | 2 | |||
| 2004.1.g.e | 10 | |||
| 2004.1.g.f | 10 | |||
| 2004.1.k | \(\chi_{2004}(23, \cdot)\) | None | 0 | 82 |
| 2004.1.l | \(\chi_{2004}(7, \cdot)\) | None | 0 | 82 |
| 2004.1.m | \(\chi_{2004}(13, \cdot)\) | None | 0 | 82 |
| 2004.1.n | \(\chi_{2004}(29, \cdot)\) | None | 0 | 82 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2004))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(2004)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 6}\)