Defining parameters
| Level: | \( N \) | = | \( 2891 = 7^{2} \cdot 59 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 4 \) | ||
| Newform subspaces: | \( 17 \) | ||
| Sturm bound: | \(682080\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2891))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3566 | 2836 | 730 |
| Cusp forms | 86 | 71 | 15 |
| Eisenstein series | 3480 | 2765 | 715 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 71 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2891))\)
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 |
|---|---|---|---|---|
| 2891.1.c | \(\chi_{2891}(589, \cdot)\) | 2891.1.c.a | 1 | 1 |
| 2891.1.c.b | 1 | |||
| 2891.1.c.c | 1 | |||
| 2891.1.c.d | 1 | |||
| 2891.1.c.e | 1 | |||
| 2891.1.c.f | 1 | |||
| 2891.1.c.g | 1 | |||
| 2891.1.d | \(\chi_{2891}(2302, \cdot)\) | None | 0 | 1 |
| 2891.1.f | \(\chi_{2891}(178, \cdot)\) | None | 0 | 2 |
| 2891.1.g | \(\chi_{2891}(471, \cdot)\) | 2891.1.g.a | 2 | 2 |
| 2891.1.g.b | 2 | |||
| 2891.1.g.c | 2 | |||
| 2891.1.g.d | 2 | |||
| 2891.1.g.e | 2 | |||
| 2891.1.j | \(\chi_{2891}(237, \cdot)\) | None | 0 | 6 |
| 2891.1.k | \(\chi_{2891}(176, \cdot)\) | 2891.1.k.a | 6 | 6 |
| 2891.1.k.b | 12 | |||
| 2891.1.p | \(\chi_{2891}(58, \cdot)\) | 2891.1.p.a | 12 | 12 |
| 2891.1.p.b | 12 | |||
| 2891.1.p.c | 12 | |||
| 2891.1.q | \(\chi_{2891}(355, \cdot)\) | None | 0 | 12 |
| 2891.1.r | \(\chi_{2891}(48, \cdot)\) | None | 0 | 28 |
| 2891.1.s | \(\chi_{2891}(50, \cdot)\) | None | 0 | 28 |
| 2891.1.w | \(\chi_{2891}(18, \cdot)\) | None | 0 | 56 |
| 2891.1.x | \(\chi_{2891}(19, \cdot)\) | None | 0 | 56 |
| 2891.1.ba | \(\chi_{2891}(8, \cdot)\) | None | 0 | 168 |
| 2891.1.bb | \(\chi_{2891}(20, \cdot)\) | None | 0 | 168 |
| 2891.1.bd | \(\chi_{2891}(3, \cdot)\) | None | 0 | 336 |
| 2891.1.be | \(\chi_{2891}(2, \cdot)\) | None | 0 | 336 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2891))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(2891)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(413))\)\(^{\oplus 2}\)