Defining parameters
| Level: | \( N \) | = | \( 891 = 3^{4} \cdot 11 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(58320\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(891))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1128 | 530 | 598 |
| Cusp forms | 48 | 26 | 22 |
| Eisenstein series | 1080 | 504 | 576 |
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 \(S_{1}^{\mathrm{new}}(\Gamma_1(891))\)
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 |
|---|---|---|---|---|
| 891.1.b | \(\chi_{891}(485, \cdot)\) | None | 0 | 1 |
| 891.1.c | \(\chi_{891}(406, \cdot)\) | 891.1.c.a | 1 | 1 |
| 891.1.c.b | 1 | |||
| 891.1.h | \(\chi_{891}(109, \cdot)\) | None | 0 | 2 |
| 891.1.i | \(\chi_{891}(188, \cdot)\) | None | 0 | 2 |
| 891.1.l | \(\chi_{891}(244, \cdot)\) | None | 0 | 4 |
| 891.1.m | \(\chi_{891}(80, \cdot)\) | None | 0 | 4 |
| 891.1.p | \(\chi_{891}(89, \cdot)\) | None | 0 | 6 |
| 891.1.q | \(\chi_{891}(10, \cdot)\) | 891.1.q.a | 6 | 6 |
| 891.1.s | \(\chi_{891}(26, \cdot)\) | None | 0 | 8 |
| 891.1.t | \(\chi_{891}(28, \cdot)\) | None | 0 | 8 |
| 891.1.w | \(\chi_{891}(43, \cdot)\) | 891.1.w.a | 18 | 18 |
| 891.1.x | \(\chi_{891}(23, \cdot)\) | None | 0 | 18 |
| 891.1.z | \(\chi_{891}(71, \cdot)\) | None | 0 | 24 |
| 891.1.ba | \(\chi_{891}(19, \cdot)\) | None | 0 | 24 |
| 891.1.be | \(\chi_{891}(5, \cdot)\) | None | 0 | 72 |
| 891.1.bf | \(\chi_{891}(7, \cdot)\) | None | 0 | 72 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(891))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(891)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(297))\)\(^{\oplus 2}\)