Defining parameters
| Level: | \( N \) | = | \( 1089 = 3^{2} \cdot 11^{2} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 6 \) | ||
| Newform subspaces: | \( 7 \) | ||
| Sturm bound: | \(87120\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1089))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1342 | 680 | 662 |
| Cusp forms | 62 | 48 | 14 |
| Eisenstein series | 1280 | 632 | 648 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 28 | 0 | 20 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1089))\)
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 |
|---|---|---|---|---|
| 1089.1.b | \(\chi_{1089}(485, \cdot)\) | None | 0 | 1 |
| 1089.1.c | \(\chi_{1089}(604, \cdot)\) | 1089.1.c.a | 2 | 1 |
| 1089.1.h | \(\chi_{1089}(241, \cdot)\) | 1089.1.h.a | 4 | 2 |
| 1089.1.i | \(\chi_{1089}(122, \cdot)\) | 1089.1.i.a | 2 | 2 |
| 1089.1.k | \(\chi_{1089}(118, \cdot)\) | 1089.1.k.a | 8 | 4 |
| 1089.1.l | \(\chi_{1089}(251, \cdot)\) | None | 0 | 4 |
| 1089.1.p | \(\chi_{1089}(10, \cdot)\) | None | 0 | 10 |
| 1089.1.q | \(\chi_{1089}(89, \cdot)\) | None | 0 | 10 |
| 1089.1.r | \(\chi_{1089}(245, \cdot)\) | 1089.1.r.a | 8 | 8 |
| 1089.1.s | \(\chi_{1089}(40, \cdot)\) | 1089.1.s.a | 8 | 8 |
| 1089.1.s.b | 16 | |||
| 1089.1.w | \(\chi_{1089}(23, \cdot)\) | None | 0 | 20 |
| 1089.1.x | \(\chi_{1089}(43, \cdot)\) | None | 0 | 20 |
| 1089.1.z | \(\chi_{1089}(26, \cdot)\) | None | 0 | 40 |
| 1089.1.ba | \(\chi_{1089}(19, \cdot)\) | None | 0 | 40 |
| 1089.1.be | \(\chi_{1089}(7, \cdot)\) | None | 0 | 80 |
| 1089.1.bf | \(\chi_{1089}(5, \cdot)\) | None | 0 | 80 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1089))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(1089)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 2}\)