Defining parameters
| Level: | \( N \) | = | \( 927 = 3^{2} \cdot 103 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(63648\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(927))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 885 | 478 | 407 |
| Cusp forms | 69 | 23 | 46 |
| Eisenstein series | 816 | 455 | 361 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 23 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(927))\)
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 |
|---|---|---|---|---|
| 927.1.b | \(\chi_{927}(413, \cdot)\) | None | 0 | 1 |
| 927.1.d | \(\chi_{927}(514, \cdot)\) | 927.1.d.a | 1 | 1 |
| 927.1.d.b | 2 | |||
| 927.1.d.c | 4 | |||
| 927.1.i | \(\chi_{927}(365, \cdot)\) | None | 0 | 2 |
| 927.1.k | \(\chi_{927}(205, \cdot)\) | None | 0 | 2 |
| 927.1.l | \(\chi_{927}(253, \cdot)\) | None | 0 | 2 |
| 927.1.m | \(\chi_{927}(778, \cdot)\) | None | 0 | 2 |
| 927.1.q | \(\chi_{927}(104, \cdot)\) | None | 0 | 2 |
| 927.1.r | \(\chi_{927}(458, \cdot)\) | None | 0 | 2 |
| 927.1.s | \(\chi_{927}(56, \cdot)\) | None | 0 | 2 |
| 927.1.t | \(\chi_{927}(160, \cdot)\) | None | 0 | 2 |
| 927.1.v | \(\chi_{927}(10, \cdot)\) | 927.1.v.a | 16 | 16 |
| 927.1.x | \(\chi_{927}(8, \cdot)\) | None | 0 | 16 |
| 927.1.bc | \(\chi_{927}(40, \cdot)\) | None | 0 | 32 |
| 927.1.bd | \(\chi_{927}(38, \cdot)\) | None | 0 | 32 |
| 927.1.be | \(\chi_{927}(17, \cdot)\) | None | 0 | 32 |
| 927.1.bf | \(\chi_{927}(14, \cdot)\) | None | 0 | 32 |
| 927.1.bj | \(\chi_{927}(70, \cdot)\) | None | 0 | 32 |
| 927.1.bk | \(\chi_{927}(109, \cdot)\) | None | 0 | 32 |
| 927.1.bl | \(\chi_{927}(22, \cdot)\) | None | 0 | 32 |
| 927.1.bn | \(\chi_{927}(2, \cdot)\) | None | 0 | 32 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(927))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(927)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(103))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(309))\)\(^{\oplus 2}\)