Defining parameters
| Level: | \( N \) | = | \( 833 = 7^{2} \cdot 17 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(56448\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(833))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 976 | 736 | 240 |
| Cusp forms | 16 | 8 | 8 |
| Eisenstein series | 960 | 728 | 232 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 8 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(833))\)
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 |
|---|---|---|---|---|
| 833.1.c | \(\chi_{833}(783, \cdot)\) | None | 0 | 1 |
| 833.1.d | \(\chi_{833}(832, \cdot)\) | None | 0 | 1 |
| 833.1.f | \(\chi_{833}(293, \cdot)\) | None | 0 | 2 |
| 833.1.h | \(\chi_{833}(509, \cdot)\) | 833.1.h.a | 4 | 2 |
| 833.1.h.b | 4 | |||
| 833.1.i | \(\chi_{833}(460, \cdot)\) | None | 0 | 2 |
| 833.1.m | \(\chi_{833}(195, \cdot)\) | None | 0 | 4 |
| 833.1.n | \(\chi_{833}(166, \cdot)\) | None | 0 | 4 |
| 833.1.p | \(\chi_{833}(118, \cdot)\) | None | 0 | 6 |
| 833.1.q | \(\chi_{833}(69, \cdot)\) | None | 0 | 6 |
| 833.1.s | \(\chi_{833}(99, \cdot)\) | None | 0 | 8 |
| 833.1.w | \(\chi_{833}(19, \cdot)\) | None | 0 | 8 |
| 833.1.y | \(\chi_{833}(13, \cdot)\) | None | 0 | 12 |
| 833.1.ba | \(\chi_{833}(52, \cdot)\) | None | 0 | 12 |
| 833.1.bb | \(\chi_{833}(33, \cdot)\) | None | 0 | 12 |
| 833.1.bd | \(\chi_{833}(79, \cdot)\) | None | 0 | 16 |
| 833.1.be | \(\chi_{833}(76, \cdot)\) | None | 0 | 24 |
| 833.1.bh | \(\chi_{833}(38, \cdot)\) | None | 0 | 24 |
| 833.1.bj | \(\chi_{833}(22, \cdot)\) | None | 0 | 48 |
| 833.1.bk | \(\chi_{833}(26, \cdot)\) | None | 0 | 48 |
| 833.1.bm | \(\chi_{833}(11, \cdot)\) | None | 0 | 96 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(833))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(833)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 2}\)