Defining parameters
| Level: | \( N \) | = | \( 848 = 2^{4} \cdot 53 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(44928\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(848))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 789 | 245 | 544 |
| Cusp forms | 61 | 15 | 46 |
| Eisenstein series | 728 | 230 | 498 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 15 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(848))\)
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 |
|---|---|---|---|---|
| 848.1.d | \(\chi_{848}(319, \cdot)\) | None | 0 | 1 |
| 848.1.e | \(\chi_{848}(423, \cdot)\) | None | 0 | 1 |
| 848.1.f | \(\chi_{848}(847, \cdot)\) | 848.1.f.a | 1 | 1 |
| 848.1.f.b | 2 | |||
| 848.1.g | \(\chi_{848}(743, \cdot)\) | None | 0 | 1 |
| 848.1.i | \(\chi_{848}(189, \cdot)\) | None | 0 | 2 |
| 848.1.k | \(\chi_{848}(129, \cdot)\) | None | 0 | 2 |
| 848.1.n | \(\chi_{848}(553, \cdot)\) | None | 0 | 2 |
| 848.1.p | \(\chi_{848}(211, \cdot)\) | None | 0 | 2 |
| 848.1.q | \(\chi_{848}(107, \cdot)\) | None | 0 | 2 |
| 848.1.t | \(\chi_{848}(613, \cdot)\) | None | 0 | 2 |
| 848.1.w | \(\chi_{848}(119, \cdot)\) | None | 0 | 12 |
| 848.1.x | \(\chi_{848}(143, \cdot)\) | 848.1.x.a | 12 | 12 |
| 848.1.y | \(\chi_{848}(7, \cdot)\) | None | 0 | 12 |
| 848.1.z | \(\chi_{848}(15, \cdot)\) | None | 0 | 12 |
| 848.1.bc | \(\chi_{848}(61, \cdot)\) | None | 0 | 24 |
| 848.1.bf | \(\chi_{848}(11, \cdot)\) | None | 0 | 24 |
| 848.1.bg | \(\chi_{848}(99, \cdot)\) | None | 0 | 24 |
| 848.1.bi | \(\chi_{848}(41, \cdot)\) | None | 0 | 24 |
| 848.1.bl | \(\chi_{848}(33, \cdot)\) | None | 0 | 24 |
| 848.1.bn | \(\chi_{848}(5, \cdot)\) | None | 0 | 24 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(848))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(848)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(212))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(424))\)\(^{\oplus 2}\)