Defining parameters
| Level: | \( N \) | = | \( 248 = 2^{3} \cdot 31 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(3840\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(248))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 197 | 63 | 134 |
| Cusp forms | 17 | 5 | 12 |
| Eisenstein series | 180 | 58 | 122 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 5 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(248))\)
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 |
|---|---|---|---|---|
| 248.1.d | \(\chi_{248}(63, \cdot)\) | None | 0 | 1 |
| 248.1.e | \(\chi_{248}(185, \cdot)\) | None | 0 | 1 |
| 248.1.f | \(\chi_{248}(187, \cdot)\) | None | 0 | 1 |
| 248.1.g | \(\chi_{248}(61, \cdot)\) | 248.1.g.a | 1 | 1 |
| 248.1.g.b | 2 | |||
| 248.1.g.c | 2 | |||
| 248.1.l | \(\chi_{248}(37, \cdot)\) | None | 0 | 2 |
| 248.1.m | \(\chi_{248}(67, \cdot)\) | None | 0 | 2 |
| 248.1.n | \(\chi_{248}(57, \cdot)\) | None | 0 | 2 |
| 248.1.o | \(\chi_{248}(87, \cdot)\) | None | 0 | 2 |
| 248.1.r | \(\chi_{248}(29, \cdot)\) | None | 0 | 4 |
| 248.1.s | \(\chi_{248}(35, \cdot)\) | None | 0 | 4 |
| 248.1.w | \(\chi_{248}(89, \cdot)\) | None | 0 | 4 |
| 248.1.x | \(\chi_{248}(39, \cdot)\) | None | 0 | 4 |
| 248.1.z | \(\chi_{248}(7, \cdot)\) | None | 0 | 8 |
| 248.1.ba | \(\chi_{248}(17, \cdot)\) | None | 0 | 8 |
| 248.1.be | \(\chi_{248}(19, \cdot)\) | None | 0 | 8 |
| 248.1.bf | \(\chi_{248}(13, \cdot)\) | None | 0 | 8 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(248))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(248)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 2}\)