Defining parameters
| Level: | \( N \) | = | \( 352 = 2^{5} \cdot 11 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(7680\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(352))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 342 | 94 | 248 |
| Cusp forms | 22 | 4 | 18 |
| Eisenstein series | 320 | 90 | 230 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(352))\)
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 |
|---|---|---|---|---|
| 352.1.b | \(\chi_{352}(241, \cdot)\) | None | 0 | 1 |
| 352.1.d | \(\chi_{352}(287, \cdot)\) | None | 0 | 1 |
| 352.1.f | \(\chi_{352}(111, \cdot)\) | None | 0 | 1 |
| 352.1.h | \(\chi_{352}(65, \cdot)\) | None | 0 | 1 |
| 352.1.k | \(\chi_{352}(23, \cdot)\) | None | 0 | 2 |
| 352.1.l | \(\chi_{352}(153, \cdot)\) | None | 0 | 2 |
| 352.1.o | \(\chi_{352}(21, \cdot)\) | None | 0 | 4 |
| 352.1.p | \(\chi_{352}(67, \cdot)\) | None | 0 | 4 |
| 352.1.r | \(\chi_{352}(129, \cdot)\) | None | 0 | 4 |
| 352.1.t | \(\chi_{352}(15, \cdot)\) | 352.1.t.a | 4 | 4 |
| 352.1.v | \(\chi_{352}(31, \cdot)\) | None | 0 | 4 |
| 352.1.x | \(\chi_{352}(17, \cdot)\) | None | 0 | 4 |
| 352.1.y | \(\chi_{352}(41, \cdot)\) | None | 0 | 8 |
| 352.1.z | \(\chi_{352}(71, \cdot)\) | None | 0 | 8 |
| 352.1.bd | \(\chi_{352}(3, \cdot)\) | None | 0 | 16 |
| 352.1.be | \(\chi_{352}(13, \cdot)\) | None | 0 | 16 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(352))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(352)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 2}\)