Defining parameters
| Level: | \( N \) | = | \( 176 = 2^{4} \cdot 11 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(1920\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(176))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 152 | 42 | 110 |
| Cusp forms | 12 | 1 | 11 |
| Eisenstein series | 140 | 41 | 99 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 1 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(176))\)
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 |
|---|---|---|---|---|
| 176.1.b | \(\chi_{176}(153, \cdot)\) | None | 0 | 1 |
| 176.1.d | \(\chi_{176}(111, \cdot)\) | None | 0 | 1 |
| 176.1.f | \(\chi_{176}(23, \cdot)\) | None | 0 | 1 |
| 176.1.h | \(\chi_{176}(65, \cdot)\) | 176.1.h.a | 1 | 1 |
| 176.1.k | \(\chi_{176}(67, \cdot)\) | None | 0 | 2 |
| 176.1.l | \(\chi_{176}(21, \cdot)\) | None | 0 | 2 |
| 176.1.n | \(\chi_{176}(17, \cdot)\) | None | 0 | 4 |
| 176.1.p | \(\chi_{176}(71, \cdot)\) | None | 0 | 4 |
| 176.1.r | \(\chi_{176}(15, \cdot)\) | None | 0 | 4 |
| 176.1.t | \(\chi_{176}(41, \cdot)\) | None | 0 | 4 |
| 176.1.u | \(\chi_{176}(13, \cdot)\) | None | 0 | 8 |
| 176.1.v | \(\chi_{176}(3, \cdot)\) | None | 0 | 8 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(176))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(176)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)