Defining parameters
| Level: | \( N \) | = | \( 171 = 3^{2} \cdot 19 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(2160\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(171))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 155 | 84 | 71 |
| Cusp forms | 11 | 7 | 4 |
| Eisenstein series | 144 | 77 | 67 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 3 | 4 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(171))\)
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 the newforms together with their dimension.
| Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
|---|---|---|---|---|
| 171.1.b | \(\chi_{171}(134, \cdot)\) | None | 0 | 1 |
| 171.1.c | \(\chi_{171}(37, \cdot)\) | 171.1.c.a | 1 | 1 |
| 171.1.i | \(\chi_{171}(88, \cdot)\) | None | 0 | 2 |
| 171.1.j | \(\chi_{171}(68, \cdot)\) | None | 0 | 2 |
| 171.1.n | \(\chi_{171}(11, \cdot)\) | None | 0 | 2 |
| 171.1.o | \(\chi_{171}(94, \cdot)\) | 171.1.o.a | 4 | 2 |
| 171.1.p | \(\chi_{171}(46, \cdot)\) | 171.1.p.a | 2 | 2 |
| 171.1.q | \(\chi_{171}(20, \cdot)\) | None | 0 | 2 |
| 171.1.r | \(\chi_{171}(26, \cdot)\) | None | 0 | 2 |
| 171.1.s | \(\chi_{171}(31, \cdot)\) | None | 0 | 2 |
| 171.1.z | \(\chi_{171}(5, \cdot)\) | None | 0 | 6 |
| 171.1.ba | \(\chi_{171}(10, \cdot)\) | None | 0 | 6 |
| 171.1.bb | \(\chi_{171}(17, \cdot)\) | None | 0 | 6 |
| 171.1.bc | \(\chi_{171}(22, \cdot)\) | None | 0 | 6 |
| 171.1.be | \(\chi_{171}(13, \cdot)\) | None | 0 | 6 |
| 171.1.bf | \(\chi_{171}(23, \cdot)\) | None | 0 | 6 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(171))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(171)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)