Defining parameters
| Level: | \( N \) | = | \( 160 = 2^{5} \cdot 5 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(1536\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(160))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 132 | 32 | 100 |
| Cusp forms | 4 | 2 | 2 |
| Eisenstein series | 128 | 30 | 98 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 2 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(160))\)
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 |
|---|---|---|---|---|
| 160.1.b | \(\chi_{160}(31, \cdot)\) | None | 0 | 1 |
| 160.1.e | \(\chi_{160}(79, \cdot)\) | None | 0 | 1 |
| 160.1.g | \(\chi_{160}(111, \cdot)\) | None | 0 | 1 |
| 160.1.h | \(\chi_{160}(159, \cdot)\) | None | 0 | 1 |
| 160.1.i | \(\chi_{160}(57, \cdot)\) | None | 0 | 2 |
| 160.1.k | \(\chi_{160}(39, \cdot)\) | None | 0 | 2 |
| 160.1.m | \(\chi_{160}(17, \cdot)\) | None | 0 | 2 |
| 160.1.p | \(\chi_{160}(33, \cdot)\) | 160.1.p.a | 2 | 2 |
| 160.1.r | \(\chi_{160}(71, \cdot)\) | None | 0 | 2 |
| 160.1.t | \(\chi_{160}(137, \cdot)\) | None | 0 | 2 |
| 160.1.v | \(\chi_{160}(13, \cdot)\) | None | 0 | 4 |
| 160.1.w | \(\chi_{160}(11, \cdot)\) | None | 0 | 4 |
| 160.1.y | \(\chi_{160}(19, \cdot)\) | None | 0 | 4 |
| 160.1.bb | \(\chi_{160}(53, \cdot)\) | None | 0 | 4 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(160))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(160)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 1}\)