Defining parameters
| Level: | \( N \) | = | \( 161 = 7 \cdot 23 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(2112\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(161))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 144 | 114 | 30 |
| Cusp forms | 12 | 10 | 2 |
| Eisenstein series | 132 | 104 | 28 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 10 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(161))\)
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 |
|---|---|---|---|---|
| 161.1.b | \(\chi_{161}(139, \cdot)\) | None | 0 | 1 |
| 161.1.d | \(\chi_{161}(22, \cdot)\) | None | 0 | 1 |
| 161.1.f | \(\chi_{161}(114, \cdot)\) | None | 0 | 2 |
| 161.1.h | \(\chi_{161}(24, \cdot)\) | None | 0 | 2 |
| 161.1.j | \(\chi_{161}(15, \cdot)\) | None | 0 | 10 |
| 161.1.l | \(\chi_{161}(6, \cdot)\) | 161.1.l.a | 10 | 10 |
| 161.1.n | \(\chi_{161}(3, \cdot)\) | None | 0 | 20 |
| 161.1.p | \(\chi_{161}(11, \cdot)\) | None | 0 | 20 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(161))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(161)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)