Defining parameters
| Level: | \( N \) | \(=\) | \( 161 = 7 \cdot 23 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 161.l (of order \(22\) and degree \(10\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 161 \) |
| Character field: | \(\Q(\zeta_{22})\) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(16\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(161, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 30 | 30 | 0 |
| Cusp forms | 10 | 10 | 0 |
| Eisenstein series | 20 | 20 | 0 |
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 \(S_{1}^{\mathrm{new}}(161, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 161.1.l.a | $10$ | $0.080$ | \(\Q(\zeta_{22})\) | $D_{11}$ | \(\Q(\sqrt{-7}) \) | None | \(-2\) | \(0\) | \(0\) | \(-1\) | \(q+(-\zeta_{22}+\zeta_{22}^{8})q^{2}+(\zeta_{22}^{2}-\zeta_{22}^{5}+\cdots)q^{4}+\cdots\) |