Defining parameters
| Level: | \( N \) | \(=\) | \( 168 = 2^{3} \cdot 3 \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 168.s (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 168 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(32\) | ||
| Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(168, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 12 | 12 | 0 |
| Cusp forms | 4 | 4 | 0 |
| Eisenstein series | 8 | 8 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(168, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 168.1.s.a | $2$ | $0.084$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-6}) \) | None | \(-1\) | \(-1\) | \(1\) | \(-1\) | \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots\) |
| 168.1.s.b | $2$ | $0.084$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-6}) \) | None | \(1\) | \(1\) | \(-1\) | \(-1\) | \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\cdots\) |