Defining parameters
| Level: | \( N \) | \(=\) | \( 129 = 3 \cdot 43 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 129.l (of order \(14\) and degree \(6\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 129 \) |
| Character field: | \(\Q(\zeta_{14})\) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(14\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(129, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 18 | 18 | 0 |
| Cusp forms | 6 | 6 | 0 |
| Eisenstein series | 12 | 12 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 6 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(129, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 129.1.l.a | $6$ | $0.064$ | \(\Q(\zeta_{14})\) | $D_{7}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-1\) | \(0\) | \(-2\) | \(q-\zeta_{14}^{5}q^{3}+\zeta_{14}^{4}q^{4}+(-\zeta_{14}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots\) |