Defining parameters
| Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3969.l (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 63 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(504\) | ||
| Trace bound: | \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3969, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 120 | 12 | 108 |
| Cusp forms | 24 | 4 | 20 |
| Eisenstein series | 96 | 8 | 88 |
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 \(S_{1}^{\mathrm{new}}(3969, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 3969.1.l.a | $2$ | $1.981$ | \(\Q(\sqrt{-3}) \) | $D_{6}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{6}q^{4}+(-1+\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{16}+\cdots\) |
| 3969.1.l.b | $2$ | $1.981$ | \(\Q(\sqrt{-3}) \) | $D_{6}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{6}q^{4}+(1-\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{16}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3969, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3969, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)