Defining parameters
| Level: | \( N \) | \(=\) | \( 3328 = 2^{8} \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3328.v (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 104 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(448\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3328, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 84 | 20 | 64 |
| Cusp forms | 36 | 12 | 24 |
| Eisenstein series | 48 | 8 | 40 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 4 | 8 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3328, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 3328.1.v.a | $4$ | $1.661$ | \(\Q(\zeta_{12})\) | $A_{4}$ | None | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{7}+\zeta_{12}^{2}q^{11}+\cdots\) |
| 3328.1.v.b | $4$ | $1.661$ | \(\Q(\zeta_{12})\) | $D_{3}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{12}^{3}q^{5}-\zeta_{12}^{4}q^{9}+\zeta_{12}^{5}q^{13}+\cdots\) |
| 3328.1.v.c | $4$ | $1.661$ | \(\Q(\zeta_{12})\) | $A_{4}$ | None | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+\zeta_{12}^{2}q^{3}-\zeta_{12}q^{7}-\zeta_{12}^{2}q^{11}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3328, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3328, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(1664, [\chi])\)\(^{\oplus 2}\)