Defining parameters
| Level: | \( N \) | \(=\) | \( 3328 = 2^{8} \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3328.bl (of order \(12\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
| Character field: | \(\Q(\zeta_{12})\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(448\) | ||
| Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3328, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 132 | 24 | 108 |
| Cusp forms | 36 | 8 | 28 |
| Eisenstein series | 96 | 16 | 80 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 8 | 0 | 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.bl.a | $4$ | $1.661$ | \(\Q(\zeta_{12})\) | $D_{12}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+(-\zeta_{12}-\zeta_{12}^{2})q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{4}q^{13}+\cdots\) |
| 3328.1.bl.b | $4$ | $1.661$ | \(\Q(\zeta_{12})\) | $D_{12}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q+(\zeta_{12}+\zeta_{12}^{2})q^{5}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{4}q^{13}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3328, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3328, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(832, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1664, [\chi])\)\(^{\oplus 2}\)