Defining parameters
| Level: | \( N \) | \(=\) | \( 3456 = 2^{7} \cdot 3^{3} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3456.bn (of order \(18\) and degree \(6\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 216 \) |
| Character field: | \(\Q(\zeta_{18})\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(576\) | ||
| Trace bound: | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3456, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 132 | 12 | 120 |
| Cusp forms | 36 | 12 | 24 |
| Eisenstein series | 96 | 0 | 96 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 12 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3456, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 3456.1.bn.a | $6$ | $1.725$ | \(\Q(\zeta_{18})\) | $D_{18}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{18}^{4}q^{3}+\zeta_{18}^{8}q^{9}+(\zeta_{18}^{2}+\zeta_{18}^{6}+\cdots)q^{11}+\cdots\) |
| 3456.1.bn.b | $6$ | $1.725$ | \(\Q(\zeta_{18})\) | $D_{18}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{18}^{4}q^{3}+\zeta_{18}^{8}q^{9}+(-\zeta_{18}^{2}-\zeta_{18}^{6}+\cdots)q^{11}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3456, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3456, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(1728, [\chi])\)\(^{\oplus 2}\)