Defining parameters
| Level: | \( N \) | \(=\) | \( 3456 = 2^{7} \cdot 3^{3} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3456.t (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 72 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(576\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3456, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 156 | 4 | 152 |
| Cusp forms | 60 | 4 | 56 |
| 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 | 4 | 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.t.a | $4$ | $1.725$ | \(\Q(\zeta_{12})\) | $D_{6}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{11}-q^{17}+(\zeta_{12}+\cdots)q^{19}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3456, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3456, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(864, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)