Defining parameters
| Level: | \( N \) | \(=\) | \( 2916 = 2^{2} \cdot 3^{6} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2916.k (of order \(18\) and degree \(6\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 27 \) |
| Character field: | \(\Q(\zeta_{18})\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(486\) | ||
| Trace bound: | \(37\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2916, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 360 | 18 | 342 |
| Cusp forms | 36 | 18 | 18 |
| Eisenstein series | 324 | 0 | 324 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 18 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2916, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 2916.1.k.a | $6$ | $1.455$ | \(\Q(\zeta_{18})\) | $D_{3}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{18}^{8}q^{7}+\zeta_{18}^{4}q^{13}+\zeta_{18}^{6}q^{19}+\cdots\) |
| 2916.1.k.b | $6$ | $1.455$ | \(\Q(\zeta_{18})\) | $D_{3}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{18}^{8}q^{7}-\zeta_{18}^{4}q^{13}-\zeta_{18}^{6}q^{19}+\cdots\) |
| 2916.1.k.c | $6$ | $1.455$ | \(\Q(\zeta_{18})\) | $D_{3}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{18}^{8}q^{7}-\zeta_{18}^{4}q^{13}-\zeta_{18}^{6}q^{19}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2916, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2916, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(729, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1458, [\chi])\)\(^{\oplus 2}\)