Defining parameters
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.f (of order \(18\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 27 \) |
Character field: | \(\Q(\zeta_{18})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(81\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(729, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 114 | 24 | 90 |
Cusp forms | 6 | 6 | 0 |
Eisenstein series | 108 | 18 | 90 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 6 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(729, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
729.1.f.a | $6$ | $0.364$ | \(\Q(\zeta_{18})\) | $D_{3}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{18}q^{4}-\zeta_{18}^{8}q^{7}-\zeta_{18}^{4}q^{13}+\cdots\) |