Defining parameters
Level: | \( N \) | \(=\) | \( 1083 = 3 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1083.l (of order \(18\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 57 \) |
Character field: | \(\Q(\zeta_{18})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(126\) | ||
Trace bound: | \(12\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1083, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 132 | 108 | 24 |
Cusp forms | 12 | 12 | 0 |
Eisenstein series | 120 | 96 | 24 |
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 \(S_{1}^{\mathrm{new}}(1083, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1083.1.l.a | $6$ | $0.540$ | \(\Q(\zeta_{18})\) | $D_{3}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(3\) | \(q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{4}q^{4}+\zeta_{18}^{3}q^{7}+\cdots\) |
1083.1.l.b | $6$ | $0.540$ | \(\Q(\zeta_{18})\) | $D_{3}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(3\) | \(q-\zeta_{18}^{8}q^{3}+\zeta_{18}^{4}q^{4}+\zeta_{18}^{3}q^{7}+\cdots\) |