Defining parameters
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.s (of order \(30\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 99 \) |
Character field: | \(\Q(\zeta_{30})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(132\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1089, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 120 | 88 | 32 |
Cusp forms | 24 | 24 | 0 |
Eisenstein series | 96 | 64 | 32 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 8 | 0 | 16 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1089, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1089.1.s.a | $8$ | $0.543$ | \(\Q(\zeta_{15})\) | $D_{3}$ | \(\Q(\sqrt{-11}) \) | None | \(0\) | \(1\) | \(-1\) | \(0\) | \(q-\zeta_{30}^{7}q^{3}-\zeta_{30}^{13}q^{4}+\zeta_{30}q^{5}+\cdots\) |
1089.1.s.b | $16$ | $0.543$ | 16.0.\(\cdots\).1 | $S_{4}$ | None | None | \(0\) | \(-2\) | \(-2\) | \(0\) | \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(\beta _{3}+\beta _{15})q^{5}+\cdots\) |