Defining parameters
Level: | \( N \) | \(=\) | \( 1161 = 3^{3} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1161.bz (of order \(42\) and degree \(12\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 43 \) |
Character field: | \(\Q(\zeta_{42})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(132\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1161, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 84 | 12 | 72 |
Cusp forms | 12 | 12 | 0 |
Eisenstein series | 72 | 0 | 72 |
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 \(S_{1}^{\mathrm{new}}(1161, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1161.1.bz.a | $12$ | $0.579$ | \(\Q(\zeta_{21})\) | $D_{42}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{42}^{3}q^{4}+(-\zeta_{42}+\zeta_{42}^{13})q^{7}+\cdots\) |