Defining parameters
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.x (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 91 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(121\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1183, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 64 | 48 | 16 |
Cusp forms | 8 | 8 | 0 |
Eisenstein series | 56 | 40 | 16 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 0 | 8 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1183, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1183.1.x.a | $8$ | $0.590$ | \(\Q(\zeta_{24})\) | $A_{4}$ | None | None | \(0\) | \(-4\) | \(0\) | \(0\) | \(q+\zeta_{24}^{3}q^{2}-\zeta_{24}^{4}q^{3}+\zeta_{24}^{7}q^{5}+\cdots\) |