Defining parameters
| Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 117.j (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(14\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(117, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 10 | 4 | 6 |
| Cusp forms | 2 | 2 | 0 |
| Eisenstein series | 8 | 2 | 6 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 2 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(117, [\chi])\) into newform subspaces
| Label | Dim. | \(A\) | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 117.1.j.a | $2$ | $0.058$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(-2\) | \(q+iq^{4}+(-1-i)q^{7}-iq^{13}-q^{16}+\cdots\) |