Defining parameters
| Level: | \( N \) | = | \( 1161 = 3^{3} \cdot 43 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Character orbit: | \([\chi]\) | = | 1161.i (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | = | \( 129 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newforms: | \( 3 \) | ||
| Sturm bound: | \(132\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1161, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 26 | 14 | 12 |
| Cusp forms | 14 | 14 | 0 |
| Eisenstein series | 12 | 0 | 12 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 2 | 0 | 4 | 8 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1161, [\chi])\) into irreducible Hecke orbits
| Label | Dim. | \(A\) | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||||
| 1161.1.i.a | \(2\) | \(0.579\) | \(\Q(\sqrt{-3}) \) | \(D_{3}\) | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(-2\) | \(q+q^{4}-\zeta_{6}q^{7}+\zeta_{6}q^{13}+q^{16}-\zeta_{6}^{2}q^{19}+\cdots\) |
| 1161.1.i.b | \(4\) | \(0.579\) | \(\Q(\sqrt{-2}, \sqrt{-3})\) | \(S_{4}\) | None | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{3}q^{2}-q^{4}-\beta _{1}q^{5}+(-2+2\beta _{2}+\cdots)q^{10}+\cdots\) |
| 1161.1.i.c | \(8\) | \(0.579\) | 8.0.12960000.1 | \(A_{5}\) | None | None | \(0\) | \(0\) | \(0\) | \(2\) | \(q+\beta _{7}q^{2}+(-\beta _{3}-\beta _{6}-\beta _{7})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\) |