Defining parameters
| Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
| Weight: | \( k \) | \(=\) | \( 11 \) |
| Character orbit: | \([\chi]\) | \(=\) | 9.b (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(11\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{11}(9, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 12 | 4 | 8 |
| Cusp forms | 8 | 4 | 4 |
| Eisenstein series | 4 | 0 | 4 |
Trace form
Decomposition of \(S_{11}^{\mathrm{new}}(9, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 9.11.b.a | $4$ | $5.718$ | \(\Q(\sqrt{-2}, \sqrt{385})\) | None | \(0\) | \(0\) | \(0\) | \(-44464\) | \(q-\beta _{1}q^{2}+(-1073-\beta _{2})q^{4}+(-35\beta _{1}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{11}^{\mathrm{old}}(9, [\chi])\) into lower level spaces
\( S_{11}^{\mathrm{old}}(9, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)