Defining parameters
| Level: | \( N \) | \(=\) | \( 591 = 3 \cdot 197 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 591.d (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 591 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(66\) | ||
| Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(591, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 12 | 12 | 0 |
| Cusp forms | 10 | 10 | 0 |
| Eisenstein series | 2 | 2 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 10 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(591, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 591.1.d.a | $5$ | $0.295$ | \(\Q(\zeta_{22})^+\) | $D_{11}$ | \(\Q(\sqrt{-591}) \) | None | \(-1\) | \(5\) | \(-1\) | \(-1\) | \(q+\beta _{4}q^{2}+q^{3}+(1-\beta _{3})q^{4}+\beta _{2}q^{5}+\cdots\) |
| 591.1.d.b | $5$ | $0.295$ | \(\Q(\zeta_{22})^+\) | $D_{11}$ | \(\Q(\sqrt{-591}) \) | None | \(1\) | \(-5\) | \(1\) | \(-1\) | \(q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}-q^{3}+\cdots\) |