Defining parameters
| Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 567.d (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(72\) | ||
| Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(567, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 19 | 8 | 11 |
| Cusp forms | 7 | 4 | 3 |
| Eisenstein series | 12 | 4 | 8 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(567, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 567.1.d.a | $1$ | $0.283$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-7}) \) | None | \(-1\) | \(0\) | \(0\) | \(1\) | \(q-q^{2}+q^{7}+q^{8}-q^{11}-q^{14}-q^{16}+\cdots\) |
| 567.1.d.b | $1$ | $0.283$ | \(\Q\) | $D_{3}$ | \(\Q(\sqrt{-7}) \) | None | \(1\) | \(0\) | \(0\) | \(1\) | \(q+q^{2}+q^{7}-q^{8}+q^{11}+q^{14}-q^{16}+\cdots\) |
| 567.1.d.c | $2$ | $0.283$ | \(\Q(\sqrt{3}) \) | $D_{6}$ | \(\Q(\sqrt{-7}) \) | None | \(0\) | \(0\) | \(0\) | \(-2\) | \(q-\beta q^{2}+2q^{4}-q^{7}-\beta q^{8}+\beta q^{11}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(567, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(567, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)