Defining parameters
| Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 624.bs (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 39 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(112\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(624, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 32 | 6 | 26 |
| Cusp forms | 8 | 2 | 6 |
| Eisenstein series | 24 | 4 | 20 |
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 \(S_{1}^{\mathrm{new}}(624, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 624.1.bs.a | $2$ | $0.311$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(1\) | \(0\) | \(-1\) | \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{13}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(624, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(624, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 3}\)