Defining parameters
| Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 576.n (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 72 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(288\) | ||
| Trace bound: | \(5\) | ||
| Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(576, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 408 | 96 | 312 |
| Cusp forms | 360 | 96 | 264 |
| Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(576, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 576.3.n.a | $8$ | $15.695$ | \(\Q(\zeta_{24})\) | \(\Q(\sqrt{-2}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{24}^{6}-\zeta_{24}^{7})q^{3}+(-7+7\zeta_{24}^{2}+\cdots)q^{9}+\cdots\) |
| 576.3.n.b | $24$ | $15.695$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
| 576.3.n.c | $32$ | $15.695$ | None | \(0\) | \(0\) | \(-18\) | \(0\) | ||
| 576.3.n.d | $32$ | $15.695$ | None | \(0\) | \(0\) | \(18\) | \(0\) | ||
Decomposition of \(S_{3}^{\mathrm{old}}(576, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)