Defining parameters
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.r (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 72 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(864, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 336 | 28 | 308 |
Cusp forms | 240 | 20 | 220 |
Eisenstein series | 96 | 8 | 88 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(864, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
864.2.r.a | $4$ | $6.899$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(8\) | \(q+2\zeta_{12}q^{5}+4\zeta_{12}^{2}q^{7}+(3\zeta_{12}-3\zeta_{12}^{3})q^{11}+\cdots\) |
864.2.r.b | $16$ | $6.899$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-6\) | \(q+(\beta _{4}-\beta _{5}-\beta _{11})q^{5}+(-1+\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(864, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)