Defining parameters
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 12 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(576, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 120 | 8 | 112 |
Cusp forms | 72 | 8 | 64 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(576, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
576.2.c.a | $2$ | $4.599$ | \(\Q(\sqrt{-2}) \) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta q^{5}-4q^{13}+\beta q^{17}-13q^{25}+\cdots\) |
576.2.c.b | $2$ | $4.599$ | \(\Q(\sqrt{-2}) \) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta q^{5}+4q^{13}+5\beta q^{17}+3q^{25}+\cdots\) |
576.2.c.c | $4$ | $4.599$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+\zeta_{8}^{3}q^{11}-4q^{13}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(576, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(576, [\chi]) \cong \)