Defining parameters
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 12 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(288, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 352 | 28 | 324 |
Cusp forms | 320 | 28 | 292 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(288, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
288.8.c.a | $12$ | $89.967$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-37\beta _{4}+\beta _{8})q^{5}+(5\beta _{1}+\beta _{3})q^{7}+\cdots\) |
288.8.c.b | $16$ | $89.967$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-7\beta _{8}+\beta _{12})q^{5}+\beta _{4}q^{7}+(-3\beta _{9}+\cdots)q^{11}+\cdots\) |
Decomposition of \(S_{8}^{\mathrm{old}}(288, [\chi])\) into lower level spaces
\( S_{8}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)