Properties

Label 288.8.c
Level $288$
Weight $8$
Character orbit 288.c
Rep. character $\chi_{288}(287,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $2$
Sturm bound $384$
Trace bound $1$

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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

\( 28 q + O(q^{10}) \) \( 28 q + 14128 q^{13} - 478476 q^{25} + 1433592 q^{37} - 239292 q^{49} + 259816 q^{61} + 12364800 q^{73} + 7000440 q^{85} + 18139936 q^{97} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(288, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
288.8.c.a 288.c 12.b $12$ $89.967$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-37\beta _{4}+\beta _{8})q^{5}+(5\beta _{1}+\beta _{3})q^{7}+\cdots\)
288.8.c.b 288.c 12.b $16$ $89.967$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-7\beta _{8}+\beta _{12})q^{5}+\beta _{4}q^{7}+(-3\beta _{9}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)