Properties

Label 288.8.d
Level $288$
Weight $8$
Character orbit 288.d
Rep. character $\chi_{288}(145,\cdot)$
Character field $\Q$
Dimension $34$
Newform subspaces $4$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
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 36 316
Cusp forms 320 34 286
Eisenstein series 32 2 30

Trace form

\( 34 q + 688 q^{7} + O(q^{10}) \) \( 34 q + 688 q^{7} + 1456 q^{17} - 144712 q^{23} - 476814 q^{25} - 446768 q^{31} - 79960 q^{41} + 510024 q^{47} + 3805218 q^{49} - 920752 q^{55} + 1103984 q^{65} - 2424408 q^{71} + 4623692 q^{73} - 6990368 q^{79} + 9783536 q^{89} - 20789440 q^{95} + 2997452 q^{97} + O(q^{100}) \)

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.d.a 288.d 8.b $2$ $89.967$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(1508\) $\mathrm{U}(1)[D_{2}]$ \(q+197\beta q^{5}+754q^{7}-2378\beta q^{11}+\cdots\)
288.8.d.b 288.d 8.b $6$ $89.967$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(0\) \(688\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{2}-\beta _{3})q^{5}+(115+\beta _{1})q^{7}+(3\beta _{2}+\cdots)q^{11}+\cdots\)
288.8.d.c 288.d 8.b $12$ $89.967$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(-136\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{5}+(-11+\beta _{4})q^{7}+(-10\beta _{1}+\cdots)q^{11}+\cdots\)
288.8.d.d 288.d 8.b $14$ $89.967$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(0\) \(-1372\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}+(-98+\beta _{3})q^{7}+(-4\beta _{2}+\cdots)q^{11}+\cdots\)

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

\( S_{8}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)