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Properties

Label 288.2.r
Level $288$
Weight $2$
Character orbit 288.r
Rep. character $\chi_{288}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(288, [\chi])\).

Total New Old
Modular forms 112 28 84
Cusp forms 80 20 60
Eisenstein series 32 8 24

Trace form

\( 20 q + 2 q^{7} - 4 q^{9} + 10 q^{15} - 8 q^{17} + 14 q^{23} + 2 q^{31} - 18 q^{33} - 2 q^{39} + 2 q^{41} - 18 q^{47} + 28 q^{55} + 4 q^{57} - 50 q^{63} - 22 q^{65} - 48 q^{71} - 8 q^{73} + 2 q^{79} - 8 q^{81}+ \cdots - 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(288, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
288.2.r.a 288.r 72.n $4$ $2.300$ \(\Q(\zeta_{12})\) None 72.2.n.a \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+2\zeta_{12}q^{5}+4\zeta_{12}^{2}q^{7}+\cdots\)
288.2.r.b 288.r 72.n $16$ $2.300$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 72.2.n.b \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{12}q^{3}+(-\beta _{4}-\beta _{7}+\beta _{8}-\beta _{11}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(288, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)