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Properties

Label 288.2.p
Level $288$
Weight $2$
Character orbit 288.p
Rep. character $\chi_{288}(47,\cdot)$
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.p (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

\( 20 q + 4 q^{3} - 4 q^{9} + 6 q^{11} + 8 q^{19} - 4 q^{25} + 16 q^{27} - 2 q^{33} - 18 q^{41} + 2 q^{43} - 4 q^{49} - 28 q^{51} - 20 q^{57} - 30 q^{59} - 6 q^{65} + 2 q^{67} - 8 q^{73} - 68 q^{75} + 8 q^{81}+ \cdots - 10 q^{99}+O(q^{100}) \) 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.p.a 288.p 72.l $4$ $2.300$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) 72.2.l.a \(0\) \(-2\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(1-2\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
288.2.p.b 288.p 72.l $16$ $2.300$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 72.2.l.b \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{3}-\beta _{8})q^{3}-\beta _{9}q^{5}-\beta _{4}q^{7}+\cdots\)

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

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