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Properties

Label 288.4.r
Level $288$
Weight $4$
Character orbit 288.r
Rep. character $\chi_{288}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $68$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 288.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(288, [\chi])\).

Total New Old
Modular forms 304 76 228
Cusp forms 272 68 204
Eisenstein series 32 8 24

Trace form

\( 68 q + 2 q^{7} - 4 q^{9} + O(q^{10}) \) \( 68 q + 2 q^{7} - 4 q^{9} + 58 q^{15} - 8 q^{17} - 274 q^{23} + 648 q^{25} + 2 q^{31} + 174 q^{33} - 242 q^{39} - 22 q^{41} + 942 q^{47} - 1080 q^{49} + 508 q^{55} - 68 q^{57} - 722 q^{63} - 502 q^{65} + 3984 q^{71} - 8 q^{73} + 2 q^{79} + 1072 q^{81} - 3354 q^{87} - 856 q^{89} + 2792 q^{95} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(288, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
288.4.r.a 288.r 72.n $68$ $16.993$ None 72.4.n.a \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(288, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)