Properties

Label 216.3.j
Level $216$
Weight $3$
Character orbit 216.j
Rep. character $\chi_{216}(125,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $44$
Newform subspaces $1$
Sturm bound $108$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 216.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(108\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(216, [\chi])\).

Total New Old
Modular forms 156 52 104
Cusp forms 132 44 88
Eisenstein series 24 8 16

Trace form

\( 44 q + 3 q^{2} - q^{4} - 2 q^{7} + O(q^{10}) \) \( 44 q + 3 q^{2} - q^{4} - 2 q^{7} + 4 q^{10} + 48 q^{14} - q^{16} + 66 q^{20} + 7 q^{22} + 6 q^{23} - 72 q^{25} + 28 q^{28} - 2 q^{31} + 93 q^{32} + 9 q^{34} - 99 q^{38} - 56 q^{40} - 66 q^{41} + 72 q^{46} + 6 q^{47} - 72 q^{49} - 189 q^{50} - 42 q^{52} + 92 q^{55} - 270 q^{56} - 38 q^{58} + 2 q^{64} + 6 q^{65} - 387 q^{68} - 4 q^{70} - 8 q^{73} + 432 q^{74} - 63 q^{76} - 2 q^{79} + 186 q^{82} + 615 q^{86} - 77 q^{88} + 624 q^{92} - 186 q^{94} - 144 q^{95} - 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(216, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
216.3.j.a 216.j 72.j $44$ $5.886$ None \(3\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(216, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(216, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)