Properties

Label 189.2.v
Level $189$
Weight $2$
Character orbit 189.v
Rep. character $\chi_{189}(22,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $108$
Newform subspaces $2$
Sturm bound $48$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.v (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(189, [\chi])\).

Total New Old
Modular forms 156 108 48
Cusp forms 132 108 24
Eisenstein series 24 0 24

Trace form

\( 108 q - 6 q^{5} - 18 q^{8} - 6 q^{9} + O(q^{10}) \) \( 108 q - 6 q^{5} - 18 q^{8} - 6 q^{9} - 12 q^{11} - 36 q^{12} - 18 q^{15} - 30 q^{18} + 6 q^{20} - 18 q^{22} - 12 q^{23} + 72 q^{24} - 18 q^{25} - 36 q^{26} + 6 q^{27} + 36 q^{29} - 48 q^{30} - 18 q^{31} + 42 q^{32} - 48 q^{33} - 18 q^{34} - 24 q^{35} + 48 q^{36} - 24 q^{38} - 24 q^{39} - 66 q^{41} - 30 q^{42} - 18 q^{43} - 12 q^{44} + 42 q^{45} - 54 q^{47} - 78 q^{48} + 144 q^{50} + 60 q^{51} - 54 q^{52} + 72 q^{53} - 36 q^{54} + 42 q^{57} - 54 q^{58} + 42 q^{59} + 126 q^{60} - 54 q^{64} + 48 q^{65} + 6 q^{66} + 18 q^{67} + 6 q^{68} + 48 q^{69} - 72 q^{71} + 30 q^{72} + 12 q^{74} - 24 q^{75} + 108 q^{76} - 120 q^{78} + 36 q^{79} - 180 q^{80} - 42 q^{81} - 30 q^{83} - 24 q^{84} + 36 q^{85} - 24 q^{86} - 96 q^{87} + 108 q^{88} + 48 q^{89} + 6 q^{90} - 42 q^{92} + 114 q^{93} - 54 q^{94} - 36 q^{95} + 144 q^{96} - 18 q^{97} - 6 q^{98} - 66 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(189, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
189.2.v.a 189.v 27.e $54$ $1.509$ None 189.2.v.a \(0\) \(-3\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{9}]$
189.2.v.b 189.v 27.e $54$ $1.509$ None 189.2.v.b \(0\) \(3\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(189, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(189, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)