Properties

Label 189.2.f
Level $189$
Weight $2$
Character orbit 189.f
Rep. character $\chi_{189}(64,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $12$
Newform subspaces $2$
Sturm bound $48$
Trace bound $2$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 60 12 48
Cusp forms 36 12 24
Eisenstein series 24 0 24

Trace form

\( 12 q + 2 q^{2} - 6 q^{4} - 2 q^{5} + O(q^{10}) \) \( 12 q + 2 q^{2} - 6 q^{4} - 2 q^{5} + 4 q^{11} + 4 q^{14} - 6 q^{16} + 12 q^{17} - 12 q^{19} - 22 q^{20} + 6 q^{22} + 12 q^{23} + 8 q^{26} + 10 q^{29} + 6 q^{31} - 8 q^{32} - 6 q^{34} - 16 q^{35} - 12 q^{37} + 14 q^{38} - 12 q^{40} - 22 q^{41} + 6 q^{43} - 76 q^{44} + 24 q^{46} - 6 q^{47} - 6 q^{49} + 4 q^{50} + 18 q^{52} + 24 q^{53} - 12 q^{55} + 12 q^{56} + 18 q^{58} - 12 q^{59} + 96 q^{62} + 10 q^{65} + 12 q^{67} + 12 q^{68} - 36 q^{71} - 36 q^{73} - 24 q^{74} + 6 q^{76} + 8 q^{77} + 6 q^{79} + 8 q^{80} - 30 q^{83} - 18 q^{85} + 40 q^{86} - 6 q^{88} - 20 q^{89} - 12 q^{91} + 18 q^{92} - 6 q^{94} + 4 q^{95} - 4 q^{98} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
189.2.f.a 189.f 9.c $6$ $1.509$ 6.0.309123.1 None \(-1\) \(0\) \(-5\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{5})q^{2}+(-1+\beta _{2}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
189.2.f.b 189.f 9.c $6$ $1.509$ \(\Q(\zeta_{18})\) None \(3\) \(0\) \(3\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\zeta_{18}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(189, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)