Properties

Label 189.2.i
Level $189$
Weight $2$
Character orbit 189.i
Rep. character $\chi_{189}(143,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $2$
Sturm bound $48$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(1\)
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 20 40
Cusp forms 36 12 24
Eisenstein series 24 8 16

Trace form

\( 12 q - 10 q^{4} + 3 q^{5} - 2 q^{7} + O(q^{10}) \) \( 12 q - 10 q^{4} + 3 q^{5} - 2 q^{7} - 6 q^{10} + 9 q^{11} - 3 q^{13} - 18 q^{14} + 2 q^{16} - 9 q^{17} - 6 q^{19} - 6 q^{20} + 2 q^{22} + 6 q^{23} + 3 q^{25} + 6 q^{26} - 2 q^{28} + 24 q^{29} + 6 q^{34} - q^{37} - 27 q^{38} + 24 q^{40} - 6 q^{41} + 2 q^{43} + 27 q^{44} - 4 q^{46} - 30 q^{47} + 6 q^{49} + 9 q^{50} - 15 q^{52} - 24 q^{53} + 24 q^{56} - q^{58} + 36 q^{59} + 24 q^{62} + 4 q^{64} + 12 q^{67} + 24 q^{68} + 15 q^{70} - 6 q^{73} + 51 q^{74} - 48 q^{77} - 24 q^{79} - 45 q^{80} - 30 q^{83} + 9 q^{85} - 57 q^{86} - 11 q^{88} + 27 q^{89} - 15 q^{91} - 30 q^{92} - 3 q^{97} + 21 q^{98} + O(q^{100}) \)

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.i.a 189.i 63.i $2$ $1.509$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+2\zeta_{6})q^{2}-q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
189.2.i.b 189.i 63.i $10$ $1.509$ 10.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{3}-\beta _{5})q^{2}+(-1-2\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)

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

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