Properties

Label 189.2.g
Level $189$
Weight $2$
Character orbit 189.g
Rep. character $\chi_{189}(100,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $12$
Newform subspaces $2$
Sturm bound $48$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
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

\( 12 q - q^{2} - 3 q^{4} + 10 q^{5} + 12 q^{8} + O(q^{10}) \) \( 12 q - q^{2} - 3 q^{4} + 10 q^{5} + 12 q^{8} - 6 q^{10} - 2 q^{11} - 3 q^{13} - 11 q^{14} + 3 q^{16} - 9 q^{17} - 4 q^{20} - 6 q^{22} - 6 q^{25} - 16 q^{26} - 6 q^{28} - 8 q^{29} - 3 q^{31} + 7 q^{32} - 4 q^{35} - 3 q^{37} + 38 q^{38} + 12 q^{40} - 10 q^{41} - 6 q^{43} + 5 q^{44} - 27 q^{47} + 12 q^{49} - 23 q^{50} + 30 q^{52} + 12 q^{53} - 6 q^{55} + 48 q^{56} + 18 q^{58} - 30 q^{59} + 12 q^{62} - 36 q^{64} + 16 q^{65} - 6 q^{67} + 60 q^{68} - 24 q^{70} + 30 q^{71} + 12 q^{73} - 78 q^{74} + 6 q^{76} + 26 q^{77} - 12 q^{79} - 19 q^{80} - 18 q^{83} - 3 q^{85} - 14 q^{86} + 6 q^{88} - 41 q^{89} + 21 q^{91} - 30 q^{92} - 3 q^{94} + 13 q^{95} - 3 q^{97} - 61 q^{98} + O(q^{100}) \)

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.g.a 189.g 63.g $2$ $1.509$ \(\Q(\sqrt{-3}) \) None 63.2.g.a \(1\) \(0\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
189.2.g.b 189.g 63.g $10$ $1.509$ 10.0.\(\cdots\).1 None 63.2.g.b \(-2\) \(0\) \(8\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(1+\cdots)q^{5}+\cdots\)

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

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