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Properties

Label 171.2.g
Level $171$
Weight $2$
Character orbit 171.g
Rep. character $\chi_{171}(106,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $36$
Newform subspaces $3$
Sturm bound $40$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 171.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(40\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(171, [\chi])\).

Total New Old
Modular forms 44 44 0
Cusp forms 36 36 0
Eisenstein series 8 8 0

Trace form

\( 36 q + 3 q^{2} - 2 q^{3} - 15 q^{4} - 2 q^{5} + 2 q^{6} - 3 q^{7} - 24 q^{8} - 4 q^{9} + O(q^{10}) \) \( 36 q + 3 q^{2} - 2 q^{3} - 15 q^{4} - 2 q^{5} + 2 q^{6} - 3 q^{7} - 24 q^{8} - 4 q^{9} - 6 q^{10} - q^{11} - 3 q^{12} - 10 q^{14} - 11 q^{15} - 9 q^{16} - 5 q^{17} + 18 q^{18} - 9 q^{19} - q^{20} + 11 q^{21} + 5 q^{23} + 27 q^{24} + 18 q^{25} + 4 q^{26} - 5 q^{27} - 6 q^{28} - 32 q^{29} - 17 q^{30} - 6 q^{31} + 27 q^{32} + 34 q^{33} + 30 q^{34} - 3 q^{35} - 22 q^{36} - 6 q^{37} + 30 q^{38} - 12 q^{40} - 32 q^{41} + 19 q^{42} - 9 q^{43} + 28 q^{44} - 29 q^{45} + 42 q^{47} - 33 q^{48} - 9 q^{49} + q^{50} - 28 q^{51} + 15 q^{52} + 14 q^{53} + 35 q^{54} + 3 q^{55} - 18 q^{56} - 6 q^{58} - 58 q^{59} + 50 q^{60} + 12 q^{61} + 50 q^{62} - 18 q^{63} - 36 q^{64} + 42 q^{65} + 10 q^{66} - 3 q^{67} - 4 q^{68} + 3 q^{69} - 48 q^{70} + 21 q^{71} + 18 q^{72} + 2 q^{74} - 100 q^{75} + 21 q^{76} + 32 q^{77} - 58 q^{78} - 22 q^{80} + 8 q^{81} - 3 q^{82} - 5 q^{83} + 18 q^{84} - 9 q^{85} + 33 q^{86} - 21 q^{87} - 15 q^{88} + 40 q^{89} - 62 q^{90} + 15 q^{91} - 17 q^{92} + 6 q^{93} - 6 q^{94} - 22 q^{95} - 5 q^{96} + 12 q^{97} + 14 q^{98} + 14 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(171, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
171.2.g.a 171.g 171.g $2$ $1.365$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(6\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
171.2.g.b 171.g 171.g $2$ $1.365$ \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(-2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(2-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
171.2.g.c 171.g 171.g $32$ $1.365$ None \(1\) \(-2\) \(-6\) \(1\) $\mathrm{SU}(2)[C_{3}]$