Properties

Label 171.3.j
Level $171$
Weight $3$
Character orbit 171.j
Rep. character $\chi_{171}(68,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $76$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 171.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(171, [\chi])\).

Total New Old
Modular forms 84 84 0
Cusp forms 76 76 0
Eisenstein series 8 8 0

Trace form

\( 76q - 5q^{3} - 146q^{4} - 3q^{5} + 23q^{6} - q^{7} - 13q^{9} + O(q^{10}) \) \( 76q - 5q^{3} - 146q^{4} - 3q^{5} + 23q^{6} - q^{7} - 13q^{9} + 6q^{10} - 24q^{11} + 15q^{12} + 8q^{13} - 3q^{14} - 14q^{15} + 262q^{16} - 135q^{17} + 30q^{18} + 4q^{19} + 69q^{20} - 40q^{21} - 3q^{22} - 81q^{24} + 151q^{25} - 59q^{27} + 14q^{28} - 30q^{29} + 265q^{30} + 14q^{31} + 31q^{33} - 33q^{34} - 75q^{35} + 41q^{36} + 14q^{37} + 63q^{38} - 78q^{39} + 12q^{40} - 201q^{41} - 122q^{42} - 58q^{43} + 183q^{44} + 145q^{45} - 84q^{46} - 21q^{47} + 159q^{48} - 171q^{49} - 363q^{50} - 103q^{51} - 202q^{52} + 36q^{53} - 370q^{54} - 27q^{55} + 300q^{56} - 3q^{57} + 6q^{58} - 84q^{59} - 145q^{60} + 8q^{61} + 120q^{62} + 3q^{63} - 680q^{64} - 6q^{65} + 271q^{66} - 16q^{67} + 666q^{68} + 81q^{69} - 42q^{70} + 135q^{71} + 381q^{72} + 65q^{73} - 139q^{75} - 155q^{76} - 366q^{77} - 514q^{78} + 32q^{79} - 66q^{80} + 179q^{81} - 42q^{82} - 177q^{83} + 546q^{84} - 102q^{85} - 375q^{87} + 162q^{88} + 216q^{89} - 575q^{90} + 265q^{91} + 201q^{93} + 6q^{94} + 789q^{95} + 511q^{96} + 254q^{97} + 882q^{98} - 64q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(171, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
171.3.j.a \(76\) \(4.659\) None \(0\) \(-5\) \(-3\) \(-1\)