Properties

Label 169.2.g
Level $169$
Weight $2$
Character orbit 169.g
Rep. character $\chi_{169}(14,\cdot)$
Character field $\Q(\zeta_{13})$
Dimension $156$
Newform subspaces $1$
Sturm bound $30$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 169.g (of order \(13\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{13})\)
Newform subspaces: \( 1 \)
Sturm bound: \(30\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(169, [\chi])\).

Total New Old
Modular forms 180 180 0
Cusp forms 156 156 0
Eisenstein series 24 24 0

Trace form

\( 156q - 10q^{2} - 9q^{3} - 20q^{4} - 7q^{5} - q^{6} - 5q^{7} + 2q^{8} - 14q^{9} + O(q^{10}) \) \( 156q - 10q^{2} - 9q^{3} - 20q^{4} - 7q^{5} - q^{6} - 5q^{7} + 2q^{8} - 14q^{9} + q^{10} - q^{11} + 11q^{12} - 65q^{13} + 9q^{14} - 41q^{15} + 3q^{17} - 13q^{18} - 6q^{19} + 29q^{20} + 19q^{21} - 22q^{22} - 82q^{23} - 31q^{24} + 2q^{25} + 26q^{26} + 21q^{27} + 43q^{28} + 13q^{29} - 81q^{30} - 33q^{31} - 93q^{32} + 35q^{33} - 24q^{34} + 27q^{35} + 54q^{36} + 25q^{37} - 56q^{38} - 13q^{39} - 52q^{40} + 29q^{41} - 63q^{42} + 21q^{43} + 45q^{44} + 33q^{46} - 69q^{47} + 54q^{48} - 54q^{49} + 80q^{50} - 16q^{51} + 13q^{52} - 45q^{53} + 29q^{54} - 83q^{55} + 91q^{56} - 11q^{57} + 25q^{58} - 57q^{59} + 51q^{60} + 39q^{61} + 4q^{62} + 26q^{63} + 86q^{64} + 65q^{65} - 138q^{66} - 101q^{67} + 36q^{68} + 32q^{69} - 90q^{70} + 20q^{71} + 13q^{72} + 61q^{73} - 4q^{74} - 67q^{75} - 107q^{76} + 67q^{77} + 13q^{78} + 57q^{79} + 160q^{80} + 78q^{81} - 31q^{82} - 59q^{83} - 36q^{84} - 61q^{85} + 41q^{86} - 9q^{87} - 45q^{88} - 66q^{89} + 191q^{90} + 39q^{91} + 79q^{92} - 80q^{93} - 21q^{94} - 28q^{95} + 70q^{96} + 7q^{97} + 158q^{98} + 130q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(169, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
169.2.g.a \(156\) \(1.349\) None \(-10\) \(-9\) \(-7\) \(-5\)