Properties

Label 169.2.k
Level $169$
Weight $2$
Character orbit 169.k
Rep. character $\chi_{169}(4,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $360$
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.k (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{78})\)
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 408 408 0
Cusp forms 360 360 0
Eisenstein series 48 48 0

Trace form

\( 360q - 23q^{2} - 24q^{3} - 41q^{4} - 26q^{5} - 32q^{6} - 26q^{7} - 26q^{8} - 11q^{9} + O(q^{10}) \) \( 360q - 23q^{2} - 24q^{3} - 41q^{4} - 26q^{5} - 32q^{6} - 26q^{7} - 26q^{8} - 11q^{9} - 27q^{10} - 26q^{11} - 14q^{12} - 34q^{13} - 30q^{14} - 84q^{15} - 13q^{16} - 31q^{17} + 52q^{18} - 33q^{19} - 29q^{20} - 26q^{21} - 33q^{22} + 57q^{23} + 58q^{24} + 2q^{25} - 29q^{26} - 30q^{27} - 26q^{28} - 19q^{29} + 178q^{30} - 78q^{31} - 30q^{32} - 26q^{33} - 91q^{34} - 18q^{35} - 51q^{36} - 41q^{37} + 25q^{38} + 12q^{39} - 134q^{40} - 17q^{41} + 250q^{42} - 28q^{43} + 42q^{45} + 18q^{46} + 117q^{47} - 57q^{48} - 117q^{49} - 20q^{50} - 59q^{51} + 37q^{52} - 75q^{53} + 118q^{54} + 64q^{55} - 42q^{56} - 104q^{57} - 87q^{58} + 170q^{59} + 78q^{60} - 15q^{61} + 19q^{62} + 39q^{63} + 32q^{64} - 17q^{65} + 73q^{66} + 20q^{67} - 76q^{68} - 11q^{69} + 46q^{71} - 198q^{72} - 26q^{73} + 29q^{74} - 70q^{75} + 58q^{76} + 6q^{77} + 128q^{78} - 54q^{79} - 24q^{80} - 7q^{81} + 81q^{82} + 234q^{83} - 273q^{84} - 74q^{85} + 52q^{86} - 112q^{87} + 256q^{88} - 27q^{89} + 28q^{90} - 78q^{91} - 34q^{92} + 51q^{93} + 28q^{94} - 11q^{95} + 143q^{96} + 40q^{97} - 47q^{98} + O(q^{100}) \)

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.k.a \(360\) \(1.349\) None \(-23\) \(-24\) \(-26\) \(-26\)