Properties

Label 169.2.h
Level $169$
Weight $2$
Character orbit 169.h
Rep. character $\chi_{169}(12,\cdot)$
Character field $\Q(\zeta_{26})$
Dimension $168$
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.h (of order \(26\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{26})\)
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 192 192 0
Cusp forms 168 168 0
Eisenstein series 24 24 0

Trace form

\( 168q - 13q^{2} - 13q^{3} + q^{4} - 13q^{5} - 13q^{6} - 13q^{7} - 13q^{8} - 27q^{9} + O(q^{10}) \) \( 168q - 13q^{2} - 13q^{3} + q^{4} - 13q^{5} - 13q^{6} - 13q^{7} - 13q^{8} - 27q^{9} - 9q^{10} - 13q^{11} - 9q^{12} + 52q^{13} - 15q^{14} + 39q^{15} - 31q^{16} - 11q^{17} + 26q^{18} - 13q^{20} - 13q^{21} - 6q^{22} - 102q^{23} - 91q^{24} + 3q^{25} - 13q^{26} - 19q^{27} - 13q^{28} - 17q^{29} + 23q^{30} + 39q^{31} - 13q^{33} + 52q^{34} - 21q^{35} + 11q^{36} - 13q^{37} - 40q^{38} - 65q^{39} + 53q^{40} - 13q^{41} + 101q^{42} - 3q^{43} - 39q^{44} - 78q^{45} - 39q^{46} - 39q^{47} + 8q^{48} + 85q^{49} - 13q^{50} + 62q^{51} - 78q^{52} + 18q^{53} + 65q^{54} - 103q^{55} + 3q^{56} + 65q^{57} + 39q^{58} + 91q^{59} - 117q^{60} - 23q^{61} - 64q^{62} - 78q^{63} + 15q^{64} - 13q^{65} + 134q^{66} - 65q^{67} + 40q^{68} - 40q^{69} + 26q^{71} + 156q^{72} - 13q^{73} - 53q^{74} + 35q^{75} + 221q^{76} + 3q^{77} - 143q^{78} - 23q^{79} - 43q^{81} - 129q^{82} + 117q^{83} + 234q^{84} + 26q^{85} - 91q^{86} + 79q^{87} + 95q^{88} + 17q^{90} + 39q^{91} - 89q^{92} + 52q^{93} - 61q^{94} + 122q^{95} - 182q^{96} - 91q^{97} - 13q^{98} + O(q^{100}) \)

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.h.a \(168\) \(1.349\) None \(-13\) \(-13\) \(-13\) \(-13\)