Properties

Label 167.2.c
Level $167$
Weight $2$
Character orbit 167.c
Rep. character $\chi_{167}(2,\cdot)$
Character field $\Q(\zeta_{83})$
Dimension $1066$
Newform subspaces $1$
Sturm bound $28$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 167.c (of order \(83\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 167 \)
Character field: \(\Q(\zeta_{83})\)
Newform subspaces: \( 1 \)
Sturm bound: \(28\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(167, [\chi])\).

Total New Old
Modular forms 1230 1230 0
Cusp forms 1066 1066 0
Eisenstein series 164 164 0

Trace form

\( 1066q - 81q^{2} - 81q^{3} - 89q^{4} - 79q^{5} - 63q^{6} - 81q^{7} - 71q^{8} - 84q^{9} + O(q^{10}) \) \( 1066q - 81q^{2} - 81q^{3} - 89q^{4} - 79q^{5} - 63q^{6} - 81q^{7} - 71q^{8} - 84q^{9} - 63q^{10} - 71q^{11} - 57q^{12} - 73q^{13} - 57q^{14} - 57q^{15} - 59q^{16} - 63q^{17} - 43q^{18} - 63q^{19} - 31q^{20} - 35q^{21} - 55q^{22} - 61q^{23} + 3q^{24} - 82q^{25} - 9q^{26} - 39q^{27} - 43q^{28} - 55q^{29} + 33q^{30} - 59q^{31} - 17q^{32} - 43q^{33} - 21q^{34} - 13q^{35} + 35q^{36} - 67q^{37} - 3q^{38} - 9q^{39} + 55q^{40} - 29q^{41} + 48q^{42} - 39q^{43} + 16q^{44} - 7q^{45} + 5q^{46} - 51q^{47} + 44q^{48} - 56q^{49} + 9q^{50} - 9q^{51} + 7q^{52} - 29q^{53} + 30q^{54} + 3q^{55} + 35q^{56} - 23q^{57} - 29q^{58} + 7q^{59} + 81q^{60} - 23q^{61} + 2q^{62} - 11q^{63} + 27q^{64} - 33q^{65} + 17q^{66} - 39q^{67} + 53q^{68} + 23q^{69} + 53q^{70} + 9q^{71} + 106q^{72} - 51q^{73} + 29q^{74} + 53q^{75} + 33q^{76} + 37q^{77} + 67q^{78} - 5q^{79} + 87q^{80} + 63q^{82} + 19q^{83} + 170q^{84} + 11q^{85} - 15q^{86} + 83q^{87} + 93q^{88} + 21q^{89} + 109q^{90} + 19q^{91} + 69q^{92} + 13q^{93} + 107q^{94} + 89q^{95} + 187q^{96} - 37q^{97} + 12q^{98} + 117q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(167, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
167.2.c.a \(1066\) \(1.334\) None \(-81\) \(-81\) \(-79\) \(-81\)