Properties

Label 667.2.x
Level $667$
Weight $2$
Character orbit 667.x
Rep. character $\chi_{667}(10,\cdot)$
Character field $\Q(\zeta_{308})$
Dimension $6960$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 667 = 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 667.x (of order \(308\) and degree \(120\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 667 \)
Character field: \(\Q(\zeta_{308})\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(667, [\chi])\).

Total New Old
Modular forms 7440 7440 0
Cusp forms 6960 6960 0
Eisenstein series 480 480 0

Trace form

\( 6960q - 112q^{2} - 108q^{3} - 126q^{4} - 154q^{5} - 126q^{6} - 110q^{7} - 102q^{8} - 126q^{9} + O(q^{10}) \) \( 6960q - 112q^{2} - 108q^{3} - 126q^{4} - 154q^{5} - 126q^{6} - 110q^{7} - 102q^{8} - 126q^{9} - 132q^{10} - 132q^{11} - 94q^{12} - 126q^{13} - 132q^{14} - 132q^{15} - 234q^{16} - 132q^{17} - 74q^{18} - 110q^{19} - 110q^{20} - 198q^{21} - 98q^{23} - 528q^{24} + 190q^{25} - 50q^{26} + 18q^{27} - 82q^{29} - 264q^{30} - 92q^{31} - 196q^{32} - 154q^{33} - 154q^{34} - 70q^{35} - 262q^{36} - 132q^{37} - 154q^{38} - 168q^{39} - 132q^{40} - 132q^{41} - 154q^{42} - 44q^{43} + 66q^{44} - 232q^{46} - 320q^{47} - 14q^{48} - 94q^{49} + 10q^{50} + 462q^{51} - 282q^{52} - 110q^{53} - 156q^{54} - 204q^{55} + 110q^{56} - 248q^{58} - 184q^{59} - 132q^{60} - 132q^{61} - 126q^{62} - 154q^{63} - 252q^{64} - 110q^{65} - 242q^{66} - 154q^{67} - 94q^{69} - 420q^{70} - 70q^{71} + 224q^{72} - 88q^{73} - 148q^{75} - 132q^{76} + 524q^{77} + 174q^{78} - 132q^{79} - 154q^{80} + 50q^{81} - 82q^{82} - 242q^{83} - 264q^{84} - 216q^{85} + 120q^{87} - 440q^{88} - 176q^{90} + 28q^{92} - 280q^{93} - 86q^{94} + 96q^{95} - 84q^{96} - 356q^{98} - 396q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(667, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
667.2.x.a \(6960\) \(5.326\) None \(-112\) \(-108\) \(-154\) \(-110\)