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Properties

Label 667.2.s
Level $667$
Weight $2$
Character orbit 667.s
Rep. character $\chi_{667}(16,\cdot)$
Character field $\Q(\zeta_{77})$
Dimension $3480$
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.s (of order \(77\) and degree \(60\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 667 \)
Character field: \(\Q(\zeta_{77})\)
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 3720 3720 0
Cusp forms 3480 3480 0
Eisenstein series 240 240 0

Trace form

\( 3480q - 49q^{2} - 45q^{3} + 7q^{4} - 49q^{5} - 39q^{6} - 49q^{7} - 50q^{8} + q^{9} + O(q^{10}) \) \( 3480q - 49q^{2} - 45q^{3} + 7q^{4} - 49q^{5} - 39q^{6} - 49q^{7} - 50q^{8} + q^{9} - 53q^{10} - 25q^{11} - 134q^{12} - 25q^{13} - 65q^{14} - 65q^{15} - 111q^{16} - 112q^{17} - 91q^{18} - 35q^{19} - 81q^{20} - 7q^{21} - 78q^{22} + 2q^{23} + 72q^{24} - 93q^{25} - 43q^{26} + 15q^{27} - 156q^{28} - 63q^{29} - 140q^{30} - 59q^{31} + 41q^{32} - 13q^{33} - 97q^{34} - 9q^{35} + 153q^{36} - 67q^{37} + q^{38} + 9q^{39} - 121q^{40} - 132q^{41} - 137q^{42} + 15q^{43} + 95q^{44} - 36q^{45} + 44q^{46} - 120q^{47} + 222q^{48} - 233q^{49} + 57q^{50} - 231q^{51} + 51q^{52} - 89q^{53} + 4q^{54} - 241q^{55} + 155q^{56} - 14q^{57} - 12q^{58} - 164q^{59} - 59q^{60} - 29q^{61} + 139q^{62} + 25q^{63} + 76q^{64} - 89q^{65} + 169q^{66} - 49q^{67} - 104q^{68} - 48q^{69} - 180q^{70} - 31q^{71} + 35q^{72} - 57q^{73} - 478q^{74} - 212q^{75} - 69q^{76} - 266q^{77} + 97q^{78} + 35q^{79} - 39q^{80} - 95q^{81} - 209q^{82} - 11q^{83} + 147q^{84} + 137q^{85} - 600q^{86} + 72q^{87} + 40q^{88} + 61q^{89} - 31q^{90} + 48q^{91} - 43q^{92} - 764q^{93} - 15q^{94} + 55q^{95} - 70q^{96} + 43q^{97} + 117q^{98} + 88q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.s.a \(3480\) \(5.326\) None \(-49\) \(-45\) \(-49\) \(-49\)