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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
667.2.s.a 667.s 667.s $3480$ $5.326$ None \(-49\) \(-45\) \(-49\) \(-49\) $\mathrm{SU}(2)[C_{77}]$