Properties

Label 667.2.u
Level $667$
Weight $2$
Character orbit 667.u
Rep. character $\chi_{667}(4,\cdot)$
Character field $\Q(\zeta_{154})$
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.u (of order \(154\) and degree \(60\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 667 \)
Character field: \(\Q(\zeta_{154})\)
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

\( 3480q - 63q^{2} - 63q^{3} - 105q^{4} - 49q^{5} - 51q^{6} - 41q^{7} - 84q^{8} - 91q^{9} + O(q^{10}) \) \( 3480q - 63q^{2} - 63q^{3} - 105q^{4} - 49q^{5} - 51q^{6} - 41q^{7} - 84q^{8} - 91q^{9} - 63q^{10} - 91q^{11} - 65q^{13} - 63q^{14} - 63q^{15} + 85q^{16} - 63q^{18} - 63q^{19} - 41q^{20} - 91q^{21} - 82q^{22} - 100q^{23} + 56q^{24} - 77q^{25} - 63q^{26} - 21q^{27} - 60q^{28} - 35q^{29} - 180q^{30} - 49q^{31} - 77q^{32} - 49q^{33} - 41q^{34} - 81q^{35} - 71q^{36} - 49q^{37} + 65q^{38} - 105q^{39} - 63q^{40} - 65q^{42} - 91q^{43} - 49q^{44} - 204q^{45} - 112q^{47} - 28q^{48} + 307q^{49} - 119q^{50} - 251q^{51} - 77q^{52} - 49q^{53} - 28q^{54} + 189q^{55} - 133q^{56} - 86q^{57} - 56q^{58} - 100q^{59} - 105q^{60} - 7q^{61} - 229q^{62} - 235q^{63} - 196q^{64} - 57q^{65} + 49q^{66} + 95q^{67} - 196q^{68} - 98q^{69} - 75q^{71} - 35q^{72} - 63q^{73} + 354q^{74} + 49q^{76} - 378q^{77} - 19q^{78} - 175q^{79} - 243q^{80} - 7q^{81} + 47q^{82} - 83q^{83} + 49q^{84} - 105q^{85} + 632q^{86} + 160q^{88} - 161q^{89} + 119q^{90} + 80q^{91} - 37q^{92} + 476q^{93} - 143q^{94} - 7q^{95} - 30q^{96} - 35q^{97} + 7q^{98} + O(q^{100}) \)

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.u.a \(3480\) \(5.326\) None \(-63\) \(-63\) \(-49\) \(-41\)