Properties

Label 671.2.cw
Level $671$
Weight $2$
Character orbit 671.cw
Rep. character $\chi_{671}(29,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $960$
Newform subspaces $1$
Sturm bound $124$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 671 = 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 671.cw (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 671 \)
Character field: \(\Q(\zeta_{60})\)
Newform subspaces: \( 1 \)
Sturm bound: \(124\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(671, [\chi])\).

Total New Old
Modular forms 1024 1024 0
Cusp forms 960 960 0
Eisenstein series 64 64 0

Trace form

\( 960 q - 20 q^{2} - 18 q^{4} - 18 q^{5} - 20 q^{6} - 20 q^{8} + 200 q^{9} + O(q^{10}) \) \( 960 q - 20 q^{2} - 18 q^{4} - 18 q^{5} - 20 q^{6} - 20 q^{8} + 200 q^{9} - 18 q^{11} - 28 q^{12} - 10 q^{13} - 18 q^{14} - 18 q^{15} - 138 q^{16} + 30 q^{17} - 20 q^{18} - 30 q^{19} + 40 q^{20} - 8 q^{22} - 40 q^{23} - 114 q^{25} - 64 q^{26} - 20 q^{28} - 10 q^{29} - 28 q^{31} - 84 q^{33} - 64 q^{34} - 30 q^{35} + 84 q^{36} - 36 q^{37} - 62 q^{38} + 60 q^{39} + 20 q^{40} - 18 q^{42} + 98 q^{44} + 36 q^{45} - 30 q^{46} - 22 q^{47} - 198 q^{48} - 60 q^{49} - 50 q^{50} + 20 q^{51} - 12 q^{53} + 124 q^{55} + 40 q^{56} - 130 q^{57} + 16 q^{58} - 8 q^{59} + 10 q^{61} + 300 q^{62} - 90 q^{63} - 24 q^{66} - 128 q^{67} - 160 q^{68} + 100 q^{69} - 64 q^{70} - 24 q^{71} + 190 q^{72} - 10 q^{73} + 40 q^{74} - 54 q^{75} - 100 q^{77} - 300 q^{78} - 20 q^{79} + 30 q^{80} - 280 q^{81} + 104 q^{82} + 20 q^{83} - 150 q^{84} - 50 q^{85} + 6 q^{86} - 32 q^{89} + 160 q^{90} + 24 q^{91} + 16 q^{92} - 150 q^{93} - 100 q^{94} - 40 q^{95} - 160 q^{96} - 66 q^{97} + 186 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(671, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
671.2.cw.a 671.cw 671.bw $960$ $5.358$ None \(-20\) \(0\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{60}]$