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Properties

Label 671.2.cf
Level $671$
Weight $2$
Character orbit 671.cf
Rep. character $\chi_{671}(45,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $400$
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.cf (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 61 \)
Character field: \(\Q(\zeta_{30})\)
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 512 400 112
Cusp forms 480 400 80
Eisenstein series 32 0 32

Trace form

\( 400 q - 4 q^{3} - 38 q^{4} + 16 q^{5} - 32 q^{6} + 14 q^{7} - 76 q^{9} + O(q^{10}) \) \( 400 q - 4 q^{3} - 38 q^{4} + 16 q^{5} - 32 q^{6} + 14 q^{7} - 76 q^{9} - 12 q^{10} - 94 q^{12} + 4 q^{13} - 34 q^{14} - 32 q^{15} + 70 q^{16} - 76 q^{18} + 44 q^{19} + 32 q^{20} + 60 q^{21} - 2 q^{22} - 20 q^{23} - 30 q^{24} + 30 q^{25} + 56 q^{26} - 16 q^{27} - 30 q^{29} - 92 q^{30} - 46 q^{31} + 90 q^{32} - 20 q^{34} + 24 q^{35} + 34 q^{36} - 10 q^{38} - 4 q^{39} - 36 q^{40} - 4 q^{41} + 32 q^{42} + 40 q^{43} + 64 q^{45} - 188 q^{46} + 88 q^{47} - 52 q^{48} - 74 q^{49} + 88 q^{51} + 52 q^{52} - 50 q^{53} + 84 q^{54} - 140 q^{56} - 164 q^{57} + 24 q^{58} + 62 q^{59} + 424 q^{60} + 10 q^{61} - 68 q^{62} + 2 q^{63} + 168 q^{64} + 182 q^{65} + 8 q^{66} - 74 q^{67} - 24 q^{68} - 40 q^{69} - 6 q^{70} + 24 q^{71} - 84 q^{73} - 48 q^{74} - 38 q^{75} + 24 q^{76} - 14 q^{77} + 100 q^{78} - 112 q^{79} - 92 q^{80} - 88 q^{81} + 66 q^{82} - 78 q^{83} - 140 q^{84} + 30 q^{85} - 50 q^{86} - 6 q^{87} + 24 q^{88} + 70 q^{89} + 24 q^{90} - 36 q^{91} + 54 q^{92} - 12 q^{93} - 140 q^{94} - 50 q^{95} - 196 q^{96} + 32 q^{97} - 10 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.cf.a 671.cf 61.k $400$ $5.358$ None \(0\) \(-4\) \(16\) \(14\) $\mathrm{SU}(2)[C_{30}]$

Decomposition of \(S_{2}^{\mathrm{old}}(671, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(671, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(61, [\chi])\)\(^{\oplus 2}\)