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Properties

Label 671.2.cb
Level $671$
Weight $2$
Character orbit 671.cb
Rep. character $\chi_{671}(50,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $480$
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.cb (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 671 \)
Character field: \(\Q(\zeta_{20})\)
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 512 512 0
Cusp forms 480 480 0
Eisenstein series 32 32 0

Trace form

\( 480 q - 10 q^{2} - 10 q^{6} - 10 q^{8} + 100 q^{9} + O(q^{10}) \) \( 480 q - 10 q^{2} - 10 q^{6} - 10 q^{8} + 100 q^{9} - 6 q^{11} - 56 q^{12} - 20 q^{13} - 36 q^{15} + 48 q^{16} - 10 q^{18} - 76 q^{20} - 16 q^{22} + 4 q^{23} - 30 q^{24} + 84 q^{25} - 50 q^{26} - 10 q^{28} - 20 q^{29} + 10 q^{31} + 42 q^{33} - 32 q^{34} - 18 q^{37} + 20 q^{38} - 50 q^{40} - 36 q^{42} + 40 q^{44} - 20 q^{47} - 100 q^{50} - 50 q^{51} - 6 q^{53} + 20 q^{55} - 16 q^{56} + 220 q^{57} - 4 q^{58} - 10 q^{59} - 40 q^{61} - 360 q^{62} + 120 q^{63} - 64 q^{67} - 140 q^{68} + 32 q^{69} - 224 q^{70} + 42 q^{71} - 220 q^{72} - 20 q^{73} + 80 q^{74} - 116 q^{77} + 96 q^{78} - 10 q^{79} - 92 q^{81} - 50 q^{82} + 40 q^{83} - 240 q^{84} - 100 q^{85} + 120 q^{86} - 64 q^{89} + 80 q^{90} - 6 q^{91} + 146 q^{92} - 54 q^{93} + 130 q^{94} - 20 q^{95} + 40 q^{96} + 66 q^{99} + O(q^{100}) \)

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.cb.a 671.cb 671.bb $480$ $5.358$ None \(-10\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$