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Properties

Label 671.2.bc
Level $671$
Weight $2$
Character orbit 671.bc
Rep. character $\chi_{671}(210,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $208$
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.bc (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 61 \)
Character field: \(\Q(\zeta_{10})\)
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 256 208 48
Cusp forms 240 208 32
Eisenstein series 16 0 16

Trace form

\( 208 q - 4 q^{3} + 46 q^{4} - 10 q^{5} + 20 q^{6} - 30 q^{7} - 64 q^{9} + O(q^{10}) \) \( 208 q - 4 q^{3} + 46 q^{4} - 10 q^{5} + 20 q^{6} - 30 q^{7} - 64 q^{9} - 18 q^{12} + 24 q^{13} + 4 q^{14} + 32 q^{15} - 90 q^{16} + 10 q^{18} - 4 q^{19} + 4 q^{20} + 2 q^{22} - 10 q^{23} - 30 q^{24} - 50 q^{25} - 50 q^{26} - 16 q^{27} - 100 q^{28} + 20 q^{30} + 10 q^{31} + 44 q^{34} + 22 q^{36} + 10 q^{38} - 20 q^{39} + 4 q^{41} + 28 q^{42} - 40 q^{43} + 2 q^{45} - 76 q^{46} - 64 q^{47} + 72 q^{48} + 136 q^{49} - 130 q^{51} + 4 q^{52} + 80 q^{53} + 60 q^{54} - 46 q^{56} - 64 q^{57} + 60 q^{58} - 20 q^{59} - 64 q^{60} + 112 q^{61} + 68 q^{62} + 110 q^{63} + 38 q^{64} - 56 q^{65} - 8 q^{66} + 20 q^{67} - 120 q^{68} - 20 q^{69} + 66 q^{70} - 30 q^{71} - 52 q^{73} + 100 q^{75} + 36 q^{76} + 14 q^{77} - 40 q^{78} - 90 q^{79} + 62 q^{80} - 16 q^{81} - 18 q^{83} + 140 q^{84} - 30 q^{85} - 28 q^{86} - 42 q^{88} - 70 q^{89} - 60 q^{91} - 120 q^{92} - 40 q^{94} - 22 q^{95} - 80 q^{96} - 80 q^{97} + 10 q^{98} + O(q^{100}) \)

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.bc.a 671.bc 61.g $208$ $5.358$ None \(0\) \(-4\) \(-10\) \(-30\) $\mathrm{SU}(2)[C_{10}]$

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

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