Properties

Label 671.2.e
Level $671$
Weight $2$
Character orbit 671.e
Rep. character $\chi_{671}(474,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $104$
Newform subspaces $2$
Sturm bound $124$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 671 = 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 671.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 61 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(124\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 128 104 24
Cusp forms 120 104 16
Eisenstein series 8 0 8

Trace form

\( 104 q - 2 q^{2} + 4 q^{3} - 60 q^{4} - 4 q^{6} - 2 q^{7} + 12 q^{8} + 100 q^{9} + O(q^{10}) \) \( 104 q - 2 q^{2} + 4 q^{3} - 60 q^{4} - 4 q^{6} - 2 q^{7} + 12 q^{8} + 100 q^{9} - 2 q^{10} + 6 q^{12} - 8 q^{13} - 6 q^{14} - 24 q^{15} - 76 q^{16} - 16 q^{17} + 8 q^{18} + 4 q^{19} + 4 q^{20} + 8 q^{21} - 2 q^{22} - 8 q^{23} + 4 q^{24} - 40 q^{25} - 30 q^{26} + 16 q^{27} + 40 q^{28} + 20 q^{29} + 32 q^{30} - 12 q^{31} - 4 q^{32} + 16 q^{34} + 8 q^{35} - 56 q^{36} - 32 q^{37} - 40 q^{38} + 6 q^{39} - 30 q^{40} - 36 q^{41} - 8 q^{42} - 4 q^{43} + 20 q^{46} - 16 q^{47} + 12 q^{48} - 106 q^{49} + 48 q^{50} + 30 q^{51} + 12 q^{52} - 36 q^{53} - 48 q^{54} + 60 q^{57} + 8 q^{58} - 6 q^{59} + 80 q^{60} + 6 q^{61} - 68 q^{62} - 34 q^{63} + 216 q^{64} + 70 q^{65} - 8 q^{66} + 30 q^{67} - 4 q^{68} - 40 q^{69} + 44 q^{70} - 12 q^{71} + 52 q^{72} + 50 q^{73} - 34 q^{74} - 12 q^{75} + 16 q^{76} - 12 q^{77} - 12 q^{78} + 22 q^{79} - 8 q^{80} - 40 q^{81} + 28 q^{82} + 10 q^{83} - 84 q^{84} - 160 q^{85} + 26 q^{86} - 18 q^{87} - 12 q^{88} - 120 q^{89} + 10 q^{90} - 4 q^{91} - 38 q^{92} - 56 q^{93} - 52 q^{94} + 84 q^{95} - 48 q^{96} - 38 q^{97} + 56 q^{98} + O(q^{100}) \)

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.e.a 671.e 61.c $52$ $5.358$ None \(-2\) \(2\) \(0\) \(-7\) $\mathrm{SU}(2)[C_{3}]$
671.2.e.b 671.e 61.c $52$ $5.358$ None \(0\) \(2\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$

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

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