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Properties

Label 671.2.j
Level $671$
Weight $2$
Character orbit 671.j
Rep. character $\chi_{671}(245,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $240$
Newform subspaces $3$
Sturm bound $124$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 671 = 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 671.j (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 3 \)
Sturm bound: \(124\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 256 240 16
Cusp forms 240 240 0
Eisenstein series 16 0 16

Trace form

\( 240 q - 6 q^{2} - 6 q^{3} - 64 q^{4} - 2 q^{5} + 2 q^{6} - 12 q^{7} + 2 q^{8} - 62 q^{9} + O(q^{10}) \) \( 240 q - 6 q^{2} - 6 q^{3} - 64 q^{4} - 2 q^{5} + 2 q^{6} - 12 q^{7} + 2 q^{8} - 62 q^{9} + 8 q^{10} - 6 q^{11} + 20 q^{12} - 2 q^{13} + 10 q^{14} + 6 q^{15} - 76 q^{16} - 24 q^{17} + 14 q^{18} + 2 q^{19} + 14 q^{20} + 8 q^{21} + 8 q^{22} - 4 q^{23} + 42 q^{24} - 54 q^{25} + 38 q^{26} + 34 q^{28} - 36 q^{29} + 12 q^{30} - 14 q^{31} + 28 q^{32} - 26 q^{33} + 12 q^{34} - 36 q^{35} - 98 q^{36} - 18 q^{37} - 16 q^{38} + 24 q^{39} + 46 q^{40} - 8 q^{41} - 16 q^{42} + 44 q^{43} + 20 q^{44} + 88 q^{45} + 6 q^{46} + 34 q^{47} - 84 q^{48} - 56 q^{49} - 20 q^{50} + 2 q^{51} - 8 q^{52} + 42 q^{53} - 56 q^{54} - 20 q^{55} + 60 q^{56} - 46 q^{57} + 22 q^{58} - 2 q^{59} + 48 q^{60} - 6 q^{61} - 32 q^{62} - 72 q^{63} - 72 q^{64} - 32 q^{65} - 52 q^{66} - 64 q^{67} - 96 q^{68} - 44 q^{69} + 46 q^{70} - 46 q^{71} + 32 q^{72} - 12 q^{73} + 44 q^{74} + 70 q^{75} - 136 q^{76} - 46 q^{77} - 8 q^{78} + 10 q^{79} - 104 q^{80} + 10 q^{81} + 70 q^{82} + 38 q^{83} - 8 q^{84} + 16 q^{85} + 56 q^{86} + 104 q^{87} - 76 q^{88} - 24 q^{89} - 128 q^{90} + 82 q^{91} - 22 q^{92} + 38 q^{93} - 18 q^{94} - 16 q^{95} - 36 q^{96} + 20 q^{97} - 8 q^{98} + 34 q^{99} + O(q^{100}) \)

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.j.a 671.j 11.c $4$ $5.358$ \(\Q(\zeta_{10})\) None \(2\) \(6\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(2-2\zeta_{10}+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+\cdots\)
671.2.j.b 671.j 11.c $108$ $5.358$ None \(-3\) \(5\) \(7\) \(-6\) $\mathrm{SU}(2)[C_{5}]$
671.2.j.c 671.j 11.c $128$ $5.358$ None \(-5\) \(-17\) \(-8\) \(-3\) $\mathrm{SU}(2)[C_{5}]$