↑

Properties

Label 671.2.bj
Level $671$
Weight $2$
Character orbit 671.bj
Rep. character $\chi_{671}(21,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $240$
Newform subspaces $1$
Sturm bound $124$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 671 = 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 671.bj (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 671 \)
Character field: \(\Q(\zeta_{12})\)
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 256 256 0
Cusp forms 240 240 0
Eisenstein series 16 16 0

Trace form

\( 240 q - 12 q^{4} - 12 q^{5} - 240 q^{9} + O(q^{10}) \) \( 240 q - 12 q^{4} - 12 q^{5} - 240 q^{9} - 2 q^{11} + 8 q^{12} - 12 q^{14} + 8 q^{15} + 88 q^{16} - 80 q^{20} - 2 q^{22} + 40 q^{23} + 104 q^{25} + 44 q^{26} - 12 q^{31} + 14 q^{33} - 16 q^{34} - 24 q^{36} - 24 q^{37} - 8 q^{38} + 8 q^{42} - 38 q^{44} - 96 q^{45} + 12 q^{47} - 72 q^{48} - 120 q^{49} - 8 q^{53} + 16 q^{55} - 60 q^{56} + 104 q^{58} - 12 q^{59} - 6 q^{66} - 52 q^{67} + 100 q^{69} - 96 q^{70} - 36 q^{71} + 24 q^{75} + 10 q^{77} + 60 q^{78} - 60 q^{80} + 240 q^{81} - 124 q^{82} - 76 q^{86} + 32 q^{89} - 44 q^{91} - 196 q^{92} + 20 q^{93} + 36 q^{97} - 6 q^{99} + O(q^{100}) \)

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.bj.a 671.bj 671.aj $240$ $5.358$ None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{12}]$