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Properties

Label 671.2.bw
Level $671$
Weight $2$
Character orbit 671.bw
Rep. character $\chi_{671}(98,\cdot)$
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.bw (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

\( 480 q - 20 q^{3} - 20 q^{4} - 20 q^{5} + 100 q^{9} + O(q^{10}) \) \( 480 q - 20 q^{3} - 20 q^{4} - 20 q^{5} + 100 q^{9} - 6 q^{11} - 36 q^{12} - 36 q^{15} + 128 q^{16} + 4 q^{20} - 6 q^{22} - 96 q^{23} + 84 q^{25} - 20 q^{26} - 80 q^{27} - 40 q^{31} - 8 q^{33} - 12 q^{34} - 20 q^{36} - 8 q^{37} - 20 q^{38} + 24 q^{42} - 30 q^{44} + 80 q^{45} - 20 q^{49} - 16 q^{53} - 20 q^{55} - 36 q^{56} - 4 q^{58} - 20 q^{59} - 20 q^{64} - 130 q^{66} - 124 q^{67} - 8 q^{69} - 64 q^{70} + 72 q^{71} + 64 q^{77} + 16 q^{78} - 320 q^{80} - 92 q^{81} - 60 q^{82} - 20 q^{86} - 170 q^{88} - 4 q^{89} + 44 q^{91} + 216 q^{92} - 4 q^{93} - 20 q^{97} - 154 q^{99} + O(q^{100}) \)

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