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Properties

Label 539.2.w
Level $539$
Weight $2$
Character orbit 539.w
Rep. character $\chi_{539}(10,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $648$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 539.w (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(539, [\chi])\).

Total New Old
Modular forms 696 696 0
Cusp forms 648 648 0
Eisenstein series 48 48 0

Trace form

\( 648 q - 22 q^{3} - 78 q^{4} - 28 q^{5} - 76 q^{9} + O(q^{10}) \) \( 648 q - 22 q^{3} - 78 q^{4} - 28 q^{5} - 76 q^{9} - 3 q^{11} - 10 q^{12} - 36 q^{14} - 28 q^{15} + 14 q^{16} + 28 q^{20} + 20 q^{22} + 30 q^{23} - 82 q^{25} - 18 q^{26} + 14 q^{27} - 48 q^{31} - 32 q^{33} - 56 q^{34} - 152 q^{36} - 28 q^{37} - 8 q^{38} - 100 q^{42} + 62 q^{44} + 240 q^{45} - 80 q^{47} - 156 q^{49} - 76 q^{53} - 21 q^{55} + 52 q^{56} - 210 q^{58} - 44 q^{59} - 392 q^{60} + 68 q^{64} + 126 q^{66} - 18 q^{67} - 196 q^{69} + 58 q^{70} - 80 q^{71} + 50 q^{75} + 15 q^{77} + 42 q^{78} - 72 q^{80} + 126 q^{81} - 82 q^{82} + 84 q^{86} + 203 q^{88} - 186 q^{89} + 258 q^{91} + 82 q^{92} - 82 q^{93} - 116 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(539, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
539.2.w.a 539.w 539.w $648$ $4.304$ None \(0\) \(-22\) \(-28\) \(0\) $\mathrm{SU}(2)[C_{42}]$