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Properties

Label 539.2.p
Level $539$
Weight $2$
Character orbit 539.p
Rep. character $\chi_{539}(76,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $324$
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.p (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{14})\)
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 348 348 0
Cusp forms 324 324 0
Eisenstein series 24 24 0

Trace form

\( 324 q - 14 q^{3} + 42 q^{4} - 14 q^{5} + 40 q^{9} + O(q^{10}) \) \( 324 q - 14 q^{3} + 42 q^{4} - 14 q^{5} + 40 q^{9} - 6 q^{11} - 14 q^{12} - 12 q^{14} - 2 q^{15} - 74 q^{16} - 70 q^{20} - 35 q^{22} - 24 q^{23} + 16 q^{25} - 42 q^{26} - 56 q^{27} - 7 q^{33} + 14 q^{34} - 10 q^{36} - 14 q^{37} - 70 q^{38} + 106 q^{42} + 43 q^{44} - 126 q^{45} + 14 q^{47} - 48 q^{49} + 58 q^{53} + 105 q^{55} + 74 q^{56} + 42 q^{58} + 14 q^{59} + 98 q^{60} + 22 q^{64} - 105 q^{66} - 36 q^{67} + 154 q^{69} - 22 q^{70} + 50 q^{71} - 14 q^{75} + 12 q^{77} + 12 q^{81} - 14 q^{82} - 84 q^{86} + 37 q^{88} + 42 q^{89} - 282 q^{91} - 154 q^{92} - 32 q^{93} + 80 q^{99} + O(q^{100}) \)

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.p.a 539.p 539.p $324$ $4.304$ None \(0\) \(-14\) \(-14\) \(0\) $\mathrm{SU}(2)[C_{14}]$