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Properties

Label 539.2.z
Level $539$
Weight $2$
Character orbit 539.z
Rep. character $\chi_{539}(6,\cdot)$
Character field $\Q(\zeta_{70})$
Dimension $1296$
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.z (of order \(70\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{70})\)
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 1392 1392 0
Cusp forms 1296 1296 0
Eisenstein series 96 96 0

Trace form

\( 1296 q - 25 q^{2} - 21 q^{3} - 67 q^{4} - 21 q^{5} - 35 q^{6} - 25 q^{7} - 25 q^{8} - 65 q^{9} + O(q^{10}) \) \( 1296 q - 25 q^{2} - 21 q^{3} - 67 q^{4} - 21 q^{5} - 35 q^{6} - 25 q^{7} - 25 q^{8} - 65 q^{9} - 19 q^{11} - 56 q^{12} - 35 q^{13} - 8 q^{14} + 27 q^{15} + 49 q^{16} - 60 q^{18} + 35 q^{20} - 50 q^{22} - 26 q^{23} - 245 q^{24} - 41 q^{25} + 7 q^{26} - 84 q^{27} - 60 q^{28} - 45 q^{29} - 30 q^{30} - 28 q^{33} + 56 q^{34} - 75 q^{35} - 45 q^{36} - 11 q^{37} + 35 q^{38} - 25 q^{39} + 175 q^{40} - 35 q^{41} - 211 q^{42} - 108 q^{44} + 56 q^{45} - 5 q^{46} + 56 q^{47} + 13 q^{49} - 10 q^{50} + 75 q^{51} - 35 q^{52} - 123 q^{53} - 140 q^{55} + 186 q^{56} + 55 q^{57} + 133 q^{58} - 49 q^{59} + 237 q^{60} - 35 q^{61} + 35 q^{62} - 15 q^{63} + 53 q^{64} + 70 q^{66} - 144 q^{67} - 189 q^{69} - 63 q^{70} + 5 q^{71} + 35 q^{72} + 70 q^{73} - 125 q^{74} - 21 q^{75} - 37 q^{77} - 300 q^{78} - 30 q^{79} + 143 q^{81} - 21 q^{82} - 35 q^{83} + 35 q^{84} - 75 q^{85} - 146 q^{86} - 212 q^{88} - 112 q^{89} - 35 q^{90} - 103 q^{91} + 14 q^{92} + 37 q^{93} - 805 q^{94} - 15 q^{95} - 35 q^{96} + 340 q^{99} + O(q^{100}) \)

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.z.a 539.z 539.z $1296$ $4.304$ None \(-25\) \(-21\) \(-21\) \(-25\) $\mathrm{SU}(2)[C_{70}]$