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Properties

Label 539.2.v
Level $539$
Weight $2$
Character orbit 539.v
Rep. character $\chi_{539}(15,\cdot)$
Character field $\Q(\zeta_{35})$
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.v (of order \(35\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{35})\)
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

\( 1296 q - 15 q^{2} - 15 q^{3} + 37 q^{4} - 19 q^{5} - 27 q^{6} - 19 q^{7} - 23 q^{8} + 35 q^{9} + O(q^{10}) \) \( 1296 q - 15 q^{2} - 15 q^{3} + 37 q^{4} - 19 q^{5} - 27 q^{6} - 19 q^{7} - 23 q^{8} + 35 q^{9} - 40 q^{10} - 19 q^{11} - 60 q^{12} - 19 q^{13} - 24 q^{14} - 57 q^{15} + 17 q^{16} - 26 q^{17} - 72 q^{18} + 4 q^{19} + 13 q^{20} - 68 q^{21} + 30 q^{22} - 26 q^{23} - 133 q^{24} + 3 q^{25} + 13 q^{26} - 72 q^{27} + 52 q^{28} - 3 q^{29} - 46 q^{30} - 24 q^{31} - 64 q^{32} - 12 q^{33} - 120 q^{34} + 15 q^{35} + 31 q^{36} - 35 q^{37} + 5 q^{38} - 47 q^{39} - 121 q^{40} + 11 q^{41} + 119 q^{42} - 60 q^{43} + 8 q^{44} + 108 q^{45} - 11 q^{46} - 54 q^{47} - 10 q^{48} + 41 q^{49} - 46 q^{50} - 99 q^{51} - 75 q^{52} + 45 q^{53} - 78 q^{54} + 70 q^{55} - 234 q^{56} + 43 q^{57} - 123 q^{58} - 35 q^{59} - 107 q^{60} - 21 q^{61} - 109 q^{62} - 11 q^{63} + 109 q^{64} - 60 q^{65} + 44 q^{66} - 16 q^{67} + 120 q^{68} + 129 q^{69} - 43 q^{70} + 61 q^{71} + 37 q^{72} - 52 q^{73} + 61 q^{74} - 35 q^{75} + q^{77} - 340 q^{78} - 66 q^{79} + 78 q^{80} - q^{81} - 71 q^{82} - 7 q^{83} + 121 q^{84} - 45 q^{85} - 80 q^{86} + 144 q^{87} - 180 q^{88} + 72 q^{89} + 103 q^{90} - 151 q^{91} + 104 q^{92} - 31 q^{93} - 429 q^{94} + 89 q^{95} + 207 q^{96} - 344 q^{97} + 190 q^{98} - 520 q^{99} + O(q^{100}) \)

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.v.a 539.v 539.v $1296$ $4.304$ None \(-15\) \(-15\) \(-19\) \(-19\) $\mathrm{SU}(2)[C_{35}]$