Properties

Label 539.2.bc
Level $539$
Weight $2$
Character orbit 539.bc
Rep. character $\chi_{539}(4,\cdot)$
Character field $\Q(\zeta_{105})$
Dimension $2592$
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.bc (of order \(105\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{105})\)
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 2784 2784 0
Cusp forms 2592 2592 0
Eisenstein series 192 192 0

Trace form

\( 2592 q - 39 q^{2} - 39 q^{3} - 91 q^{4} - 41 q^{5} - 30 q^{6} - 35 q^{7} - 22 q^{8} - 89 q^{9} + O(q^{10}) \) \( 2592 q - 39 q^{2} - 39 q^{3} - 91 q^{4} - 41 q^{5} - 30 q^{6} - 35 q^{7} - 22 q^{8} - 89 q^{9} - 116 q^{10} - 62 q^{11} - 96 q^{12} - 38 q^{13} - 42 q^{14} + 12 q^{15} - 95 q^{16} - 10 q^{17} - 24 q^{18} - 70 q^{19} - 58 q^{20} - 94 q^{21} - 90 q^{22} - 160 q^{23} + 91 q^{24} - 99 q^{25} - 55 q^{26} + 27 q^{27} - 130 q^{28} - 42 q^{29} - 50 q^{30} - 12 q^{31} - 104 q^{32} - 30 q^{33} - 72 q^{34} - 51 q^{35} + 56 q^{36} - 49 q^{37} - 17 q^{38} - 55 q^{39} - 299 q^{40} - 104 q^{41} - 38 q^{42} - 60 q^{43} + 37 q^{44} - 138 q^{45} - 55 q^{46} + 30 q^{47} - 230 q^{48} + 91 q^{49} - 62 q^{50} - 189 q^{51} - 39 q^{52} - 93 q^{53} - 198 q^{54} - 67 q^{55} + 312 q^{56} - 88 q^{57} + 201 q^{58} - 73 q^{59} + 407 q^{60} - 60 q^{61} - 74 q^{62} - 64 q^{63} - 34 q^{64} - 114 q^{65} - 107 q^{66} - 8 q^{67} - 168 q^{68} - 84 q^{69} - 17 q^{70} - 106 q^{71} - 55 q^{72} - 5 q^{73} - 31 q^{74} - 31 q^{75} - 24 q^{76} - 109 q^{77} + 148 q^{78} - 33 q^{79} - 18 q^{80} - 215 q^{81} - 55 q^{82} - 56 q^{83} + 293 q^{84} + 86 q^{86} + 18 q^{87} + 252 q^{88} - 78 q^{89} - 136 q^{90} + 34 q^{91} - 86 q^{92} - 92 q^{93} + 375 q^{94} + 106 q^{95} - 99 q^{96} + 236 q^{97} + 104 q^{98} + 376 q^{99} + O(q^{100}) \)

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.bc.a 539.bc 539.ac $2592$ $4.304$ None \(-39\) \(-39\) \(-41\) \(-35\) $\mathrm{SU}(2)[C_{105}]$