Properties

Label 89.2.g
Level $89$
Weight $2$
Character orbit 89.g
Rep. character $\chi_{89}(5,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $140$
Newform subspaces $1$
Sturm bound $15$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 89 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 89.g (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 89 \)
Character field: \(\Q(\zeta_{44})\)
Newform subspaces: \( 1 \)
Sturm bound: \(15\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(89, [\chi])\).

Total New Old
Modular forms 180 180 0
Cusp forms 140 140 0
Eisenstein series 40 40 0

Trace form

\( 140 q - 20 q^{2} - 20 q^{3} - 32 q^{4} - 22 q^{5} - 14 q^{6} - 20 q^{7} - 16 q^{8} + O(q^{10}) \) \( 140 q - 20 q^{2} - 20 q^{3} - 32 q^{4} - 22 q^{5} - 14 q^{6} - 20 q^{7} - 16 q^{8} - 22 q^{10} - 18 q^{11} + 6 q^{12} - 18 q^{13} + 76 q^{14} - 36 q^{15} - 40 q^{16} - 22 q^{17} - 22 q^{18} - 12 q^{19} - 22 q^{20} - 22 q^{21} + 66 q^{22} - 8 q^{23} - 8 q^{24} - 16 q^{25} + 6 q^{26} + 40 q^{27} - 4 q^{28} - 38 q^{29} + 104 q^{30} - 26 q^{31} - 8 q^{32} - 16 q^{33} + 20 q^{35} - 22 q^{36} - 22 q^{38} - 54 q^{39} + 88 q^{40} - 34 q^{41} - 22 q^{42} + 126 q^{43} + 2 q^{44} - 18 q^{45} - 32 q^{46} - 22 q^{47} + 220 q^{48} - 22 q^{49} - 36 q^{50} + 20 q^{51} - 18 q^{52} + 66 q^{53} - 74 q^{54} + 100 q^{56} + 14 q^{57} - 46 q^{58} + 48 q^{59} - 74 q^{60} + 62 q^{61} - 8 q^{62} - 66 q^{63} + 184 q^{64} + 20 q^{65} + 112 q^{66} - 46 q^{67} + 22 q^{68} + 242 q^{69} + 16 q^{70} - 22 q^{71} + 154 q^{72} - 24 q^{73} + 32 q^{74} - 98 q^{75} - 90 q^{76} + 90 q^{77} - 218 q^{78} - 66 q^{79} - 110 q^{80} - 26 q^{81} + 90 q^{82} - 106 q^{83} - 330 q^{84} + 12 q^{85} - 114 q^{86} - 42 q^{87} - 296 q^{88} - 102 q^{89} - 12 q^{90} - 58 q^{91} - 146 q^{92} + 52 q^{93} - 110 q^{94} + 114 q^{95} - 374 q^{96} - 40 q^{97} + 88 q^{98} - 132 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(89, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
89.2.g.a 89.g 89.g $140$ $0.711$ None \(-20\) \(-20\) \(-22\) \(-20\) $\mathrm{SU}(2)[C_{44}]$