Properties

Label 143.2.u
Level $143$
Weight $2$
Character orbit 143.u
Rep. character $\chi_{143}(4,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $96$
Newform subspaces $1$
Sturm bound $28$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 143.u (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(28\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(143, [\chi])\).

Total New Old
Modular forms 128 128 0
Cusp forms 96 96 0
Eisenstein series 32 32 0

Trace form

\( 96 q - 9 q^{2} - 3 q^{3} - 13 q^{4} - 9 q^{6} - 9 q^{7} + 11 q^{9} + O(q^{10}) \) \( 96 q - 9 q^{2} - 3 q^{3} - 13 q^{4} - 9 q^{6} - 9 q^{7} + 11 q^{9} + 12 q^{10} - 30 q^{11} - 52 q^{12} + 5 q^{13} - 16 q^{14} + 3 q^{15} + 7 q^{16} - 15 q^{17} + 3 q^{19} - 21 q^{20} + 23 q^{22} - 18 q^{23} + 3 q^{24} + 8 q^{25} - 6 q^{26} - 36 q^{27} - 33 q^{28} + 28 q^{29} + 27 q^{30} - 48 q^{32} - 15 q^{33} - 14 q^{35} + 16 q^{36} - 9 q^{37} - 22 q^{38} - 5 q^{39} + 24 q^{40} - 27 q^{41} + 47 q^{42} + 56 q^{43} - 24 q^{45} - 45 q^{46} - q^{48} + 27 q^{49} + 18 q^{50} - 31 q^{52} + 66 q^{53} + 6 q^{54} + 7 q^{55} + 42 q^{56} - 123 q^{58} - 36 q^{59} + 9 q^{61} - 27 q^{62} + 60 q^{63} + 60 q^{64} - 34 q^{65} + 146 q^{66} - 48 q^{67} + 60 q^{68} - 31 q^{69} - 153 q^{71} + 51 q^{72} - 17 q^{74} - 63 q^{75} + 246 q^{76} + 24 q^{77} - 52 q^{79} + 69 q^{80} + 9 q^{81} - 29 q^{82} + 72 q^{84} + 21 q^{85} - 142 q^{87} - 121 q^{88} + 54 q^{89} + 46 q^{90} + 67 q^{91} + 6 q^{92} + 36 q^{93} - 43 q^{94} - 95 q^{95} + 108 q^{97} - 6 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(143, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
143.2.u.a 143.u 143.u $96$ $1.142$ None \(-9\) \(-3\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{30}]$