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Properties

Label 143.2.s
Level $143$
Weight $2$
Character orbit 143.s
Rep. character $\chi_{143}(8,\cdot)$
Character field $\Q(\zeta_{20})$
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.s (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{20})\)
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

\( 96 q - 10 q^{2} - 12 q^{3} - 6 q^{5} - 10 q^{6} - 10 q^{7} - 10 q^{8} - 28 q^{9} + O(q^{10}) \) \( 96 q - 10 q^{2} - 12 q^{3} - 6 q^{5} - 10 q^{6} - 10 q^{7} - 10 q^{8} - 28 q^{9} + 8 q^{11} - 20 q^{13} + 12 q^{14} + 10 q^{15} + 24 q^{16} - 10 q^{18} - 10 q^{19} + 4 q^{20} - 32 q^{22} - 50 q^{24} - 34 q^{26} - 12 q^{27} - 10 q^{28} + 18 q^{31} - 48 q^{33} + 44 q^{34} + 80 q^{35} - 18 q^{37} - 90 q^{39} - 100 q^{40} + 50 q^{41} - 56 q^{42} - 14 q^{44} + 60 q^{45} + 50 q^{46} + 28 q^{47} + 152 q^{48} - 60 q^{50} - 60 q^{52} - 24 q^{53} + 28 q^{55} - 10 q^{57} + 14 q^{58} + 4 q^{59} + 32 q^{60} + 20 q^{61} - 60 q^{63} + 116 q^{66} - 100 q^{67} - 80 q^{68} + 26 q^{71} + 170 q^{72} - 40 q^{73} - 20 q^{74} + 196 q^{78} + 60 q^{79} - 82 q^{80} - 68 q^{81} - 110 q^{83} + 220 q^{84} + 30 q^{85} - 22 q^{86} + 48 q^{89} + 38 q^{91} + 48 q^{92} + 60 q^{93} + 160 q^{94} - 160 q^{96} - 40 q^{97} + 70 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.s.a 143.s 143.s $96$ $1.142$ None \(-10\) \(-12\) \(-6\) \(-10\) $\mathrm{SU}(2)[C_{20}]$