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Properties

Label 143.4.n
Level $143$
Weight $4$
Character orbit 143.n
Rep. character $\chi_{143}(25,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $160$
Newform subspaces $1$
Sturm bound $56$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 143.n (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(56\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(143, [\chi])\).

Total New Old
Modular forms 176 176 0
Cusp forms 160 160 0
Eisenstein series 16 16 0

Trace form

\( 160 q - 6 q^{3} + 146 q^{4} - 426 q^{9} + O(q^{10}) \) \( 160 q - 6 q^{3} + 146 q^{4} - 426 q^{9} + 184 q^{10} + 84 q^{12} - 39 q^{13} - 158 q^{14} - 634 q^{16} - 116 q^{17} - 1026 q^{22} + 184 q^{23} + 506 q^{25} - 450 q^{26} - 210 q^{27} + 188 q^{29} - 1424 q^{30} + 1762 q^{35} + 1086 q^{36} - 418 q^{38} + 529 q^{39} - 1190 q^{40} + 1444 q^{42} + 4288 q^{43} - 2128 q^{48} + 902 q^{49} + 350 q^{51} - 1746 q^{52} - 2866 q^{53} + 486 q^{55} - 6436 q^{56} + 570 q^{61} + 1702 q^{62} + 5834 q^{64} + 810 q^{65} + 3954 q^{66} - 3112 q^{68} + 4656 q^{69} + 5140 q^{74} - 854 q^{75} - 144 q^{77} - 4904 q^{78} - 1730 q^{79} + 1622 q^{81} + 5578 q^{82} - 8556 q^{87} - 3538 q^{88} - 12996 q^{90} + 5315 q^{91} + 9394 q^{92} + 4646 q^{94} + 1922 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(143, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
143.4.n.a 143.n 143.n $160$ $8.437$ None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$