Properties

Label 143.4.w
Level $143$
Weight $4$
Character orbit 143.w
Rep. character $\chi_{143}(2,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $640$
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.w (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{60})\)
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 704 704 0
Cusp forms 640 640 0
Eisenstein series 64 64 0

Trace form

\( 640 q - 20 q^{2} - 6 q^{3} - 18 q^{4} - 12 q^{5} - 20 q^{6} - 20 q^{7} - 20 q^{8} + 642 q^{9} + O(q^{10}) \) \( 640 q - 20 q^{2} - 6 q^{3} - 18 q^{4} - 12 q^{5} - 20 q^{6} - 20 q^{7} - 20 q^{8} + 642 q^{9} - 140 q^{11} - 60 q^{13} + 24 q^{14} - 144 q^{15} - 1310 q^{16} - 30 q^{17} - 20 q^{18} - 20 q^{19} + 942 q^{20} - 38 q^{22} - 960 q^{23} - 760 q^{24} - 516 q^{26} - 864 q^{27} - 20 q^{28} - 710 q^{29} - 30 q^{30} + 260 q^{31} - 1354 q^{33} + 1508 q^{34} - 1310 q^{35} + 3540 q^{36} - 348 q^{37} - 1860 q^{39} + 1240 q^{40} + 2200 q^{41} - 1174 q^{42} - 124 q^{44} - 936 q^{45} + 1340 q^{46} - 2564 q^{47} - 490 q^{48} - 18 q^{49} + 1230 q^{50} + 1430 q^{52} - 3912 q^{53} - 692 q^{55} + 1296 q^{56} - 20 q^{57} - 2556 q^{58} - 668 q^{59} + 6556 q^{60} + 470 q^{61} - 30 q^{62} - 5010 q^{63} + 24980 q^{66} - 5384 q^{67} - 250 q^{68} - 18 q^{69} + 1262 q^{70} + 1296 q^{71} + 11020 q^{72} - 1940 q^{73} - 10 q^{74} - 8862 q^{75} + 10476 q^{78} - 9400 q^{79} + 12112 q^{80} + 4294 q^{81} - 9414 q^{82} - 4500 q^{83} + 920 q^{84} + 140 q^{85} - 4708 q^{86} - 10182 q^{88} - 2208 q^{89} + 9988 q^{91} - 9440 q^{92} + 13400 q^{93} - 3210 q^{94} - 9330 q^{95} - 6270 q^{96} + 4872 q^{97} + 6876 q^{99} + O(q^{100}) \)

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.w.a 143.w 143.w $640$ $8.437$ None \(-20\) \(-6\) \(-12\) \(-20\) $\mathrm{SU}(2)[C_{60}]$