Properties

Label 43.3.f
Level $43$
Weight $3$
Character orbit 43.f
Rep. character $\chi_{43}(2,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $42$
Newform subspaces $1$
Sturm bound $11$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 43.f (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 1 \)
Sturm bound: \(11\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(43, [\chi])\).

Total New Old
Modular forms 54 54 0
Cusp forms 42 42 0
Eisenstein series 12 12 0

Trace form

\( 42 q - 7 q^{2} - 7 q^{3} + 5 q^{4} - 7 q^{5} - 20 q^{6} + 21 q^{8} - 36 q^{9} + O(q^{10}) \) \( 42 q - 7 q^{2} - 7 q^{3} + 5 q^{4} - 7 q^{5} - 20 q^{6} + 21 q^{8} - 36 q^{9} - 5 q^{10} - 24 q^{11} - 35 q^{12} - 34 q^{13} + 69 q^{14} + 7 q^{15} - 39 q^{16} + 22 q^{17} - 70 q^{18} - 49 q^{19} + 133 q^{20} + 77 q^{22} + 42 q^{23} - 349 q^{24} + 10 q^{25} + 49 q^{26} - 7 q^{27} + 105 q^{28} + 63 q^{29} - 252 q^{30} - 152 q^{31} + 343 q^{32} + 329 q^{33} + 161 q^{34} + 58 q^{35} + 576 q^{36} - 289 q^{38} + 77 q^{39} - 101 q^{40} + 133 q^{41} - 79 q^{43} + 148 q^{44} + 84 q^{45} - 504 q^{46} + 6 q^{47} - 595 q^{48} - 302 q^{49} + 161 q^{51} - 267 q^{52} - 394 q^{53} - 227 q^{54} - 637 q^{55} + 355 q^{56} - 7 q^{57} + 165 q^{58} - 46 q^{59} - 657 q^{60} - 175 q^{61} - 91 q^{62} + 511 q^{63} + 725 q^{64} + 161 q^{65} - 227 q^{66} - 756 q^{67} - 586 q^{68} + 441 q^{69} + 1526 q^{70} + 266 q^{71} + 1078 q^{72} - 252 q^{73} + 204 q^{74} + 112 q^{75} + 994 q^{76} + 791 q^{77} + 94 q^{78} - 178 q^{79} - 428 q^{81} + 245 q^{82} + 238 q^{83} + 66 q^{84} + 365 q^{86} + 426 q^{87} - 119 q^{88} + 252 q^{89} - 926 q^{90} - 224 q^{91} - 764 q^{92} + 133 q^{94} + 11 q^{95} - 2602 q^{96} - 491 q^{97} - 553 q^{98} + 431 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(43, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
43.3.f.a 43.f 43.f $42$ $1.172$ None \(-7\) \(-7\) \(-7\) \(0\) $\mathrm{SU}(2)[C_{14}]$