Properties

Label 43.9.h
Level $43$
Weight $9$
Character orbit 43.h
Rep. character $\chi_{43}(3,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $336$
Newform subspaces $1$
Sturm bound $33$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 43.h (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 1 \)
Sturm bound: \(33\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(43, [\chi])\).

Total New Old
Modular forms 360 360 0
Cusp forms 336 336 0
Eisenstein series 24 24 0

Trace form

\( 336q - 14q^{2} + 70q^{3} + 6460q^{4} - 11q^{5} - 1798q^{6} + 5010q^{7} + 5362q^{8} - 40176q^{9} + O(q^{10}) \) \( 336q - 14q^{2} + 70q^{3} + 6460q^{4} - 11q^{5} - 1798q^{6} + 5010q^{7} + 5362q^{8} - 40176q^{9} - 12505q^{10} - 31942q^{11} - 54796q^{12} - 75596q^{13} + 111780q^{14} + 4037q^{15} - 688224q^{16} - 5977q^{17} - 280532q^{18} - 552290q^{19} - 494171q^{20} + 141291q^{21} - 432782q^{22} - 619546q^{23} - 298136q^{24} - 2392669q^{25} - 113675q^{26} - 14q^{27} - 1143258q^{28} + 4198855q^{29} - 795576q^{30} + 3391610q^{31} + 3704176q^{32} + 469240q^{33} + 3670777q^{34} - 2602743q^{35} - 32236515q^{36} + 7009521q^{37} + 1762126q^{38} - 573251q^{39} - 41379997q^{40} - 11003050q^{41} + 7113655q^{43} + 64459560q^{44} + 11644332q^{45} - 14793057q^{46} + 9244886q^{47} - 34730249q^{48} + 82140290q^{49} - 80542767q^{50} - 7776902q^{51} - 98888784q^{52} + 39659528q^{53} + 139217042q^{54} + 96182224q^{55} - 59364207q^{56} - 94760066q^{57} + 149491596q^{58} - 74665213q^{59} + 188098449q^{60} + 55854238q^{61} - 52173383q^{62} + 40219829q^{63} + 13742518q^{64} + 87064978q^{65} - 64965481q^{66} + 210933441q^{67} - 248367043q^{68} + 405756759q^{69} - 362301191q^{70} - 34975301q^{71} - 125412979q^{72} - 216767388q^{73} + 53341380q^{74} + 436840145q^{75} - 29249062q^{76} - 59286141q^{77} + 204702644q^{78} + 71493313q^{79} - 737037738q^{80} - 235365082q^{81} - 806662220q^{82} + 254450510q^{83} - 979300857q^{84} + 50436244q^{86} + 696609678q^{87} + 65867942q^{88} + 949059334q^{89} + 1083992303q^{90} - 184351501q^{91} + 379980750q^{92} - 271490850q^{93} - 369651898q^{94} - 1349611517q^{95} - 1044343058q^{96} - 850069303q^{97} - 271546964q^{98} + 148520290q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(43, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
43.9.h.a \(336\) \(17.517\) None \(-14\) \(70\) \(-11\) \(5010\)