## Defining parameters

 Level: $$N$$ = $$43$$ Weight: $$k$$ = $$8$$ Nonzero newspaces: $$4$$ Newform subspaces: $$5$$ Sturm bound: $$1232$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(\Gamma_1(43))$$.

Total New Old
Modular forms 560 558 2
Cusp forms 518 518 0
Eisenstein series 42 40 2

## Trace form

 $$518q - 21q^{2} - 21q^{3} - 21q^{4} - 21q^{5} - 21q^{6} - 21q^{7} - 21q^{8} - 21q^{9} + O(q^{10})$$ $$518q - 21q^{2} - 21q^{3} - 21q^{4} - 21q^{5} - 21q^{6} - 21q^{7} - 21q^{8} - 21q^{9} - 21q^{10} - 21q^{11} - 21q^{12} - 21q^{13} - 21q^{14} - 21q^{15} - 21q^{16} - 21q^{17} - 21q^{18} - 21q^{19} - 21q^{20} - 21q^{21} - 21q^{22} - 21q^{23} - 21q^{24} - 21q^{25} - 21q^{26} - 21q^{27} - 21q^{28} - 21q^{29} - 21q^{30} - 1190728q^{31} + 771435q^{32} + 2427873q^{33} + 1863267q^{34} - 619479q^{35} - 5225493q^{36} - 2297295q^{37} - 3293493q^{38} - 379722q^{39} + 4827627q^{40} + 1239798q^{41} + 6223350q^{42} + 7205814q^{43} + 3542742q^{44} - 76566q^{45} - 4285365q^{46} - 2021838q^{47} - 20611605q^{48} - 5764822q^{49} - 6144117q^{50} + 427497q^{51} + 13239275q^{52} + 9149553q^{53} + 15798867q^{54} + 5312601q^{55} - 11985813q^{56} - 8144220q^{57} - 21q^{58} - 21q^{59} - 21q^{60} - 21q^{61} - 21q^{62} - 21q^{63} - 21q^{64} - 21q^{65} - 21q^{66} - 21q^{67} - 21q^{68} - 48370707q^{69} + 4714479q^{70} + 22589217q^{71} + 120082809q^{72} + 15431493q^{73} + 11062758q^{74} - 29859396q^{75} - 59743908q^{76} - 63678783q^{77} - 135245040q^{78} - 32739273q^{79} - 35889021q^{80} + 196371q^{81} + 46358109q^{82} + 34694247q^{83} + 208194777q^{84} + 51586458q^{85} + 99474291q^{86} + 101585988q^{87} + 50096067q^{88} + 4567647q^{89} - 83301771q^{90} - 41336505q^{91} - 151812591q^{92} - 146893005q^{93} - 153129165q^{94} - 67840521q^{95} - 150139374q^{96} - 18361623q^{97} + 54510078q^{98} + 136813908q^{99} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(\Gamma_1(43))$$

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
43.8.a $$\chi_{43}(1, \cdot)$$ 43.8.a.a 11 1
43.8.a.b 13
43.8.c $$\chi_{43}(6, \cdot)$$ 43.8.c.a 50 2
43.8.e $$\chi_{43}(4, \cdot)$$ 43.8.e.a 144 6
43.8.g $$\chi_{43}(9, \cdot)$$ 43.8.g.a 300 12