## Defining parameters

 Level: $$N$$ = $$43$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$4$$ Newform subspaces: $$5$$ Sturm bound: $$924$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(43))$$.

Total New Old
Modular forms 406 404 2
Cusp forms 364 364 0
Eisenstein series 42 40 2

## Trace form

 $$364q - 21q^{2} - 21q^{3} - 21q^{4} - 21q^{5} - 21q^{6} - 21q^{7} - 21q^{8} - 21q^{9} + O(q^{10})$$ $$364q - 21q^{2} - 21q^{3} - 21q^{4} - 21q^{5} - 21q^{6} - 21q^{7} - 21q^{8} - 21q^{9} - 21q^{10} - 21q^{11} - 21q^{12} - 21q^{13} - 21q^{14} - 21q^{15} - 21q^{16} - 21q^{17} - 21q^{18} - 21q^{19} - 21q^{20} - 21q^{21} - 21q^{22} - 21q^{23} - 21q^{24} - 21q^{25} - 21q^{26} - 21q^{27} - 21q^{28} - 21q^{29} - 21q^{30} - 30464q^{31} - 59829q^{32} + 15477q^{33} + 80367q^{34} + 63777q^{35} + 145131q^{36} + 32781q^{37} + 10395q^{38} - 26922q^{39} - 190869q^{40} - 32760q^{41} - 148218q^{42} - 180726q^{43} - 119658q^{44} - 93576q^{45} - 13797q^{46} + 14490q^{47} + 266091q^{48} + 117628q^{49} + 252315q^{50} + 135681q^{51} + 324331q^{52} + 75117q^{53} - 20433q^{54} - 155463q^{55} - 362229q^{56} - 107814q^{57} - 21q^{58} - 21q^{59} - 21q^{60} - 21q^{61} - 21q^{62} - 21q^{63} - 21q^{64} - 21q^{65} - 21q^{66} - 21q^{67} - 21q^{68} - 726831q^{69} - 695121q^{70} - 71799q^{71} + 579369q^{72} + 229761q^{73} + 991494q^{74} + 1010604q^{75} + 901236q^{76} + 599613q^{77} + 813792q^{78} + 83559q^{79} - 172221q^{80} - 492093q^{81} - 964131q^{82} - 496377q^{83} - 2572983q^{84} - 606942q^{85} - 1199373q^{86} - 1373652q^{87} - 916125q^{88} - 328041q^{89} - 746571q^{90} + 21063q^{91} + 558369q^{92} + 858627q^{93} + 1250739q^{94} + 795879q^{95} + 3000522q^{96} + 1481613q^{97} + 1693566q^{98} + 1469244q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(43))$$

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
43.6.a $$\chi_{43}(1, \cdot)$$ 43.6.a.a 8 1
43.6.a.b 10
43.6.c $$\chi_{43}(6, \cdot)$$ 43.6.c.a 34 2
43.6.e $$\chi_{43}(4, \cdot)$$ 43.6.e.a 108 6
43.6.g $$\chi_{43}(9, \cdot)$$ 43.6.g.a 204 12