## Defining parameters

 Level: $$N$$ = $$43$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$4$$ Newform subspaces: $$5$$ Sturm bound: $$616$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(43))$$.

Total New Old
Modular forms 252 250 2
Cusp forms 210 210 0
Eisenstein series 42 40 2

## Trace form

 $$210q - 21q^{2} - 21q^{3} - 21q^{4} - 21q^{5} - 21q^{6} - 21q^{7} - 21q^{8} - 21q^{9} + O(q^{10})$$ $$210q - 21q^{2} - 21q^{3} - 21q^{4} - 21q^{5} - 21q^{6} - 21q^{7} - 21q^{8} - 21q^{9} - 21q^{10} - 21q^{11} - 21q^{12} - 21q^{13} - 21q^{14} - 21q^{15} - 21q^{16} - 21q^{17} - 21q^{18} - 21q^{19} - 21q^{20} - 21q^{21} - 21q^{22} - 21q^{23} - 21q^{24} - 21q^{25} - 21q^{26} - 21q^{27} - 21q^{28} - 21q^{29} - 21q^{30} - 651q^{31} - 2877q^{32} - 2037q^{33} - 1911q^{34} - 609q^{35} - 21q^{36} + 483q^{37} + 1827q^{38} + 1449q^{39} + 6027q^{40} + 819q^{41} + 3486q^{42} + 4389q^{43} + 3318q^{44} + 3759q^{45} + 2499q^{46} + 441q^{47} + 1995q^{48} - 21q^{49} - 1197q^{50} - 1281q^{51} - 5397q^{52} - 2877q^{53} - 5691q^{54} - 4809q^{55} - 5901q^{56} - 1197q^{57} - 21q^{58} - 21q^{59} - 21q^{60} - 21q^{61} - 21q^{62} - 21q^{63} - 21q^{64} - 21q^{65} - 21q^{66} - 21q^{67} - 21q^{68} - 7875q^{69} - 13041q^{70} - 5271q^{71} - 20391q^{72} - 3003q^{73} - 6930q^{74} - 3696q^{75} - 756q^{76} + 1617q^{77} + 7896q^{78} + 3591q^{79} + 9219q^{80} + 10899q^{81} + 15309q^{82} + 6615q^{83} + 31185q^{84} + 7098q^{85} + 14259q^{86} + 17388q^{87} + 13083q^{88} + 6111q^{89} + 24549q^{90} + 4599q^{91} + 9009q^{92} + 4851q^{93} + 2163q^{94} - 441q^{95} - 6846q^{96} - 5943q^{97} - 10458q^{98} - 14280q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(43))$$

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
43.4.a $$\chi_{43}(1, \cdot)$$ 43.4.a.a 4 1
43.4.a.b 6
43.4.c $$\chi_{43}(6, \cdot)$$ 43.4.c.a 20 2
43.4.e $$\chi_{43}(4, \cdot)$$ 43.4.e.a 60 6
43.4.g $$\chi_{43}(9, \cdot)$$ 43.4.g.a 120 12