## Defining parameters

 Level: $$N$$ = $$43$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Newform subspaces: $$7$$ Sturm bound: $$308$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(43))$$.

Total New Old
Modular forms 98 98 0
Cusp forms 57 57 0
Eisenstein series 41 41 0

## Trace form

 $$57q - 18q^{2} - 17q^{3} - 14q^{4} - 15q^{5} - 9q^{6} - 13q^{7} - 6q^{8} - 8q^{9} + O(q^{10})$$ $$57q - 18q^{2} - 17q^{3} - 14q^{4} - 15q^{5} - 9q^{6} - 13q^{7} - 6q^{8} - 8q^{9} - 3q^{10} - 9q^{11} + 7q^{12} - 7q^{13} + 3q^{14} + 3q^{15} + 10q^{16} - 3q^{17} + 18q^{18} - q^{19} + 21q^{20} + 11q^{21} + 15q^{22} + 3q^{23} + 39q^{24} + 10q^{25} + 21q^{26} + 19q^{27} + 35q^{28} + 9q^{29} + 51q^{30} + 4q^{31} - 15q^{33} - 30q^{34} - 15q^{35} - 42q^{36} - 25q^{37} - 45q^{38} - 14q^{39} - 99q^{40} - 30q^{42} - 83q^{43} - 42q^{44} - 48q^{45} - 33q^{46} + 6q^{47} - 65q^{48} - 13q^{49} - 12q^{50} + 9q^{51} - 35q^{52} - 9q^{53} + 36q^{54} + 9q^{55} + 57q^{56} + 52q^{57} + 69q^{58} + 39q^{59} + 147q^{60} + 41q^{61} + 75q^{62} + 83q^{63} + 106q^{64} + 63q^{65} + 123q^{66} + 47q^{67} + 105q^{68} + 33q^{69} + 39q^{70} + 9q^{71} - 36q^{72} + 11q^{73} - 54q^{74} - 44q^{75} - 28q^{76} - 51q^{77} - 126q^{78} - 25q^{79} - 3q^{80} - 68q^{81} - 105q^{82} - 21q^{83} - 217q^{84} - 18q^{85} - 60q^{86} - 132q^{87} - 51q^{88} - 15q^{89} - 165q^{90} + 7q^{91} - 63q^{92} - 61q^{93} - 45q^{94} + 15q^{95} - 42q^{96} - 49q^{97} + 3q^{98} - 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(43))$$

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
43.2.a $$\chi_{43}(1, \cdot)$$ 43.2.a.a 1 1
43.2.a.b 2
43.2.c $$\chi_{43}(6, \cdot)$$ 43.2.c.a 2 2
43.2.c.b 4
43.2.e $$\chi_{43}(4, \cdot)$$ 43.2.e.a 6 6
43.2.e.b 6
43.2.g $$\chi_{43}(9, \cdot)$$ 43.2.g.a 36 12