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

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

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