# Properties

 Label 43.5 Level 43 Weight 5 Dimension 287 Nonzero newspaces 4 Newform subspaces 5 Sturm bound 770 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$43$$ Weight: $$k$$ = $$5$$ Nonzero newspaces: $$4$$ Newform subspaces: $$5$$ Sturm bound: $$770$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(\Gamma_1(43))$$.

Total New Old
Modular forms 329 329 0
Cusp forms 287 287 0
Eisenstein series 42 42 0

## Trace form

 $$287q - 21q^{2} - 21q^{3} - 21q^{4} - 21q^{5} - 21q^{6} - 21q^{7} - 21q^{8} - 21q^{9} + O(q^{10})$$ $$287q - 21q^{2} - 21q^{3} - 21q^{4} - 21q^{5} - 21q^{6} - 21q^{7} - 21q^{8} - 21q^{9} - 21q^{10} - 21q^{11} - 21q^{12} - 21q^{13} - 21q^{14} - 21q^{15} - 21q^{16} - 21q^{17} - 21q^{18} - 21q^{19} - 21q^{20} - 21q^{21} - 21q^{22} - 21q^{23} - 21q^{24} - 21q^{25} - 21q^{26} - 21q^{27} - 21q^{28} - 21q^{29} - 21q^{30} + 4522q^{31} + 15099q^{32} + 5649q^{33} - 2037q^{34} - 6195q^{35} - 24213q^{36} - 10311q^{37} - 20181q^{38} - 10164q^{39} - 25557q^{40} - 1722q^{41} + 8904q^{43} + 14070q^{44} + 25494q^{45} + 25515q^{46} + 7224q^{47} + 60459q^{48} + 16786q^{49} + 24171q^{50} + 7917q^{51} + 4459q^{52} - 6951q^{53} - 27237q^{54} - 32235q^{55} - 49413q^{56} - 11676q^{57} - 21q^{58} - 21q^{59} - 21q^{60} - 21q^{61} - 21q^{62} - 21q^{63} - 21q^{64} - 21q^{65} - 21q^{66} - 21q^{67} - 21q^{68} + 79275q^{69} + 107079q^{70} + 31731q^{71} + 68229q^{72} - 1029q^{73} - 43680q^{74} - 73521q^{75} - 93954q^{76} - 90741q^{77} - 204498q^{78} - 61509q^{79} - 113421q^{80} - 98133q^{81} - 97671q^{82} - 27237q^{83} - 62811q^{84} + 28707q^{86} + 71358q^{87} + 83811q^{88} + 54411q^{89} + 292929q^{90} + 73563q^{91} + 198429q^{92} + 163947q^{93} + 161763q^{94} + 75579q^{95} + 213192q^{96} + 75579q^{97} + 51576q^{98} + 4095q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(\Gamma_1(43))$$

We only show spaces with odd 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
43.5.b $$\chi_{43}(42, \cdot)$$ 43.5.b.a 1 1
43.5.b.b 12
43.5.d $$\chi_{43}(7, \cdot)$$ 43.5.d.a 28 2
43.5.f $$\chi_{43}(2, \cdot)$$ 43.5.f.a 78 6
43.5.h $$\chi_{43}(3, \cdot)$$ 43.5.h.a 168 12