## Defining parameters

 Level: $$N$$ = $$43$$ Weight: $$k$$ = $$7$$ Nonzero newspaces: $$4$$ Newform subspaces: $$5$$ Sturm bound: $$1078$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(\Gamma_1(43))$$.

Total New Old
Modular forms 483 483 0
Cusp forms 441 441 0
Eisenstein series 42 42 0

## Trace form

 $$441q - 21q^{2} - 21q^{3} - 21q^{4} - 21q^{5} - 21q^{6} - 21q^{7} - 21q^{8} - 21q^{9} + O(q^{10})$$ $$441q - 21q^{2} - 21q^{3} - 21q^{4} - 21q^{5} - 21q^{6} - 21q^{7} - 21q^{8} - 21q^{9} - 21q^{10} - 21q^{11} - 21q^{12} - 21q^{13} - 21q^{14} - 21q^{15} - 21q^{16} - 21q^{17} - 21q^{18} - 21q^{19} - 21q^{20} - 21q^{21} - 21q^{22} - 21q^{23} - 21q^{24} - 21q^{25} - 21q^{26} - 21q^{27} - 21q^{28} - 21q^{29} - 21q^{30} + 194019q^{31} + 114219q^{32} - 326613q^{33} - 574581q^{34} - 230517q^{35} - 21q^{36} + 216699q^{37} + 724395q^{38} + 476259q^{39} + 1403115q^{40} + 102459q^{41} - 564501q^{43} - 860202q^{44} - 1428861q^{45} - 1229781q^{46} - 267981q^{47} - 1306389q^{48} - 21q^{49} + 809067q^{50} + 816459q^{51} + 3010539q^{52} + 1193787q^{53} + 1224699q^{54} - 248997q^{55} - 2304981q^{56} - 952581q^{57} - 21q^{58} - 21q^{59} - 21q^{60} - 21q^{61} - 21q^{62} - 21q^{63} - 21q^{64} - 21q^{65} - 21q^{66} - 21q^{67} - 21q^{68} + 6157515q^{69} + 2929479q^{70} - 1249521q^{71} - 12446091q^{72} - 2683821q^{73} - 7675920q^{74} - 4593771q^{75} - 972426q^{76} + 2188347q^{77} + 10252494q^{78} + 4356051q^{79} + 9932979q^{80} + 9915339q^{81} + 10899609q^{82} + 3251619q^{83} + 7876197q^{84} - 3669981q^{86} - 8959062q^{87} - 10154445q^{88} - 6156549q^{89} - 30098271q^{90} - 6569661q^{91} - 14348691q^{92} - 8379861q^{93} - 3950877q^{94} + 776979q^{95} + 12537504q^{96} + 10446387q^{97} + 16960104q^{98} + 20162205q^{99} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(\Gamma_1(43))$$

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
43.7.b $$\chi_{43}(42, \cdot)$$ 43.7.b.a 1 1
43.7.b.b 20
43.7.d $$\chi_{43}(7, \cdot)$$ 43.7.d.a 42 2
43.7.f $$\chi_{43}(2, \cdot)$$ 43.7.f.a 126 6
43.7.h $$\chi_{43}(3, \cdot)$$ 43.7.h.a 252 12