## Defining parameters

 Level: $$N$$ = $$41$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$6$$ Newform subspaces: $$6$$ Sturm bound: $$280$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(41))$$.

Total New Old
Modular forms 90 90 0
Cusp forms 51 51 0
Eisenstein series 39 39 0

## Trace form

 $$51q - 17q^{2} - 16q^{3} - 13q^{4} - 14q^{5} - 8q^{6} - 12q^{7} - 5q^{8} - 7q^{9} + O(q^{10})$$ $$51q - 17q^{2} - 16q^{3} - 13q^{4} - 14q^{5} - 8q^{6} - 12q^{7} - 5q^{8} - 7q^{9} - 2q^{10} - 8q^{11} + 8q^{12} - 6q^{13} + 4q^{14} + 4q^{15} + 11q^{16} - 2q^{17} + 19q^{18} + 22q^{20} + 12q^{21} + 16q^{22} + 4q^{23} + 40q^{24} + 11q^{25} + 22q^{26} + 20q^{27} + 36q^{28} + 10q^{29} + 12q^{30} - 8q^{31} - 27q^{32} - 32q^{33} - 16q^{34} - 12q^{35} - 69q^{36} - 42q^{37} - 44q^{39} - 70q^{40} + q^{41} - 104q^{42} + 4q^{43} - 56q^{44} - 22q^{45} + 12q^{46} - 32q^{47} - 36q^{48} - 3q^{49} + 23q^{50} - 8q^{51} + 8q^{52} + 14q^{53} + 60q^{54} + 52q^{55} + 100q^{56} + 60q^{57} + 70q^{58} + 40q^{59} + 148q^{60} + 42q^{61} + 76q^{62} + 84q^{63} + 107q^{64} + 54q^{65} + 44q^{66} - 12q^{67} + 6q^{68} - 4q^{69} - 76q^{70} - 28q^{71} - 5q^{72} - 26q^{73} - 26q^{74} - 56q^{75} - 180q^{76} - 4q^{77} - 52q^{78} - 20q^{79} - 74q^{80} - 89q^{81} - 137q^{82} - 36q^{83} - 76q^{84} - 82q^{85} - 88q^{86} + 20q^{87} - 40q^{88} - 10q^{89} - 86q^{90} - 68q^{91} + 28q^{92} + 28q^{93} - 56q^{94} + 20q^{95} + 32q^{96} - 2q^{97} + 51q^{98} + 76q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(41))$$

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
41.2.a $$\chi_{41}(1, \cdot)$$ 41.2.a.a 3 1
41.2.b $$\chi_{41}(40, \cdot)$$ 41.2.b.a 2 1
41.2.c $$\chi_{41}(9, \cdot)$$ 41.2.c.a 6 2
41.2.d $$\chi_{41}(10, \cdot)$$ 41.2.d.a 8 4
41.2.f $$\chi_{41}(4, \cdot)$$ 41.2.f.a 8 4
41.2.g $$\chi_{41}(2, \cdot)$$ 41.2.g.a 24 8