## Defining parameters

 Level: $$N$$ = $$61$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newforms: $$10$$ Sturm bound: $$620$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(61))$$.

Total New Old
Modular forms 185 185 0
Cusp forms 126 126 0
Eisenstein series 59 59 0

## Trace form

 $$126q - 27q^{2} - 26q^{3} - 23q^{4} - 24q^{5} - 18q^{6} - 22q^{7} - 15q^{8} - 17q^{9} + O(q^{10})$$ $$126q - 27q^{2} - 26q^{3} - 23q^{4} - 24q^{5} - 18q^{6} - 22q^{7} - 15q^{8} - 17q^{9} - 12q^{10} - 18q^{11} - 2q^{12} - 16q^{13} - 6q^{14} - 6q^{15} + q^{16} - 12q^{17} + 9q^{18} - 10q^{19} + 12q^{20} + 2q^{21} + 6q^{22} - 6q^{23} + 30q^{24} + q^{25} + 12q^{26} + 10q^{27} + 26q^{28} + 42q^{30} + 2q^{31} + 33q^{32} + 18q^{33} + 24q^{34} + 18q^{35} + 61q^{36} + 8q^{37} + 30q^{38} + 26q^{39} + 60q^{40} + 12q^{41} + 66q^{42} + 14q^{43} + 54q^{44} + 48q^{45} + 42q^{46} - 12q^{47} - 6q^{48} - 43q^{49} - 12q^{50} - 18q^{51} - 157q^{52} - 6q^{53} - 90q^{54} - 78q^{55} - 90q^{56} - 70q^{57} - 60q^{58} - 30q^{59} - 132q^{60} - 99q^{61} - 144q^{62} - 56q^{63} - 143q^{64} - 6q^{65} - 6q^{66} - 82q^{67} - 84q^{68} - 54q^{69} - 66q^{70} + 12q^{71} - 60q^{72} - 16q^{73} + 9q^{74} + 24q^{75} + 10q^{76} + 36q^{77} + 138q^{78} + 50q^{79} + 156q^{80} + 91q^{81} + 96q^{82} + 54q^{83} + 194q^{84} + 78q^{85} + 102q^{86} + 90q^{87} + 150q^{88} + 60q^{89} + 204q^{90} + 82q^{91} + 138q^{92} + 98q^{93} + 114q^{94} + 90q^{95} + 222q^{96} + 68q^{97} + 141q^{98} + 126q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(61))$$

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
61.2.a $$\chi_{61}(1, \cdot)$$ 61.2.a.a 1 1
61.2.a.b 3
61.2.b $$\chi_{61}(60, \cdot)$$ 61.2.b.a 4 1
61.2.c $$\chi_{61}(13, \cdot)$$ 61.2.c.a 8 2
61.2.e $$\chi_{61}(9, \cdot)$$ 61.2.e.a 12 4
61.2.f $$\chi_{61}(14, \cdot)$$ 61.2.f.a 2 2
61.2.f.b 8
61.2.g $$\chi_{61}(3, \cdot)$$ 61.2.g.a 16 4
61.2.i $$\chi_{61}(12, \cdot)$$ 61.2.i.a 32 8
61.2.k $$\chi_{61}(4, \cdot)$$ 61.2.k.a 40 8