## Defining parameters

 Level: $$N$$ = $$11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$20$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(11))$$.

Total New Old
Modular forms 10 10 0
Cusp forms 1 1 0
Eisenstein series 9 9 0

## Trace form

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

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$

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
11.2.a $$\chi_{11}(1, \cdot)$$ 11.2.a.a 1 1
11.2.c $$\chi_{11}(3, \cdot)$$ None 0 4