## Defining parameters

 Level: $$N$$ = $$2011$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newforms: $$1$$ Sturm bound: $$337010$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(2011))$$.

Total New Old
Modular forms 1008 1008 0
Cusp forms 3 3 0
Eisenstein series 1005 1005 0

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 3 0 0 0

## Trace form

 $$3q + 3q^{4} - q^{5} + 3q^{9} + O(q^{10})$$ $$3q + 3q^{4} - q^{5} + 3q^{9} - q^{13} + 3q^{16} - q^{20} - q^{23} + 2q^{25} - q^{31} + 3q^{36} - q^{41} - q^{43} - q^{45} + 3q^{49} - q^{52} + 3q^{64} - 2q^{65} - q^{71} - q^{80} + 3q^{81} - q^{83} - q^{89} - q^{92} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(2011))$$

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
2011.1.b $$\chi_{2011}(2010, \cdot)$$ 2011.1.b.a 3 1
2011.1.e $$\chi_{2011}(206, \cdot)$$ None 0 2
2011.1.f $$\chi_{2011}(53, \cdot)$$ None 0 4
2011.1.h $$\chi_{2011}(72, \cdot)$$ None 0 8
2011.1.j $$\chi_{2011}(8, \cdot)$$ None 0 66
2011.1.m $$\chi_{2011}(2, \cdot)$$ None 0 132
2011.1.n $$\chi_{2011}(10, \cdot)$$ None 0 264
2011.1.p $$\chi_{2011}(3, \cdot)$$ None 0 528