# Properties

 Label 160.1 Level 160 Weight 1 Dimension 2 Nonzero newspaces 1 Newform subspaces 1 Sturm bound 1536 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$160 = 2^{5} \cdot 5$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$1536$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(160))$$.

Total New Old
Modular forms 132 32 100
Cusp forms 4 2 2
Eisenstein series 128 30 98

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2 q + O(q^{10})$$ $$2 q - 2 q^{13} - 2 q^{17} - 2 q^{25} + 2 q^{37} + 2 q^{45} + 2 q^{53} + 2 q^{65} + 2 q^{73} - 2 q^{81} - 2 q^{85} + 2 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(160))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
160.1.b $$\chi_{160}(31, \cdot)$$ None 0 1
160.1.e $$\chi_{160}(79, \cdot)$$ None 0 1
160.1.g $$\chi_{160}(111, \cdot)$$ None 0 1
160.1.h $$\chi_{160}(159, \cdot)$$ None 0 1
160.1.i $$\chi_{160}(57, \cdot)$$ None 0 2
160.1.k $$\chi_{160}(39, \cdot)$$ None 0 2
160.1.m $$\chi_{160}(17, \cdot)$$ None 0 2
160.1.p $$\chi_{160}(33, \cdot)$$ 160.1.p.a 2 2
160.1.r $$\chi_{160}(71, \cdot)$$ None 0 2
160.1.t $$\chi_{160}(137, \cdot)$$ None 0 2
160.1.v $$\chi_{160}(13, \cdot)$$ None 0 4
160.1.w $$\chi_{160}(11, \cdot)$$ None 0 4
160.1.y $$\chi_{160}(19, \cdot)$$ None 0 4
160.1.bb $$\chi_{160}(53, \cdot)$$ None 0 4

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(160))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(160)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 10}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 1}$$