# Properties

 Label 320.1 Level 320 Weight 1 Dimension 3 Nonzero newspaces 2 Newform subspaces 2 Sturm bound 6144 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$320 = 2^{6} \cdot 5$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$6144$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(320))$$.

Total New Old
Modular forms 298 69 229
Cusp forms 10 3 7
Eisenstein series 288 66 222

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

 $$3 q + q^{5} - q^{9} + O(q^{10})$$ $$3 q + q^{5} - q^{9} + 2 q^{13} - 2 q^{17} - q^{25} - 2 q^{29} - 2 q^{37} - 2 q^{41} - 3 q^{45} - q^{49} - 2 q^{53} + 2 q^{61} + 2 q^{65} + 2 q^{73} - q^{81} + 2 q^{85} + 2 q^{89} + 2 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(320))$$

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
320.1.b $$\chi_{320}(191, \cdot)$$ None 0 1
320.1.e $$\chi_{320}(159, \cdot)$$ None 0 1
320.1.g $$\chi_{320}(31, \cdot)$$ None 0 1
320.1.h $$\chi_{320}(319, \cdot)$$ 320.1.h.a 1 1
320.1.i $$\chi_{320}(177, \cdot)$$ None 0 2
320.1.k $$\chi_{320}(79, \cdot)$$ None 0 2
320.1.m $$\chi_{320}(33, \cdot)$$ None 0 2
320.1.p $$\chi_{320}(193, \cdot)$$ 320.1.p.a 2 2
320.1.r $$\chi_{320}(111, \cdot)$$ None 0 2
320.1.t $$\chi_{320}(17, \cdot)$$ None 0 2
320.1.v $$\chi_{320}(57, \cdot)$$ None 0 4
320.1.w $$\chi_{320}(71, \cdot)$$ None 0 4
320.1.y $$\chi_{320}(39, \cdot)$$ None 0 4
320.1.bb $$\chi_{320}(137, \cdot)$$ None 0 4
320.1.bc $$\chi_{320}(53, \cdot)$$ None 0 8
320.1.bg $$\chi_{320}(11, \cdot)$$ None 0 8
320.1.bh $$\chi_{320}(19, \cdot)$$ None 0 8
320.1.bi $$\chi_{320}(13, \cdot)$$ None 0 8

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(320))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(320)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 2}$$