# Properties

 Label 1280.1 Level 1280 Weight 1 Dimension 16 Nonzero newspaces 4 Newform subspaces 8 Sturm bound 98304 Trace bound 17

## Defining parameters

 Level: $$N$$ = $$1280 = 2^{8} \cdot 5$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$4$$ Newform subspaces: $$8$$ Sturm bound: $$98304$$ Trace bound: $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1280))$$.

Total New Old
Modular forms 1472 328 1144
Cusp forms 64 16 48
Eisenstein series 1408 312 1096

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 16 0 0 0

## Trace form

 $$16 q + 4 q^{9} + O(q^{10})$$ $$16 q + 4 q^{9} + 8 q^{25} + 8 q^{41} - 4 q^{65} - 8 q^{81} - 8 q^{89} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1280))$$

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
1280.1.b $$\chi_{1280}(511, \cdot)$$ None 0 1
1280.1.e $$\chi_{1280}(639, \cdot)$$ 1280.1.e.a 2 1
1280.1.g $$\chi_{1280}(1151, \cdot)$$ None 0 1
1280.1.h $$\chi_{1280}(1279, \cdot)$$ 1280.1.h.a 2 1
1280.1.h.b 2
1280.1.h.c 2
1280.1.i $$\chi_{1280}(833, \cdot)$$ None 0 2
1280.1.k $$\chi_{1280}(319, \cdot)$$ None 0 2
1280.1.m $$\chi_{1280}(897, \cdot)$$ 1280.1.m.a 2 2
1280.1.m.b 2
1280.1.p $$\chi_{1280}(257, \cdot)$$ 1280.1.p.a 2 2
1280.1.p.b 2
1280.1.r $$\chi_{1280}(191, \cdot)$$ None 0 2
1280.1.t $$\chi_{1280}(193, \cdot)$$ None 0 2
1280.1.v $$\chi_{1280}(33, \cdot)$$ None 0 4
1280.1.w $$\chi_{1280}(31, \cdot)$$ None 0 4
1280.1.y $$\chi_{1280}(159, \cdot)$$ None 0 4
1280.1.bb $$\chi_{1280}(353, \cdot)$$ None 0 4
1280.1.bc $$\chi_{1280}(17, \cdot)$$ None 0 8
1280.1.bg $$\chi_{1280}(111, \cdot)$$ None 0 8
1280.1.bh $$\chi_{1280}(79, \cdot)$$ None 0 8
1280.1.bi $$\chi_{1280}(177, \cdot)$$ None 0 8
1280.1.bk $$\chi_{1280}(57, \cdot)$$ None 0 16
1280.1.bn $$\chi_{1280}(39, \cdot)$$ None 0 16
1280.1.bp $$\chi_{1280}(71, \cdot)$$ None 0 16
1280.1.bq $$\chi_{1280}(137, \cdot)$$ None 0 16
1280.1.bs $$\chi_{1280}(53, \cdot)$$ None 0 32
1280.1.bu $$\chi_{1280}(19, \cdot)$$ None 0 32
1280.1.bx $$\chi_{1280}(11, \cdot)$$ None 0 32
1280.1.bz $$\chi_{1280}(13, \cdot)$$ None 0 32

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1280))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1280)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(256))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(320))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(640))$$$$^{\oplus 2}$$