# Properties

 Label 285.1 Level 285 Weight 1 Dimension 16 Nonzero newspaces 2 Newform subspaces 4 Sturm bound 5760 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$285 = 3 \cdot 5 \cdot 19$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$4$$ Sturm bound: $$5760$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(285))$$.

Total New Old
Modular forms 314 120 194
Cusp forms 26 16 10
Eisenstein series 288 104 184

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

 $$16 q - 6 q^{4} - 4 q^{6} - 2 q^{9} + O(q^{10})$$ $$16 q - 6 q^{4} - 4 q^{6} - 2 q^{9} - 4 q^{10} - 2 q^{15} + 8 q^{16} - 2 q^{19} + 10 q^{24} - 2 q^{25} - 4 q^{31} - 8 q^{34} - 6 q^{36} - 8 q^{40} - 8 q^{46} - 2 q^{49} - 4 q^{51} - 4 q^{54} + 12 q^{60} - 4 q^{61} + 4 q^{64} + 14 q^{69} - 6 q^{76} - 4 q^{79} - 2 q^{81} + 14 q^{85} + 14 q^{90} + 28 q^{94} - 12 q^{96} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(285))$$

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
285.1.d $$\chi_{285}(191, \cdot)$$ None 0 1
285.1.e $$\chi_{285}(151, \cdot)$$ None 0 1
285.1.f $$\chi_{285}(134, \cdot)$$ None 0 1
285.1.g $$\chi_{285}(94, \cdot)$$ None 0 1
285.1.j $$\chi_{285}(113, \cdot)$$ None 0 2
285.1.l $$\chi_{285}(58, \cdot)$$ None 0 2
285.1.n $$\chi_{285}(239, \cdot)$$ 285.1.n.a 2 2
285.1.n.b 2
285.1.o $$\chi_{285}(259, \cdot)$$ None 0 2
285.1.s $$\chi_{285}(11, \cdot)$$ None 0 2
285.1.t $$\chi_{285}(31, \cdot)$$ None 0 2
285.1.w $$\chi_{285}(8, \cdot)$$ None 0 4
285.1.y $$\chi_{285}(7, \cdot)$$ None 0 4
285.1.ba $$\chi_{285}(91, \cdot)$$ None 0 6
285.1.bb $$\chi_{285}(101, \cdot)$$ None 0 6
285.1.bc $$\chi_{285}(34, \cdot)$$ None 0 6
285.1.bd $$\chi_{285}(44, \cdot)$$ 285.1.bd.a 6 6
285.1.bd.b 6
285.1.bg $$\chi_{285}(28, \cdot)$$ None 0 12
285.1.bj $$\chi_{285}(2, \cdot)$$ None 0 12

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(285))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(285)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(285))$$$$^{\oplus 1}$$