# Properties

 Label 1805.1 Level 1805 Weight 1 Dimension 42 Nonzero newspaces 5 Newform subspaces 7 Sturm bound 259920 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$1805 = 5 \cdot 19^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$5$$ Newform subspaces: $$7$$ Sturm bound: $$259920$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1805))$$.

Total New Old
Modular forms 2064 1448 616
Cusp forms 48 42 6
Eisenstein series 2016 1406 610

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 42 0 0 0

## Trace form

 $$42 q - q^{4} + q^{5} + 4 q^{6} - q^{9} + O(q^{10})$$ $$42 q - q^{4} + q^{5} + 4 q^{6} - q^{9} + 2 q^{11} + q^{16} - 24 q^{20} - 3 q^{25} - 4 q^{26} - 4 q^{30} - 3 q^{36} - 32 q^{39} - 2 q^{44} + 3 q^{45} - 3 q^{49} + 2 q^{55} + 2 q^{61} + 3 q^{64} + 4 q^{74} - 3 q^{80} + q^{81} + 32 q^{96} - 2 q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1805))$$

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
1805.1.c $$\chi_{1805}(721, \cdot)$$ None 0 1
1805.1.d $$\chi_{1805}(1804, \cdot)$$ None 0 1
1805.1.f $$\chi_{1805}(362, \cdot)$$ 1805.1.f.a 2 2
1805.1.h $$\chi_{1805}(69, \cdot)$$ 1805.1.h.a 2 2
1805.1.h.b 4
1805.1.j $$\chi_{1805}(791, \cdot)$$ None 0 2
1805.1.m $$\chi_{1805}(68, \cdot)$$ 1805.1.m.a 4 4
1805.1.n $$\chi_{1805}(116, \cdot)$$ None 0 6
1805.1.o $$\chi_{1805}(299, \cdot)$$ 1805.1.o.a 6 6
1805.1.o.b 12
1805.1.r $$\chi_{1805}(28, \cdot)$$ 1805.1.r.a 12 12
1805.1.t $$\chi_{1805}(94, \cdot)$$ None 0 18
1805.1.u $$\chi_{1805}(56, \cdot)$$ None 0 18
1805.1.y $$\chi_{1805}(58, \cdot)$$ None 0 36
1805.1.z $$\chi_{1805}(31, \cdot)$$ None 0 36
1805.1.bb $$\chi_{1805}(84, \cdot)$$ None 0 36
1805.1.bd $$\chi_{1805}(7, \cdot)$$ None 0 72
1805.1.bg $$\chi_{1805}(14, \cdot)$$ None 0 108
1805.1.bh $$\chi_{1805}(21, \cdot)$$ None 0 108
1805.1.bj $$\chi_{1805}(17, \cdot)$$ None 0 216

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1805))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1805)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(361))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(1805))$$$$^{\oplus 1}$$