## Defining parameters

 Level: $$N$$ = $$1859 = 11 \cdot 13^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$4$$ Newform subspaces: $$10$$ Sturm bound: $$283920$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1859))$$.

Total New Old
Modular forms 2344 1897 447
Cusp forms 64 56 8
Eisenstein series 2280 1841 439

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 56 0 0 0

## Trace form

 $$56 q + 2 q^{3} - 2 q^{4} - 2 q^{9} + O(q^{10})$$ $$56 q + 2 q^{3} - 2 q^{4} - 2 q^{9} + 6 q^{12} - 20 q^{14} + 2 q^{22} + 2 q^{23} - 4 q^{25} - 44 q^{27} - 6 q^{36} - 6 q^{38} - 2 q^{42} - 2 q^{49} - 22 q^{53} - 2 q^{56} + 2 q^{64} + 30 q^{66} + 4 q^{69} + 2 q^{75} + 2 q^{77} + 4 q^{82} + 4 q^{88} + 8 q^{92} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1859))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
1859.1.c $$\chi_{1859}(846, \cdot)$$ 1859.1.c.a 3 1
1859.1.c.b 3
1859.1.c.c 4
1859.1.d $$\chi_{1859}(1858, \cdot)$$ 1859.1.d.a 6 1
1859.1.f $$\chi_{1859}(408, \cdot)$$ None 0 2
1859.1.i $$\chi_{1859}(868, \cdot)$$ 1859.1.i.a 4 2
1859.1.i.b 4
1859.1.i.c 12
1859.1.k $$\chi_{1859}(1374, \cdot)$$ 1859.1.k.a 6 2
1859.1.k.b 6
1859.1.k.c 8
1859.1.l $$\chi_{1859}(337, \cdot)$$ None 0 4
1859.1.m $$\chi_{1859}(508, \cdot)$$ None 0 4
1859.1.p $$\chi_{1859}(89, \cdot)$$ None 0 4
1859.1.s $$\chi_{1859}(70, \cdot)$$ None 0 8
1859.1.u $$\chi_{1859}(142, \cdot)$$ None 0 12
1859.1.v $$\chi_{1859}(131, \cdot)$$ None 0 12
1859.1.x $$\chi_{1859}(315, \cdot)$$ None 0 8
1859.1.z $$\chi_{1859}(316, \cdot)$$ None 0 8
1859.1.bc $$\chi_{1859}(34, \cdot)$$ None 0 24
1859.1.be $$\chi_{1859}(80, \cdot)$$ None 0 16
1859.1.bg $$\chi_{1859}(87, \cdot)$$ None 0 24
1859.1.bi $$\chi_{1859}(10, \cdot)$$ None 0 24
1859.1.bk $$\chi_{1859}(40, \cdot)$$ None 0 48
1859.1.bl $$\chi_{1859}(51, \cdot)$$ None 0 48
1859.1.bm $$\chi_{1859}(45, \cdot)$$ None 0 48
1859.1.bq $$\chi_{1859}(5, \cdot)$$ None 0 96
1859.1.br $$\chi_{1859}(17, \cdot)$$ None 0 96
1859.1.bt $$\chi_{1859}(29, \cdot)$$ None 0 96
1859.1.bu $$\chi_{1859}(15, \cdot)$$ None 0 192

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1859))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1859)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(143))$$$$^{\oplus 2}$$