# Properties

 Label 1856.1 Level 1856 Weight 1 Dimension 35 Nonzero newspaces 5 Newform subspaces 9 Sturm bound 215040 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$1856 = 2^{6} \cdot 29$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$5$$ Newform subspaces: $$9$$ Sturm bound: $$215040$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1856))$$.

Total New Old
Modular forms 2154 629 1525
Cusp forms 138 35 103
Eisenstein series 2016 594 1422

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 31 0 4 0

## Trace form

 $$35 q + 6 q^{5} + 3 q^{9} + O(q^{10})$$ $$35 q + 6 q^{5} + 3 q^{9} + 2 q^{13} - 2 q^{17} - 4 q^{21} - 3 q^{25} + 5 q^{29} - 4 q^{33} + 2 q^{37} - 6 q^{41} + 6 q^{45} + 7 q^{49} - 2 q^{53} - 4 q^{57} + 2 q^{61} - 8 q^{65} - 2 q^{73} + 4 q^{77} + 3 q^{81} + 4 q^{85} - 6 q^{89} + 4 q^{93} + 2 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1856))$$

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
1856.1.b $$\chi_{1856}(927, \cdot)$$ None 0 1
1856.1.d $$\chi_{1856}(639, \cdot)$$ None 0 1
1856.1.f $$\chi_{1856}(1567, \cdot)$$ None 0 1
1856.1.h $$\chi_{1856}(1855, \cdot)$$ 1856.1.h.a 1 1
1856.1.h.b 1
1856.1.h.c 1
1856.1.h.d 2
1856.1.i $$\chi_{1856}(273, \cdot)$$ None 0 2
1856.1.l $$\chi_{1856}(1409, \cdot)$$ 1856.1.l.a 2 2
1856.1.l.b 4
1856.1.o $$\chi_{1856}(175, \cdot)$$ None 0 2
1856.1.p $$\chi_{1856}(463, \cdot)$$ None 0 2
1856.1.r $$\chi_{1856}(481, \cdot)$$ None 0 2
1856.1.s $$\chi_{1856}(17, \cdot)$$ None 0 2
1856.1.w $$\chi_{1856}(231, \cdot)$$ None 0 4
1856.1.y $$\chi_{1856}(41, \cdot)$$ None 0 4
1856.1.z $$\chi_{1856}(505, \cdot)$$ None 0 4
1856.1.bb $$\chi_{1856}(407, \cdot)$$ None 0 4
1856.1.bd $$\chi_{1856}(63, \cdot)$$ 1856.1.bd.a 6 6
1856.1.bf $$\chi_{1856}(223, \cdot)$$ None 0 6
1856.1.bh $$\chi_{1856}(255, \cdot)$$ 1856.1.bh.a 6 6
1856.1.bj $$\chi_{1856}(415, \cdot)$$ None 0 6
1856.1.bk $$\chi_{1856}(133, \cdot)$$ None 0 8
1856.1.bm $$\chi_{1856}(115, \cdot)$$ None 0 8
1856.1.bo $$\chi_{1856}(59, \cdot)$$ None 0 8
1856.1.br $$\chi_{1856}(365, \cdot)$$ None 0 8
1856.1.bt $$\chi_{1856}(113, \cdot)$$ None 0 12
1856.1.bu $$\chi_{1856}(97, \cdot)$$ None 0 12
1856.1.bw $$\chi_{1856}(207, \cdot)$$ None 0 12
1856.1.bx $$\chi_{1856}(111, \cdot)$$ None 0 12
1856.1.ca $$\chi_{1856}(193, \cdot)$$ 1856.1.ca.a 12 12
1856.1.cd $$\chi_{1856}(177, \cdot)$$ None 0 12
1856.1.ce $$\chi_{1856}(7, \cdot)$$ None 0 24
1856.1.cg $$\chi_{1856}(137, \cdot)$$ None 0 24
1856.1.cj $$\chi_{1856}(73, \cdot)$$ None 0 24
1856.1.cl $$\chi_{1856}(71, \cdot)$$ None 0 24
1856.1.cn $$\chi_{1856}(37, \cdot)$$ None 0 48
1856.1.cp $$\chi_{1856}(83, \cdot)$$ None 0 48
1856.1.cr $$\chi_{1856}(35, \cdot)$$ None 0 48
1856.1.cs $$\chi_{1856}(21, \cdot)$$ None 0 48

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1856))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1856)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(116))$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(464))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(928))$$$$^{\oplus 2}$$