# Properties

 Label 896.1 Level 896 Weight 1 Dimension 28 Nonzero newspaces 4 Newform subspaces 6 Sturm bound 49152 Trace bound 23

## Defining parameters

 Level: $$N$$ = $$896 = 2^{7} \cdot 7$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$4$$ Newform subspaces: $$6$$ Sturm bound: $$49152$$ Trace bound: $$23$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(896))$$.

Total New Old
Modular forms 1058 268 790
Cusp forms 98 28 70
Eisenstein series 960 240 720

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 28 0 0 0

## Trace form

 $$28 q + 4 q^{9} + O(q^{10})$$ $$28 q + 4 q^{9} + 4 q^{23} + 4 q^{25} + 4 q^{29} + 4 q^{37} + 4 q^{43} - 8 q^{53} - 16 q^{56} - 8 q^{57} - 4 q^{63} - 8 q^{65} - 4 q^{67} - 16 q^{74} - 8 q^{77} - 8 q^{81} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(896))$$

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
896.1.c $$\chi_{896}(769, \cdot)$$ None 0 1
896.1.d $$\chi_{896}(127, \cdot)$$ None 0 1
896.1.g $$\chi_{896}(575, \cdot)$$ None 0 1
896.1.h $$\chi_{896}(321, \cdot)$$ 896.1.h.a 2 1
896.1.h.b 2
896.1.k $$\chi_{896}(351, \cdot)$$ None 0 2
896.1.l $$\chi_{896}(97, \cdot)$$ 896.1.l.a 2 2
896.1.l.b 2
896.1.n $$\chi_{896}(577, \cdot)$$ None 0 2
896.1.o $$\chi_{896}(191, \cdot)$$ None 0 2
896.1.r $$\chi_{896}(639, \cdot)$$ None 0 2
896.1.s $$\chi_{896}(129, \cdot)$$ None 0 2
896.1.v $$\chi_{896}(209, \cdot)$$ 896.1.v.a 4 4
896.1.w $$\chi_{896}(15, \cdot)$$ None 0 4
896.1.y $$\chi_{896}(95, \cdot)$$ None 0 4
896.1.bb $$\chi_{896}(33, \cdot)$$ None 0 4
896.1.be $$\chi_{896}(71, \cdot)$$ None 0 8
896.1.bf $$\chi_{896}(41, \cdot)$$ None 0 8
896.1.bg $$\chi_{896}(17, \cdot)$$ None 0 8
896.1.bj $$\chi_{896}(79, \cdot)$$ None 0 8
896.1.bl $$\chi_{896}(43, \cdot)$$ None 0 16
896.1.bm $$\chi_{896}(13, \cdot)$$ 896.1.bm.a 16 16
896.1.bo $$\chi_{896}(73, \cdot)$$ None 0 16
896.1.bp $$\chi_{896}(23, \cdot)$$ None 0 16
896.1.bs $$\chi_{896}(11, \cdot)$$ None 0 32
896.1.bv $$\chi_{896}(5, \cdot)$$ None 0 32

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(896))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(896)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(448))$$$$^{\oplus 2}$$