# Properties

 Label 891.1 Level 891 Weight 1 Dimension 26 Nonzero newspaces 3 Newform subspaces 4 Sturm bound 58320 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$891 = 3^{4} \cdot 11$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$3$$ Newform subspaces: $$4$$ Sturm bound: $$58320$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(891))$$.

Total New Old
Modular forms 1128 530 598
Cusp forms 48 26 22
Eisenstein series 1080 504 576

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 26 0 0 0

## Trace form

 $$26 q + 2 q^{4} + 3 q^{5} + O(q^{10})$$ $$26 q + 2 q^{4} + 3 q^{5} + 2 q^{16} - 15 q^{20} - 3 q^{25} - 5 q^{31} - 9 q^{36} - 2 q^{37} + 3 q^{44} + 3 q^{47} + 2 q^{49} - 2 q^{55} + 3 q^{59} - q^{64} - 5 q^{67} + 18 q^{75} + 15 q^{89} - 9 q^{93} - 5 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(891))$$

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
891.1.b $$\chi_{891}(485, \cdot)$$ None 0 1
891.1.c $$\chi_{891}(406, \cdot)$$ 891.1.c.a 1 1
891.1.c.b 1
891.1.h $$\chi_{891}(109, \cdot)$$ None 0 2
891.1.i $$\chi_{891}(188, \cdot)$$ None 0 2
891.1.l $$\chi_{891}(244, \cdot)$$ None 0 4
891.1.m $$\chi_{891}(80, \cdot)$$ None 0 4
891.1.p $$\chi_{891}(89, \cdot)$$ None 0 6
891.1.q $$\chi_{891}(10, \cdot)$$ 891.1.q.a 6 6
891.1.s $$\chi_{891}(26, \cdot)$$ None 0 8
891.1.t $$\chi_{891}(28, \cdot)$$ None 0 8
891.1.w $$\chi_{891}(43, \cdot)$$ 891.1.w.a 18 18
891.1.x $$\chi_{891}(23, \cdot)$$ None 0 18
891.1.z $$\chi_{891}(71, \cdot)$$ None 0 24
891.1.ba $$\chi_{891}(19, \cdot)$$ None 0 24
891.1.be $$\chi_{891}(5, \cdot)$$ None 0 72
891.1.bf $$\chi_{891}(7, \cdot)$$ None 0 72

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(891))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(891)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(99))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(297))$$$$^{\oplus 2}$$