# Properties

 Label 869.1 Level 869 Weight 1 Dimension 20 Nonzero newspaces 1 Newform subspaces 1 Sturm bound 62400 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$869 = 11 \cdot 79$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$62400$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(869))$$.

Total New Old
Modular forms 804 712 92
Cusp forms 24 20 4
Eisenstein series 780 692 88

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 20 0 0 0

## Trace form

 $$20q - 5q^{4} - 5q^{9} + O(q^{10})$$ $$20q - 5q^{4} - 5q^{9} - 5q^{16} + 15q^{20} - 5q^{22} - 5q^{25} + 15q^{26} - 10q^{32} - 5q^{36} - 10q^{40} - 5q^{49} - 10q^{50} - 10q^{62} - 5q^{64} - 10q^{76} - 5q^{79} - 10q^{80} - 5q^{81} + 15q^{83} - 5q^{88} + 15q^{92} + 15q^{95} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(869))$$

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
869.1.c $$\chi_{869}(791, \cdot)$$ None 0 1
869.1.d $$\chi_{869}(78, \cdot)$$ None 0 1
869.1.g $$\chi_{869}(56, \cdot)$$ None 0 2
869.1.h $$\chi_{869}(450, \cdot)$$ None 0 2
869.1.j $$\chi_{869}(157, \cdot)$$ 869.1.j.a 20 4
869.1.k $$\chi_{869}(238, \cdot)$$ None 0 4
869.1.o $$\chi_{869}(12, \cdot)$$ None 0 12
869.1.p $$\chi_{869}(10, \cdot)$$ None 0 12
869.1.s $$\chi_{869}(134, \cdot)$$ None 0 8
869.1.t $$\chi_{869}(103, \cdot)$$ None 0 8
869.1.x $$\chi_{869}(32, \cdot)$$ None 0 24
869.1.y $$\chi_{869}(34, \cdot)$$ None 0 24
869.1.ba $$\chi_{869}(8, \cdot)$$ None 0 48
869.1.bb $$\chi_{869}(14, \cdot)$$ None 0 48
869.1.bd $$\chi_{869}(3, \cdot)$$ None 0 96
869.1.be $$\chi_{869}(2, \cdot)$$ None 0 96

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(869))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(869)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(79))$$$$^{\oplus 2}$$