# Properties

 Label 189.1 Level 189 Weight 1 Dimension 4 Nonzero newspaces 2 Newform subspaces 2 Sturm bound 2592 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$189 = 3^{3} \cdot 7$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$2592$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(189))$$.

Total New Old
Modular forms 186 84 102
Cusp forms 6 4 2
Eisenstein series 180 80 100

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

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

## Trace form

 $$4q + O(q^{10})$$ $$4q - 2q^{13} - 2q^{16} - 2q^{19} - 2q^{25} - 2q^{28} - 2q^{31} + 4q^{49} + 4q^{52} + 4q^{61} + 2q^{67} - 2q^{73} + 4q^{76} + 2q^{79} - 2q^{91} - 2q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(189))$$

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
189.1.b $$\chi_{189}(134, \cdot)$$ None 0 1
189.1.d $$\chi_{189}(55, \cdot)$$ None 0 1
189.1.j $$\chi_{189}(44, \cdot)$$ None 0 2
189.1.k $$\chi_{189}(10, \cdot)$$ None 0 2
189.1.l $$\chi_{189}(118, \cdot)$$ None 0 2
189.1.m $$\chi_{189}(82, \cdot)$$ 189.1.m.a 2 2
189.1.n $$\chi_{189}(170, \cdot)$$ None 0 2
189.1.q $$\chi_{189}(53, \cdot)$$ 189.1.q.a 2 2
189.1.r $$\chi_{189}(8, \cdot)$$ None 0 2
189.1.t $$\chi_{189}(73, \cdot)$$ None 0 2
189.1.x $$\chi_{189}(40, \cdot)$$ None 0 6
189.1.y $$\chi_{189}(13, \cdot)$$ None 0 6
189.1.z $$\chi_{189}(31, \cdot)$$ None 0 6
189.1.bb $$\chi_{189}(29, \cdot)$$ None 0 6
189.1.bc $$\chi_{189}(2, \cdot)$$ None 0 6
189.1.bf $$\chi_{189}(11, \cdot)$$ None 0 6

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(189))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(189)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 2}$$