# Properties

 Label 192.1 Level 192 Weight 1 Dimension 2 Nonzero newspaces 1 Newform subspaces 1 Sturm bound 2048 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$192 = 2^{6} \cdot 3$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$2048$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(192))$$.

Total New Old
Modular forms 146 24 122
Cusp forms 2 2 0
Eisenstein series 144 22 122

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2q - 2q^{9} + O(q^{10})$$ $$2q - 2q^{9} - 2q^{25} - 2q^{49} + 4q^{57} + 4q^{73} + 2q^{81} - 4q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(192))$$

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
192.1.b $$\chi_{192}(31, \cdot)$$ None 0 1
192.1.e $$\chi_{192}(65, \cdot)$$ None 0 1
192.1.g $$\chi_{192}(127, \cdot)$$ None 0 1
192.1.h $$\chi_{192}(161, \cdot)$$ 192.1.h.a 2 1
192.1.i $$\chi_{192}(17, \cdot)$$ None 0 2
192.1.l $$\chi_{192}(79, \cdot)$$ None 0 2
192.1.m $$\chi_{192}(7, \cdot)$$ None 0 4
192.1.p $$\chi_{192}(41, \cdot)$$ None 0 4
192.1.q $$\chi_{192}(5, \cdot)$$ None 0 8
192.1.t $$\chi_{192}(19, \cdot)$$ None 0 8