# Properties

 Label 384.1 Level 384 Weight 1 Dimension 2 Nonzero newspaces 1 Newform subspaces 2 Sturm bound 8192 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$384 = 2^{7} \cdot 3$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$2$$ Sturm bound: $$8192$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(384))$$.

Total New Old
Modular forms 328 50 278
Cusp forms 8 2 6
Eisenstein series 320 48 272

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

 $$2q + 2q^{9} + O(q^{10})$$ $$2q + 2q^{9} - 2q^{25} - 4q^{33} - 2q^{49} - 4q^{73} + 2q^{81} + 4q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(384))$$

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
384.1.b $$\chi_{384}(319, \cdot)$$ None 0 1
384.1.e $$\chi_{384}(257, \cdot)$$ None 0 1
384.1.g $$\chi_{384}(127, \cdot)$$ None 0 1
384.1.h $$\chi_{384}(65, \cdot)$$ 384.1.h.a 1 1
384.1.h.b 1
384.1.i $$\chi_{384}(161, \cdot)$$ None 0 2
384.1.l $$\chi_{384}(31, \cdot)$$ None 0 2
384.1.m $$\chi_{384}(79, \cdot)$$ None 0 4
384.1.p $$\chi_{384}(17, \cdot)$$ None 0 4
384.1.q $$\chi_{384}(41, \cdot)$$ None 0 8
384.1.t $$\chi_{384}(7, \cdot)$$ None 0 8
384.1.u $$\chi_{384}(19, \cdot)$$ None 0 16
384.1.x $$\chi_{384}(5, \cdot)$$ None 0 16

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(384))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(384)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 2}$$