# Properties

 Label 1536.1 Level 1536 Weight 1 Dimension 16 Nonzero newspaces 2 Newform subspaces 5 Sturm bound 131072 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$1536 = 2^{9} \cdot 3$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$5$$ Sturm bound: $$131072$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1536))$$.

Total New Old
Modular forms 1616 240 1376
Cusp forms 80 16 64
Eisenstein series 1536 224 1312

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 16 0 0 0

## Trace form

 $$16q + O(q^{10})$$ $$16q + 8q^{33} - 16q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1536))$$

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
1536.1.b $$\chi_{1536}(1279, \cdot)$$ None 0 1
1536.1.e $$\chi_{1536}(1025, \cdot)$$ 1536.1.e.a 4 1
1536.1.e.b 4
1536.1.g $$\chi_{1536}(511, \cdot)$$ None 0 1
1536.1.h $$\chi_{1536}(257, \cdot)$$ 1536.1.h.a 2 1
1536.1.h.b 2
1536.1.h.c 4
1536.1.i $$\chi_{1536}(641, \cdot)$$ None 0 2
1536.1.l $$\chi_{1536}(127, \cdot)$$ None 0 2
1536.1.m $$\chi_{1536}(319, \cdot)$$ None 0 4
1536.1.p $$\chi_{1536}(65, \cdot)$$ None 0 4
1536.1.q $$\chi_{1536}(161, \cdot)$$ None 0 8
1536.1.t $$\chi_{1536}(31, \cdot)$$ None 0 8
1536.1.u $$\chi_{1536}(79, \cdot)$$ None 0 16
1536.1.x $$\chi_{1536}(17, \cdot)$$ None 0 16
1536.1.y $$\chi_{1536}(41, \cdot)$$ None 0 32
1536.1.bb $$\chi_{1536}(7, \cdot)$$ None 0 32
1536.1.bc $$\chi_{1536}(19, \cdot)$$ None 0 64
1536.1.bf $$\chi_{1536}(5, \cdot)$$ None 0 64

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1536))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1536)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(256))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(384))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(512))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(768))$$$$^{\oplus 2}$$