## Defining parameters

 Level: $$N$$ = $$1152 = 2^{7} \cdot 3^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$4$$ Newform subspaces: $$6$$ Sturm bound: $$73728$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1152))$$.

Total New Old
Modular forms 1374 231 1143
Cusp forms 94 15 79
Eisenstein series 1280 216 1064

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 15 0 0 0

## Trace form

 $$15 q + O(q^{10})$$ $$15 q + 6 q^{17} - q^{25} + 4 q^{33} - 6 q^{41} - q^{49} - 12 q^{57} + 10 q^{73} - 4 q^{81} - 6 q^{89} + 2 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1152))$$

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
1152.1.b $$\chi_{1152}(703, \cdot)$$ 1152.1.b.a 1 1
1152.1.b.b 2
1152.1.e $$\chi_{1152}(1025, \cdot)$$ None 0 1
1152.1.g $$\chi_{1152}(127, \cdot)$$ None 0 1
1152.1.h $$\chi_{1152}(449, \cdot)$$ 1152.1.h.a 4 1
1152.1.j $$\chi_{1152}(161, \cdot)$$ None 0 2
1152.1.m $$\chi_{1152}(415, \cdot)$$ None 0 2
1152.1.n $$\chi_{1152}(65, \cdot)$$ 1152.1.n.a 2 2
1152.1.n.b 2
1152.1.o $$\chi_{1152}(511, \cdot)$$ None 0 2
1152.1.q $$\chi_{1152}(257, \cdot)$$ None 0 2
1152.1.t $$\chi_{1152}(319, \cdot)$$ 1152.1.t.a 4 2
1152.1.u $$\chi_{1152}(271, \cdot)$$ None 0 4
1152.1.x $$\chi_{1152}(17, \cdot)$$ None 0 4
1152.1.z $$\chi_{1152}(31, \cdot)$$ None 0 4
1152.1.ba $$\chi_{1152}(353, \cdot)$$ None 0 4
1152.1.bc $$\chi_{1152}(89, \cdot)$$ None 0 8
1152.1.bf $$\chi_{1152}(55, \cdot)$$ None 0 8
1152.1.bh $$\chi_{1152}(79, \cdot)$$ None 0 8
1152.1.bi $$\chi_{1152}(113, \cdot)$$ None 0 8
1152.1.bk $$\chi_{1152}(19, \cdot)$$ None 0 16
1152.1.bn $$\chi_{1152}(53, \cdot)$$ None 0 16
1152.1.bo $$\chi_{1152}(7, \cdot)$$ None 0 16
1152.1.br $$\chi_{1152}(41, \cdot)$$ None 0 16
1152.1.bt $$\chi_{1152}(5, \cdot)$$ None 0 32
1152.1.bu $$\chi_{1152}(43, \cdot)$$ None 0 32

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1152))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1152)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(288))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(384))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(576))$$$$^{\oplus 2}$$