## Defining parameters

 Level: $$N$$ = $$1792 = 2^{8} \cdot 7$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$5$$ Newform subspaces: $$10$$ Sturm bound: $$196608$$ Trace bound: $$53$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1792))$$.

Total New Old
Modular forms 2330 582 1748
Cusp forms 218 62 156
Eisenstein series 2112 520 1592

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 54 8 0 0

## Trace form

 $$62q - 2q^{9} + O(q^{10})$$ $$62q - 2q^{9} - 4q^{17} - 2q^{25} - 4q^{33} - 2q^{49} + 8q^{53} + 16q^{57} + 8q^{63} - 8q^{65} + 8q^{67} - 4q^{73} + 8q^{77} + 2q^{81} - 4q^{89} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1792))$$

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
1792.1.c $$\chi_{1792}(769, \cdot)$$ 1792.1.c.a 1 1
1792.1.c.b 1
1792.1.c.c 2
1792.1.c.d 2
1792.1.d $$\chi_{1792}(1023, \cdot)$$ None 0 1
1792.1.g $$\chi_{1792}(127, \cdot)$$ None 0 1
1792.1.h $$\chi_{1792}(1665, \cdot)$$ None 0 1
1792.1.k $$\chi_{1792}(575, \cdot)$$ None 0 2
1792.1.l $$\chi_{1792}(321, \cdot)$$ None 0 2
1792.1.n $$\chi_{1792}(129, \cdot)$$ None 0 2
1792.1.o $$\chi_{1792}(639, \cdot)$$ 1792.1.o.a 4 2
1792.1.o.b 4
1792.1.r $$\chi_{1792}(767, \cdot)$$ None 0 2
1792.1.s $$\chi_{1792}(257, \cdot)$$ None 0 2
1792.1.v $$\chi_{1792}(97, \cdot)$$ 1792.1.v.a 4 4
1792.1.v.b 4
1792.1.w $$\chi_{1792}(351, \cdot)$$ None 0 4
1792.1.y $$\chi_{1792}(191, \cdot)$$ None 0 4
1792.1.bb $$\chi_{1792}(577, \cdot)$$ None 0 4
1792.1.be $$\chi_{1792}(15, \cdot)$$ None 0 8
1792.1.bf $$\chi_{1792}(209, \cdot)$$ 1792.1.bf.a 8 8
1792.1.bg $$\chi_{1792}(33, \cdot)$$ None 0 8
1792.1.bj $$\chi_{1792}(95, \cdot)$$ None 0 8
1792.1.bl $$\chi_{1792}(71, \cdot)$$ None 0 16
1792.1.bm $$\chi_{1792}(41, \cdot)$$ None 0 16
1792.1.bo $$\chi_{1792}(17, \cdot)$$ None 0 16
1792.1.bp $$\chi_{1792}(79, \cdot)$$ None 0 16
1792.1.bt $$\chi_{1792}(13, \cdot)$$ 1792.1.bt.a 32 32
1792.1.bu $$\chi_{1792}(43, \cdot)$$ None 0 32
1792.1.bw $$\chi_{1792}(23, \cdot)$$ None 0 32
1792.1.bz $$\chi_{1792}(73, \cdot)$$ None 0 32
1792.1.ca $$\chi_{1792}(5, \cdot)$$ None 0 64
1792.1.cd $$\chi_{1792}(11, \cdot)$$ None 0 64

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1792))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1792)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(256))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(448))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(896))$$$$^{\oplus 2}$$