# Properties

 Label 784.1 Level 784 Weight 1 Dimension 16 Nonzero newspaces 5 Newform subspaces 5 Sturm bound 37632 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$784 = 2^{4} \cdot 7^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$5$$ Newform subspaces: $$5$$ Sturm bound: $$37632$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(784))$$.

Total New Old
Modular forms 895 234 661
Cusp forms 55 16 39
Eisenstein series 840 218 622

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

 $$16 q + 2 q^{4} + O(q^{10})$$ $$16 q + 2 q^{4} + 2 q^{11} - 2 q^{16} - 2 q^{18} - 2 q^{22} + 2 q^{29} + 2 q^{37} - 2 q^{43} - 2 q^{44} - 10 q^{50} - 2 q^{53} + 2 q^{58} - 10 q^{64} - 2 q^{67} + 2 q^{72} - 2 q^{74} + 2 q^{81} - 12 q^{85} + 2 q^{86} + 2 q^{88} + 12 q^{92} - 10 q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(784))$$

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
784.1.c $$\chi_{784}(97, \cdot)$$ None 0 1
784.1.d $$\chi_{784}(687, \cdot)$$ 784.1.d.a 2 1
784.1.g $$\chi_{784}(295, \cdot)$$ None 0 1
784.1.h $$\chi_{784}(489, \cdot)$$ None 0 1
784.1.k $$\chi_{784}(99, \cdot)$$ 784.1.k.a 2 2
784.1.l $$\chi_{784}(293, \cdot)$$ None 0 2
784.1.n $$\chi_{784}(313, \cdot)$$ None 0 2
784.1.o $$\chi_{784}(263, \cdot)$$ None 0 2
784.1.r $$\chi_{784}(79, \cdot)$$ 784.1.r.a 4 2
784.1.s $$\chi_{784}(129, \cdot)$$ None 0 2
784.1.v $$\chi_{784}(67, \cdot)$$ 784.1.v.a 4 4
784.1.y $$\chi_{784}(117, \cdot)$$ 784.1.y.a 4 4
784.1.z $$\chi_{784}(41, \cdot)$$ None 0 6
784.1.ba $$\chi_{784}(71, \cdot)$$ None 0 6
784.1.bd $$\chi_{784}(15, \cdot)$$ None 0 6
784.1.be $$\chi_{784}(209, \cdot)$$ None 0 6
784.1.bi $$\chi_{784}(13, \cdot)$$ None 0 12
784.1.bj $$\chi_{784}(43, \cdot)$$ None 0 12
784.1.bm $$\chi_{784}(17, \cdot)$$ None 0 12
784.1.bn $$\chi_{784}(95, \cdot)$$ None 0 12
784.1.bq $$\chi_{784}(23, \cdot)$$ None 0 12
784.1.br $$\chi_{784}(73, \cdot)$$ None 0 12
784.1.bs $$\chi_{784}(5, \cdot)$$ None 0 24
784.1.bv $$\chi_{784}(11, \cdot)$$ None 0 24

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(784))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(784)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(392))$$$$^{\oplus 2}$$