# Properties

 Label 448.1 Level 448 Weight 1 Dimension 14 Nonzero newspaces 3 Newform subspaces 3 Sturm bound 12288 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$448 = 2^{6} \cdot 7$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$3$$ Newform subspaces: $$3$$ Sturm bound: $$12288$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(448))$$.

Total New Old
Modular forms 474 124 350
Cusp forms 42 14 28
Eisenstein series 432 110 322

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 10 4 0 0

## Trace form

 $$14q + 2q^{5} + O(q^{10})$$ $$14q + 2q^{5} + 2q^{11} - 2q^{17} + 2q^{21} - 8q^{22} - 2q^{29} - 2q^{33} - 4q^{37} - 2q^{43} - 8q^{44} - 6q^{49} + 8q^{56} - 4q^{57} - 2q^{61} - 10q^{63} - 10q^{67} - 4q^{69} + 2q^{73} + 8q^{74} - 4q^{85} + 2q^{89} + 2q^{93} + 2q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(448))$$

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
448.1.c $$\chi_{448}(321, \cdot)$$ None 0 1
448.1.d $$\chi_{448}(127, \cdot)$$ None 0 1
448.1.g $$\chi_{448}(351, \cdot)$$ None 0 1
448.1.h $$\chi_{448}(97, \cdot)$$ None 0 1
448.1.k $$\chi_{448}(15, \cdot)$$ None 0 2
448.1.l $$\chi_{448}(209, \cdot)$$ 448.1.l.a 2 2
448.1.n $$\chi_{448}(33, \cdot)$$ None 0 2
448.1.o $$\chi_{448}(95, \cdot)$$ None 0 2
448.1.r $$\chi_{448}(191, \cdot)$$ 448.1.r.a 4 2
448.1.s $$\chi_{448}(129, \cdot)$$ None 0 2
448.1.v $$\chi_{448}(41, \cdot)$$ None 0 4
448.1.w $$\chi_{448}(71, \cdot)$$ None 0 4
448.1.y $$\chi_{448}(79, \cdot)$$ None 0 4
448.1.bb $$\chi_{448}(17, \cdot)$$ None 0 4
448.1.be $$\chi_{448}(43, \cdot)$$ None 0 8
448.1.bf $$\chi_{448}(13, \cdot)$$ 448.1.bf.a 8 8
448.1.bg $$\chi_{448}(73, \cdot)$$ None 0 8
448.1.bj $$\chi_{448}(23, \cdot)$$ None 0 8
448.1.bk $$\chi_{448}(5, \cdot)$$ None 0 16
448.1.bl $$\chi_{448}(11, \cdot)$$ None 0 16

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(448))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(448)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 2}$$