# Properties

 Label 208.1 Level 208 Weight 1 Dimension 3 Nonzero newspaces 2 Newform subspaces 2 Sturm bound 2688 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$208 = 2^{4} \cdot 13$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$2688$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(208))$$.

Total New Old
Modular forms 181 53 128
Cusp forms 13 3 10
Eisenstein series 168 50 118

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 3 0 0 0

## Trace form

 $$3q + O(q^{10})$$ $$3q - 3q^{17} - 3q^{25} - 3q^{29} - 3q^{37} + 3q^{41} + 3q^{45} + 3q^{61} + 3q^{65} + 3q^{85} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(208))$$

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
208.1.c $$\chi_{208}(207, \cdot)$$ 208.1.c.a 1 1
208.1.d $$\chi_{208}(79, \cdot)$$ None 0 1
208.1.g $$\chi_{208}(183, \cdot)$$ None 0 1
208.1.h $$\chi_{208}(103, \cdot)$$ None 0 1
208.1.j $$\chi_{208}(57, \cdot)$$ None 0 2
208.1.m $$\chi_{208}(21, \cdot)$$ None 0 2
208.1.o $$\chi_{208}(51, \cdot)$$ None 0 2
208.1.q $$\chi_{208}(27, \cdot)$$ None 0 2
208.1.r $$\chi_{208}(5, \cdot)$$ None 0 2
208.1.t $$\chi_{208}(161, \cdot)$$ None 0 2
208.1.v $$\chi_{208}(55, \cdot)$$ None 0 2
208.1.x $$\chi_{208}(23, \cdot)$$ None 0 2
208.1.y $$\chi_{208}(95, \cdot)$$ 208.1.y.a 2 2
208.1.bb $$\chi_{208}(159, \cdot)$$ None 0 2
208.1.bd $$\chi_{208}(33, \cdot)$$ None 0 4
208.1.be $$\chi_{208}(37, \cdot)$$ None 0 4
208.1.bg $$\chi_{208}(3, \cdot)$$ None 0 4
208.1.bi $$\chi_{208}(43, \cdot)$$ None 0 4
208.1.bl $$\chi_{208}(141, \cdot)$$ None 0 4
208.1.bn $$\chi_{208}(41, \cdot)$$ None 0 4

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(208))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(208)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 2}$$