# Properties

 Label 200.1 Level 200 Weight 1 Dimension 4 Nonzero newspaces 2 Newforms 3 Sturm bound 2400 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$200 = 2^{3} \cdot 5^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newforms: $$3$$ Sturm bound: $$2400$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(200))$$.

Total New Old
Modular forms 180 45 135
Cusp forms 12 4 8
Eisenstein series 168 41 127

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

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

## Trace form

 $$4q$$ $$\mathstrut -\mathstrut 4q^{6}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$4q$$ $$\mathstrut -\mathstrut 4q^{6}$$ $$\mathstrut -\mathstrut 4q^{11}$$ $$\mathstrut +\mathstrut 4q^{16}$$ $$\mathstrut -\mathstrut 4q^{41}$$ $$\mathstrut +\mathstrut 4q^{51}$$ $$\mathstrut +\mathstrut 4q^{66}$$ $$\mathstrut -\mathstrut 4q^{76}$$ $$\mathstrut -\mathstrut 4q^{81}$$ $$\mathstrut +\mathstrut 8q^{86}$$ $$\mathstrut -\mathstrut 4q^{96}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(200))$$

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
200.1.b $$\chi_{200}(151, \cdot)$$ None 0 1
200.1.e $$\chi_{200}(99, \cdot)$$ 200.1.e.a 2 1
200.1.g $$\chi_{200}(51, \cdot)$$ 200.1.g.a 1 1
200.1.g.b 1
200.1.h $$\chi_{200}(199, \cdot)$$ None 0 1
200.1.i $$\chi_{200}(93, \cdot)$$ None 0 2
200.1.l $$\chi_{200}(57, \cdot)$$ None 0 2
200.1.n $$\chi_{200}(11, \cdot)$$ None 0 4
200.1.p $$\chi_{200}(39, \cdot)$$ None 0 4
200.1.r $$\chi_{200}(31, \cdot)$$ None 0 4
200.1.s $$\chi_{200}(19, \cdot)$$ None 0 4
200.1.u $$\chi_{200}(17, \cdot)$$ None 0 8
200.1.x $$\chi_{200}(13, \cdot)$$ None 0 8

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(200))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(200)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 2}$$