# Properties

 Label 200.1.e Level 200 Weight 1 Character orbit e Rep. character $$\chi_{200}(99,\cdot)$$ Character field $$\Q$$ Dimension 2 Newform subspaces 1 Sturm bound 30 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$200 = 2^{3} \cdot 5^{2}$$ Weight: $$k$$ = $$1$$ Character orbit: $$[\chi]$$ = 200.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$40$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$30$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(200, [\chi])$$.

Total New Old
Modular forms 8 4 4
Cusp forms 2 2 0
Eisenstein series 6 2 4

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2q - 2q^{4} - 2q^{6} + O(q^{10})$$ $$2q - 2q^{4} - 2q^{6} - 2q^{11} + 2q^{16} + 2q^{19} + 2q^{24} + 2q^{34} - 2q^{41} + 2q^{44} - 2q^{49} + 2q^{51} - 2q^{54} - 4q^{59} - 2q^{64} + 2q^{66} - 2q^{76} - 2q^{81} + 4q^{86} + 2q^{89} - 2q^{96} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(200, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
200.1.e.a $$2$$ $$0.100$$ $$\Q(\sqrt{-1})$$ $$D_{3}$$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}-q^{11}+\cdots$$