# Properties

 Label 200.2.d Level $200$ Weight $2$ Character orbit 200.d Rep. character $\chi_{200}(101,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $6$ Sturm bound $60$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$200 = 2^{3} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 200.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$60$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(200, [\chi])$$.

Total New Old
Modular forms 36 22 14
Cusp forms 24 16 8
Eisenstein series 12 6 6

## Trace form

 $$16 q + 2 q^{2} - 2 q^{4} - 10 q^{6} + 4 q^{7} + 8 q^{8} - 8 q^{9} + O(q^{10})$$ $$16 q + 2 q^{2} - 2 q^{4} - 10 q^{6} + 4 q^{7} + 8 q^{8} - 8 q^{9} + 4 q^{12} - 14 q^{16} - 14 q^{18} - 4 q^{22} + 4 q^{23} + 14 q^{24} + 12 q^{26} - 12 q^{28} - 8 q^{31} - 8 q^{32} - 8 q^{33} - 6 q^{34} + 4 q^{36} + 20 q^{38} + 4 q^{42} + 6 q^{44} - 20 q^{47} + 24 q^{48} + 8 q^{49} + 26 q^{54} - 48 q^{56} - 8 q^{57} - 24 q^{58} - 16 q^{62} + 20 q^{63} - 14 q^{64} + 42 q^{66} - 24 q^{68} - 8 q^{72} - 16 q^{73} - 36 q^{74} + 30 q^{76} + 24 q^{78} + 40 q^{79} - 32 q^{81} + 8 q^{82} - 24 q^{84} - 12 q^{86} + 48 q^{87} + 16 q^{88} + 36 q^{92} - 48 q^{94} + 14 q^{96} + 16 q^{97} - 18 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(200, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
200.2.d.a $2$ $1.597$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$0$$ $$-4$$ $$q+(-1+i)q^{2}-iq^{3}-2iq^{4}+(1+i)q^{6}+\cdots$$
200.2.d.b $2$ $1.597$ $$\Q(\sqrt{-7})$$ None $$-1$$ $$0$$ $$0$$ $$-8$$ $$q-\beta q^{2}+(1-2\beta )q^{3}+(-2+\beta )q^{4}+\cdots$$
200.2.d.c $2$ $1.597$ $$\Q(\sqrt{-7})$$ None $$1$$ $$0$$ $$0$$ $$8$$ $$q+\beta q^{2}+(-1+2\beta )q^{3}+(-2+\beta )q^{4}+\cdots$$
200.2.d.d $2$ $1.597$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$0$$ $$4$$ $$q+(1+i)q^{2}-iq^{3}+2iq^{4}+(1-i)q^{6}+\cdots$$
200.2.d.e $4$ $1.597$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots$$
200.2.d.f $4$ $1.597$ $$\Q(\zeta_{12})$$ None $$2$$ $$0$$ $$0$$ $$4$$ $$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(200, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(200, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 2}$$