# Properties

 Label 200.2.k Level $200$ Weight $2$ Character orbit 200.k Rep. character $\chi_{200}(43,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $32$ Newform subspaces $8$ Sturm bound $60$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$200 = 2^{3} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 200.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$40$$ Character field: $$\Q(i)$$ Newform subspaces: $$8$$ Sturm bound: $$60$$ Trace bound: $$3$$ 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 72 40 32
Cusp forms 48 32 16
Eisenstein series 24 8 16

## Trace form

 $$32 q + 2 q^{2} + 4 q^{3} + 4 q^{6} - 4 q^{8} + O(q^{10})$$ $$32 q + 2 q^{2} + 4 q^{3} + 4 q^{6} - 4 q^{8} - 8 q^{11} - 12 q^{12} - 28 q^{16} + 8 q^{17} - 10 q^{18} - 12 q^{22} - 52 q^{26} - 8 q^{27} + 20 q^{28} + 32 q^{32} + 16 q^{33} + 76 q^{36} + 4 q^{38} - 8 q^{41} + 20 q^{42} - 28 q^{43} + 8 q^{46} - 16 q^{48} - 40 q^{51} - 20 q^{52} - 32 q^{56} - 8 q^{57} - 20 q^{58} - 40 q^{62} - 100 q^{66} + 28 q^{67} + 4 q^{68} + 20 q^{72} - 16 q^{73} + 52 q^{76} + 40 q^{78} - 40 q^{81} + 28 q^{82} + 44 q^{83} + 96 q^{86} - 16 q^{88} + 56 q^{91} - 20 q^{92} + 44 q^{96} - 16 q^{97} + 6 q^{98} + O(q^{100})$$

## 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.k.a $2$ $1.597$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-2})$$ $$-2$$ $$-4$$ $$0$$ $$0$$ $$q+(-1-i)q^{2}+(-2+2i)q^{3}+2iq^{4}+\cdots$$
200.2.k.b $2$ $1.597$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-10})$$ $$-2$$ $$0$$ $$0$$ $$-4$$ $$q+(-1+i)q^{2}-2iq^{4}+(-2+2i)q^{7}+\cdots$$
200.2.k.c $2$ $1.597$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-10})$$ $$2$$ $$0$$ $$0$$ $$4$$ $$q+(1-i)q^{2}-2iq^{4}+(2-2i)q^{7}+(-2+\cdots)q^{8}+\cdots$$
200.2.k.d $2$ $1.597$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-2})$$ $$2$$ $$4$$ $$0$$ $$0$$ $$q+(1+i)q^{2}+(2-2i)q^{3}+2iq^{4}+4q^{6}+\cdots$$
200.2.k.e $4$ $1.597$ $$\Q(i, \sqrt{6})$$ $$\Q(\sqrt{-2})$$ $$-4$$ $$4$$ $$0$$ $$0$$ $$q+(-1-\beta _{2})q^{2}+(1-\beta _{2}+\beta _{3})q^{3}+\cdots$$
200.2.k.f $4$ $1.597$ $$\Q(i, \sqrt{6})$$ $$\Q(\sqrt{-2})$$ $$4$$ $$-4$$ $$0$$ $$0$$ $$q+(1+\beta _{2})q^{2}+(-1+\beta _{2}-\beta _{3})q^{3}+\cdots$$
200.2.k.g $8$ $1.597$ 8.0.3317760000.5 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{3}+\beta _{2}q^{4}+(2+\cdots)q^{6}+\cdots$$
200.2.k.h $8$ $1.597$ $$\Q(\zeta_{20})$$ None $$2$$ $$4$$ $$0$$ $$0$$ $$q+\zeta_{20}^{7}q^{2}+(1-\zeta_{20}^{3}-\zeta_{20}^{5}+\zeta_{20}^{6}+\cdots)q^{3}+\cdots$$

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

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