# Properties

 Label 200.2.v Level $200$ Weight $2$ Character orbit 200.v Rep. character $\chi_{200}(3,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $224$ Newform subspaces $3$ 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.v (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$200$$ Character field: $$\Q(\zeta_{20})$$ Newform subspaces: $$3$$ 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 256 256 0
Cusp forms 224 224 0
Eisenstein series 32 32 0

## Trace form

 $$224q - 8q^{2} - 16q^{3} - 10q^{4} - 6q^{6} - 14q^{8} - 20q^{9} + O(q^{10})$$ $$224q - 8q^{2} - 16q^{3} - 10q^{4} - 6q^{6} - 14q^{8} - 20q^{9} - 12q^{11} - 22q^{12} - 10q^{14} - 6q^{16} - 12q^{17} - 20q^{18} - 20q^{19} - 10q^{20} - 22q^{22} - 20q^{25} - 16q^{26} - 28q^{27} + 10q^{28} - 30q^{30} + 22q^{32} - 4q^{33} - 10q^{34} - 40q^{35} - 22q^{36} - 36q^{38} + 60q^{40} - 12q^{41} - 90q^{42} - 48q^{43} + 60q^{44} - 6q^{46} + 104q^{48} - 90q^{50} - 32q^{51} + 60q^{52} - 140q^{54} - 6q^{56} - 28q^{57} - 100q^{58} - 20q^{59} + 70q^{60} - 100q^{62} + 20q^{64} - 20q^{65} + 18q^{66} + 8q^{67} - 6q^{68} - 30q^{70} + 40q^{72} - 36q^{73} + 40q^{75} - 32q^{76} - 10q^{80} + 12q^{81} + 58q^{82} + 24q^{83} + 70q^{84} - 6q^{86} + 94q^{88} - 120q^{89} + 150q^{90} - 12q^{91} + 70q^{92} + 150q^{94} - 26q^{96} + 44q^{97} + 156q^{98} + O(q^{100})$$

## 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.v.a $$8$$ $$1.597$$ $$\Q(\zeta_{20})$$ None $$-8$$ $$0$$ $$10$$ $$4$$ $$q+(-1+\zeta_{20}^{5})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots$$
200.2.v.b $$8$$ $$1.597$$ $$\Q(\zeta_{20})$$ None $$-2$$ $$0$$ $$-10$$ $$-4$$ $$q+(-\zeta_{20}-\zeta_{20}^{6})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots$$
200.2.v.c $$208$$ $$1.597$$ None $$2$$ $$-16$$ $$0$$ $$0$$