# Properties

 Label 19.3.b Level $19$ Weight $3$ Character orbit 19.b Rep. character $\chi_{19}(18,\cdot)$ Character field $\Q$ Dimension $3$ Newform subspaces $2$ Sturm bound $5$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 19.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$5$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(19, [\chi])$$.

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

## Trace form

 $$3 q - 14 q^{4} - q^{5} + 26 q^{6} - 15 q^{7} + q^{9} + O(q^{10})$$ $$3 q - 14 q^{4} - q^{5} + 26 q^{6} - 15 q^{7} + q^{9} - 17 q^{11} + 74 q^{16} + 45 q^{17} - 31 q^{19} - 108 q^{20} + 40 q^{23} - 130 q^{24} + 38 q^{25} - 26 q^{26} + 70 q^{28} + 104 q^{30} + 5 q^{35} + 108 q^{36} - 130 q^{38} + 26 q^{39} - 130 q^{42} - 125 q^{43} + 192 q^{44} - 113 q^{45} + 95 q^{47} - 72 q^{49} + 130 q^{54} - 107 q^{55} + 130 q^{57} - 130 q^{58} + 23 q^{61} + 260 q^{62} - 5 q^{63} + 62 q^{64} - 260 q^{66} - 210 q^{68} + 185 q^{73} + 156 q^{74} + 32 q^{76} + 85 q^{77} + 88 q^{80} - 121 q^{81} - 260 q^{82} + 10 q^{83} - 15 q^{85} + 130 q^{87} - 750 q^{92} - 260 q^{93} + 123 q^{95} + 234 q^{96} + 107 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(19, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
19.3.b.a $1$ $0.518$ $$\Q$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$-9$$ $$-5$$ $$q+4q^{4}-9q^{5}-5q^{7}+9q^{9}+3q^{11}+\cdots$$
19.3.b.b $2$ $0.518$ $$\Q(\sqrt{-13})$$ None $$0$$ $$0$$ $$8$$ $$-10$$ $$q+\beta q^{2}-\beta q^{3}-9q^{4}+4q^{5}+13q^{6}+\cdots$$