# Properties

 Label 19.5.b Level $19$ Weight $5$ Character orbit 19.b Rep. character $\chi_{19}(18,\cdot)$ Character field $\Q$ Dimension $5$ Newform subspaces $2$ Sturm bound $8$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$19$$ Weight: $$k$$ $$=$$ $$5$$ 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: $$8$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(19, [\chi])$$.

Total New Old
Modular forms 7 7 0
Cusp forms 5 5 0
Eisenstein series 2 2 0

## Trace form

 $$5q + 10q^{4} - 11q^{5} + 26q^{6} + 63q^{7} - 197q^{9} + O(q^{10})$$ $$5q + 10q^{4} - 11q^{5} + 26q^{6} + 63q^{7} - 197q^{9} - 11q^{11} - 198q^{16} - 53q^{17} + 475q^{19} + 340q^{20} - 236q^{23} + 1910q^{24} - 1650q^{25} + 414q^{26} - 58q^{28} - 784q^{30} - 4129q^{35} - 5076q^{36} + 2166q^{38} + 6362q^{39} + 3950q^{42} + 6513q^{43} - 7784q^{44} + 7693q^{45} - 6371q^{47} + 576q^{49} - 15542q^{54} - 8313q^{55} + 10450q^{57} + 14638q^{58} + 3325q^{61} + 18396q^{62} - 28943q^{63} + 7590q^{64} - 7244q^{66} - 842q^{68} - 25201q^{73} - 17868q^{74} + 18088q^{76} + 17111q^{77} + 9856q^{80} + 47273q^{81} - 29164q^{82} + 27598q^{83} - 15845q^{85} - 7214q^{87} - 27158q^{92} - 40004q^{93} + 5833q^{95} + 47538q^{96} + 4169q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(19, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
19.5.b.a $$1$$ $$1.964$$ $$\Q$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$31$$ $$-73$$ $$q+2^{4}q^{4}+31q^{5}-73q^{7}+3^{4}q^{9}+\cdots$$
19.5.b.b $$4$$ $$1.964$$ 4.0.12107488.1 None $$0$$ $$0$$ $$-42$$ $$136$$ $$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-3+3\beta _{2})q^{4}+\cdots$$