# Properties

 Label 19.3.d Level $19$ Weight $3$ Character orbit 19.d Rep. character $\chi_{19}(8,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $6$ Newform subspaces $1$ Sturm bound $5$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 19.d (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$5$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

## Trace form

 $$6q - 3q^{2} - 9q^{3} + 5q^{4} - 2q^{5} + q^{6} + 14q^{9} + O(q^{10})$$ $$6q - 3q^{2} - 9q^{3} + 5q^{4} - 2q^{5} + q^{6} + 14q^{9} - 60q^{10} + 26q^{11} + 30q^{13} + 54q^{14} - 18q^{15} + q^{16} - 42q^{17} + 25q^{19} + 108q^{20} - 102q^{21} - 39q^{22} + 8q^{23} - 83q^{24} - 17q^{25} - 148q^{26} + 32q^{28} - 12q^{29} + 304q^{30} + 51q^{32} + 123q^{33} - 6q^{34} - 38q^{35} - 54q^{36} - 14q^{38} - 44q^{39} - 96q^{40} + 63q^{41} - 92q^{42} - 34q^{43} - 69q^{44} - 28q^{45} + 58q^{47} - 147q^{48} + 18q^{49} + 132q^{51} + 162q^{52} - 12q^{53} + 29q^{54} - 28q^{55} - 16q^{57} + 172q^{58} - 147q^{59} - 222q^{60} + 58q^{61} - 116q^{62} + 86q^{63} + 166q^{64} + 11q^{66} + 201q^{67} - 84q^{68} - 198q^{70} - 102q^{71} + 210q^{72} + 7q^{73} + 174q^{74} - 173q^{76} - 376q^{77} + 450q^{78} + 134q^{80} + 253q^{81} - 145q^{82} + 146q^{83} - 90q^{85} - 270q^{86} - 568q^{87} - 72q^{89} - 438q^{90} - 216q^{91} + 72q^{92} - 160q^{93} + 558q^{95} + 126q^{96} + 21q^{97} + 411q^{98} - 56q^{99} + O(q^{100})$$

## 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.d.a $$6$$ $$0.518$$ 6.0.6967728.1 None $$-3$$ $$-9$$ $$-2$$ $$0$$ $$q+(-1-\beta _{5})q^{2}+(\beta _{1}+2\beta _{2}+\beta _{3}+\beta _{5})q^{3}+\cdots$$