# Properties

 Label 19.7.b Level $19$ Weight $7$ Character orbit 19.b Rep. character $\chi_{19}(18,\cdot)$ Character field $\Q$ Dimension $9$ Newform subspaces $2$ Sturm bound $11$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$19$$ Weight: $$k$$ $$=$$ $$7$$ 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: $$11$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(19, [\chi])$$.

Total New Old
Modular forms 11 11 0
Cusp forms 9 9 0
Eisenstein series 2 2 0

## Trace form

 $$9q - 390q^{4} + 54q^{5} - 358q^{6} + 470q^{7} - 323q^{9} + O(q^{10})$$ $$9q - 390q^{4} + 54q^{5} - 358q^{6} + 470q^{7} - 323q^{9} - 3086q^{11} + 15642q^{16} - 3622q^{17} + 13693q^{19} - 14188q^{20} - 29642q^{23} + 64310q^{24} + 65783q^{25} - 37522q^{26} - 96778q^{28} - 187696q^{30} + 177860q^{35} + 81708q^{36} + 103318q^{38} + 43724q^{39} - 429970q^{42} + 118170q^{43} + 625544q^{44} - 230378q^{45} - 175398q^{47} - 47421q^{49} + 390202q^{54} + 4868q^{55} - 186860q^{57} - 405186q^{58} - 111610q^{61} - 1461908q^{62} + 307282q^{63} - 595914q^{64} + 1539556q^{66} + 627590q^{68} + 864018q^{73} + 2645844q^{74} - 3008264q^{76} - 2403120q^{77} + 2123488q^{80} - 3748207q^{81} + 1847172q^{82} - 647990q^{83} + 2631800q^{85} + 2802652q^{87} + 5224538q^{92} + 1507528q^{93} - 2013502q^{95} - 8462238q^{96} - 245974q^{99} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(19, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
19.7.b.a $$1$$ $$4.371$$ $$\Q$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$-54$$ $$610$$ $$q+2^{6}q^{4}-54q^{5}+610q^{7}+3^{6}q^{9}+\cdots$$
19.7.b.b $$8$$ $$4.371$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$108$$ $$-140$$ $$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-57+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$$