# Properties

 Label 18.3.b Level $18$ Weight $3$ Character orbit 18.b Rep. character $\chi_{18}(17,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $9$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$18 = 2 \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 18.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$9$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(18, [\chi])$$.

Total New Old
Modular forms 10 2 8
Cusp forms 2 2 0
Eisenstein series 8 0 8

## Trace form

 $$2 q - 4 q^{4} - 8 q^{7} + O(q^{10})$$ $$2 q - 4 q^{4} - 8 q^{7} + 12 q^{10} + 16 q^{13} + 8 q^{16} - 32 q^{19} - 48 q^{22} + 14 q^{25} + 16 q^{28} + 88 q^{31} + 36 q^{34} - 68 q^{37} - 24 q^{40} - 80 q^{43} + 48 q^{46} - 66 q^{49} - 32 q^{52} + 144 q^{55} - 12 q^{58} + 100 q^{61} - 16 q^{64} + 16 q^{67} - 48 q^{70} - 32 q^{73} + 64 q^{76} - 152 q^{79} - 132 q^{82} - 108 q^{85} + 96 q^{88} - 64 q^{91} + 240 q^{94} + 352 q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(18, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
18.3.b.a $2$ $0.490$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\beta q^{2}-2q^{4}-3\beta q^{5}-4q^{7}-2\beta q^{8}+\cdots$$