# Properties

 Label 45.2.b Level $45$ Weight $2$ Character orbit 45.b Rep. character $\chi_{45}(19,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $12$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$45 = 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 45.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(45, [\chi])$$.

Total New Old
Modular forms 10 4 6
Cusp forms 2 2 0
Eisenstein series 8 2 6

## Trace form

 $$2 q - 6 q^{4} + O(q^{10})$$ $$2 q - 6 q^{4} + 10 q^{10} - 2 q^{16} - 8 q^{19} - 10 q^{25} + 16 q^{31} + 20 q^{34} - 10 q^{40} - 40 q^{46} + 14 q^{49} + 4 q^{61} + 26 q^{64} + 24 q^{76} - 32 q^{79} - 20 q^{85} - 40 q^{94} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(45, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.2.b.a $2$ $0.359$ $$\Q(\sqrt{-5})$$ $$\Q(\sqrt{-15})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{2}-3q^{4}-\beta q^{5}-\beta q^{8}+5q^{10}+\cdots$$