# Properties

 Label 45.2.f Level $45$ Weight $2$ Character orbit 45.f Rep. character $\chi_{45}(8,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $4$ 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.f (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q(i)$$ 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 20 4 16
Cusp forms 4 4 0
Eisenstein series 16 0 16

## Trace form

 $$4 q - 8 q^{7} + O(q^{10})$$ $$4 q - 8 q^{7} - 8 q^{10} + 4 q^{13} + 4 q^{16} + 8 q^{22} + 16 q^{25} + 8 q^{28} - 16 q^{31} + 4 q^{37} - 12 q^{40} - 32 q^{43} - 16 q^{46} + 4 q^{52} + 8 q^{55} + 12 q^{58} + 32 q^{61} + 16 q^{67} + 24 q^{70} + 4 q^{73} - 4 q^{82} - 32 q^{85} - 24 q^{88} - 16 q^{91} - 44 q^{97} + O(q^{100})$$

## 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.f.a $4$ $0.359$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots$$