# Properties

 Label 1045.1.br Level $1045$ Weight $1$ Character orbit 1045.br Rep. character $\chi_{1045}(18,\cdot)$ Character field $\Q(\zeta_{20})$ Dimension $16$ Newform subspaces $2$ Sturm bound $120$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1045 = 5 \cdot 11 \cdot 19$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1045.br (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1045$$ Character field: $$\Q(\zeta_{20})$$ Newform subspaces: $$2$$ Sturm bound: $$120$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1045, [\chi])$$.

Total New Old
Modular forms 48 48 0
Cusp forms 16 16 0
Eisenstein series 32 32 0

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 16 0 0 0

## Trace form

 $$16 q - 4 q^{5} - 10 q^{7} + O(q^{10})$$ $$16 q - 4 q^{5} - 10 q^{7} + 4 q^{16} - 10 q^{17} + 4 q^{23} - 4 q^{25} + 4 q^{36} - 4 q^{47} + 10 q^{63} + 10 q^{68} - 4 q^{77} - 6 q^{80} + 4 q^{81} - 4 q^{92} - 10 q^{95} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1045, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1045.1.br.a $8$ $0.522$ $$\Q(\zeta_{20})$$ $D_{20}$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-2$$ $$-8$$ $$q-\zeta_{20}^{3}q^{4}+\zeta_{20}^{4}q^{5}+(-1-\zeta_{20}+\cdots)q^{7}+\cdots$$
1045.1.br.b $8$ $0.522$ $$\Q(\zeta_{20})$$ $D_{20}$ $$\Q(\sqrt{-19})$$ None $$0$$ $$0$$ $$-2$$ $$-2$$ $$q-\zeta_{20}^{3}q^{4}+\zeta_{20}^{8}q^{5}+(\zeta_{20}^{5}-\zeta_{20}^{6}+\cdots)q^{7}+\cdots$$