# Properties

 Label 840.1.bp Level $840$ Weight $1$ Character orbit 840.bp Rep. character $\chi_{840}(293,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $24$ Newform subspaces $4$ Sturm bound $192$ Trace bound $14$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$840 = 2^{3} \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 840.bp (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$840$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$192$$ Trace bound: $$14$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(840, [\chi])$$.

Total New Old
Modular forms 40 40 0
Cusp forms 24 24 0
Eisenstein series 16 16 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 24 0 0 0

## Trace form

 $$24q - 4q^{7} + O(q^{10})$$ $$24q - 4q^{7} + 8q^{15} - 24q^{16} + 8q^{18} - 8q^{22} + 4q^{28} - 8q^{36} + 4q^{42} + 8q^{57} - 8q^{58} - 8q^{60} - 4q^{63} + 4q^{70} - 8q^{72} - 8q^{78} - 8q^{81} + 8q^{88} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(840, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
840.1.bp.a $$4$$ $$0.419$$ $$\Q(\zeta_{8})$$ $$D_{4}$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\zeta_{8}^{3}q^{2}+\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}+\cdots$$
840.1.bp.b $$4$$ $$0.419$$ $$\Q(\zeta_{8})$$ $$D_{4}$$ $$\Q(\sqrt{-6})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+\cdots$$
840.1.bp.c $$8$$ $$0.419$$ $$\Q(\zeta_{16})$$ $$D_{8}$$ $$\Q(\sqrt{-14})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{5}q^{3}+\zeta_{16}^{4}q^{4}+\cdots$$
840.1.bp.d $$8$$ $$0.419$$ $$\Q(\zeta_{16})$$ $$D_{8}$$ $$\Q(\sqrt{-14})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{3}q^{3}+\zeta_{16}^{4}q^{4}+\cdots$$