# Properties

 Label 1407.1.cz Level $1407$ Weight $1$ Character orbit 1407.cz Rep. character $\chi_{1407}(23,\cdot)$ Character field $\Q(\zeta_{66})$ Dimension $20$ Newform subspaces $1$ Sturm bound $181$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1407 = 3 \cdot 7 \cdot 67$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1407.cz (of order $$66$$ and degree $$20$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$1407$$ Character field: $$\Q(\zeta_{66})$$ Newform subspaces: $$1$$ Sturm bound: $$181$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1407, [\chi])$$.

Total New Old
Modular forms 100 100 0
Cusp forms 20 20 0
Eisenstein series 80 80 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 20 0 0 0

## Trace form

 $$20q + q^{3} - 2q^{4} + q^{7} + q^{9} + O(q^{10})$$ $$20q + q^{3} - 2q^{4} + q^{7} + q^{9} + q^{12} + 2q^{13} - 2q^{16} + 2q^{19} + q^{21} + q^{25} - 2q^{27} + q^{28} - 4q^{31} + q^{36} + 2q^{37} + 2q^{39} - 4q^{43} + q^{48} + q^{49} - 9q^{52} + 21q^{57} + 2q^{61} - 2q^{63} - 2q^{64} + q^{67} - 12q^{73} + q^{75} + 2q^{76} - 12q^{79} + q^{81} - 10q^{84} + 2q^{91} + 2q^{93} - q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1407, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1407.1.cz.a $$20$$ $$0.702$$ $$\Q(\zeta_{33})$$ $$D_{33}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$0$$ $$1$$ $$q+\zeta_{66}^{4}q^{3}-\zeta_{66}^{27}q^{4}-\zeta_{66}^{13}q^{7}+\cdots$$