# Properties

 Label 1764.1.z Level $1764$ Weight $1$ Character orbit 1764.z Rep. character $\chi_{1764}(325,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $2$ Newform subspaces $1$ Sturm bound $336$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1764 = 2^{2} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1764.z (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$336$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1764, [\chi])$$.

Total New Old
Modular forms 108 2 106
Cusp forms 12 2 10
Eisenstein series 96 0 96

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2q + O(q^{10})$$ $$2q + 3q^{19} - q^{25} + 3q^{31} - q^{37} + 2q^{43} + q^{67} - 3q^{73} + q^{79} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1764, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1764.1.z.a $$2$$ $$0.880$$ $$\Q(\sqrt{-3})$$ $$D_{6}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(1+\zeta_{6})q^{19}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(1764, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(1764, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(252, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(441, [\chi])$$$$^{\oplus 3}$$