# Properties

 Label 1764.1.co Level $1764$ Weight $1$ Character orbit 1764.co Rep. character $\chi_{1764}(73,\cdot)$ Character field $\Q(\zeta_{42})$ Dimension $12$ 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.co (of order $$42$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$49$$ Character field: $$\Q(\zeta_{42})$$ 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 156 12 144
Cusp forms 12 12 0
Eisenstein series 144 0 144

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 12 0 0 0

## Trace form

 $$12 q - q^{7} + O(q^{10})$$ $$12 q - q^{7} + 3 q^{19} + q^{25} + 3 q^{31} + 8 q^{37} - 2 q^{43} + q^{49} + 7 q^{61} - q^{67} - 3 q^{73} - q^{79} - 3 q^{91} + O(q^{100})$$

## 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.co.a $$12$$ $$0.880$$ $$\Q(\zeta_{21})$$ $$D_{42}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-1$$ $$q-\zeta_{42}^{16}q^{7}+(-\zeta_{42}^{8}+\zeta_{42}^{10})q^{13}+\cdots$$