# Properties

 Label 1764.1.q Level $1764$ Weight $1$ Character orbit 1764.q Rep. character $\chi_{1764}(215,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $24$ Newform subspaces $2$ Sturm bound $336$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1764 = 2^{2} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1764.q (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$84$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$336$$ Trace bound: $$1$$

## Dimensions

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

Total New Old
Modular forms 88 24 64
Cusp forms 24 24 0
Eisenstein series 64 0 64

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

 $$24q + 8q^{4} + O(q^{10})$$ $$24q + 8q^{4} - 4q^{16} - 8q^{22} - 4q^{25} - 4q^{46} - 4q^{58} - 16q^{64} - 4q^{88} + O(q^{100})$$

## 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.q.a $$8$$ $$0.880$$ $$\Q(\zeta_{24})$$ $$D_{4}$$ $$\Q(\sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{9}q^{8}+\cdots$$
1764.1.q.b $$16$$ $$0.880$$ $$\Q(\zeta_{48})$$ $$D_{8}$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{48}^{20}q^{2}-\zeta_{48}^{16}q^{4}+(-\zeta_{48}^{5}+\cdots)q^{5}+\cdots$$