# Properties

 Label 1764.1.y Level $1764$ Weight $1$ Character orbit 1764.y Rep. character $\chi_{1764}(667,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $14$ Newform subspaces $4$ Sturm bound $336$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1764 = 2^{2} \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1764.y (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$28$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$336$$ Trace bound: $$2$$

## Dimensions

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

Total New Old
Modular forms 84 22 62
Cusp forms 20 14 6
Eisenstein series 64 8 56

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 14 0 0 0

## Trace form

 $$14 q - q^{2} - 3 q^{4} + 2 q^{8} + O(q^{10})$$ $$14 q - q^{2} - 3 q^{4} + 2 q^{8} - 7 q^{16} + 8 q^{22} - q^{25} + 4 q^{29} - q^{32} - 2 q^{37} - 4 q^{46} - 2 q^{50} + 2 q^{53} + 6 q^{58} + 6 q^{64} + 2 q^{74} - 16 q^{85} + 4 q^{88} + O(q^{100})$$

## 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.y.a $2$ $0.880$ $$\Q(\sqrt{-3})$$ $D_{2}$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{7})$$ $$-1$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{8}-\zeta_{6}q^{16}+\cdots$$
1764.1.y.b $4$ $0.880$ $$\Q(\sqrt{2}, \sqrt{-3})$$ $D_{4}$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$$
1764.1.y.c $4$ $0.880$ $$\Q(\zeta_{12})$$ $D_{2}$ $$\Q(\sqrt{-7})$$, $$\Q(\sqrt{-21})$$ $$\Q(\sqrt{3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{5}q^{11}+\cdots$$
1764.1.y.d $4$ $0.880$ $$\Q(\sqrt{2}, \sqrt{-3})$$ $D_{4}$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$$

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

$$S_{1}^{\mathrm{old}}(1764, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(196, [\chi])$$$$^{\oplus 3}$$