# Properties

 Label 663.1.g Level $663$ Weight $1$ Character orbit 663.g Rep. character $\chi_{663}(662,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $4$ Sturm bound $84$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$663 = 3 \cdot 13 \cdot 17$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 663.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$663$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$84$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(663, [\chi])$$.

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 6 0 0 0

## Trace form

 $$6q + 2q^{4} + 6q^{9} + O(q^{10})$$ $$6q + 2q^{4} + 6q^{9} - 2q^{13} - 2q^{16} + 6q^{25} + 2q^{36} - 8q^{42} - 4q^{43} + 2q^{49} - 2q^{51} - 6q^{52} - 6q^{64} - 4q^{69} + 6q^{81} - 4q^{87} - 8q^{94} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(663, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
663.1.g.a $$1$$ $$0.331$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-51})$$, $$\Q(\sqrt{-663})$$ $$\Q(\sqrt{13})$$ $$0$$ $$-1$$ $$0$$ $$0$$ $$q-q^{3}-q^{4}+q^{9}+q^{12}+q^{13}+q^{16}+\cdots$$
663.1.g.b $$1$$ $$0.331$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-51})$$, $$\Q(\sqrt{-663})$$ $$\Q(\sqrt{13})$$ $$0$$ $$1$$ $$0$$ $$0$$ $$q+q^{3}-q^{4}+q^{9}-q^{12}+q^{13}+q^{16}+\cdots$$
663.1.g.c $$2$$ $$0.331$$ $$\Q(\sqrt{2})$$ $$D_{4}$$ $$\Q(\sqrt{-663})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-\beta q^{2}-q^{3}+q^{4}+\beta q^{6}-\beta q^{7}+q^{9}+\cdots$$
663.1.g.d $$2$$ $$0.331$$ $$\Q(\sqrt{2})$$ $$D_{4}$$ $$\Q(\sqrt{-663})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q-\beta q^{2}+q^{3}+q^{4}-\beta q^{6}+\beta q^{7}+q^{9}+\cdots$$