# Properties

 Label 804.2.g Level 804 Weight 2 Character orbit g Rep. character $$\chi_{804}(401,\cdot)$$ Character field $$\Q$$ Dimension 22 Newform subspaces 3 Sturm bound 272 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$804 = 2^{2} \cdot 3 \cdot 67$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 804.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$201$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$272$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(804, [\chi])$$.

Total New Old
Modular forms 142 22 120
Cusp forms 130 22 108
Eisenstein series 12 0 12

## Trace form

 $$22q + 4q^{9} + O(q^{10})$$ $$22q + 4q^{9} - 2q^{15} + 10q^{25} - 6q^{33} + 20q^{37} + 12q^{39} + 6q^{49} + 8q^{55} - 8q^{67} + 24q^{73} + 20q^{81} - 28q^{91} + 18q^{93} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(804, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
804.2.g.a $$2$$ $$6.420$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{6}q^{3}-2\zeta_{6}q^{7}-3q^{9}-4\zeta_{6}q^{13}+\cdots$$
804.2.g.b $$4$$ $$6.420$$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+(2\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+(2+\cdots)q^{9}+\cdots$$
804.2.g.c $$16$$ $$6.420$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{12}q^{5}+\beta _{10}q^{7}+\beta _{2}q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(804, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(804, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(201, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(402, [\chi])$$$$^{\oplus 2}$$