# Properties

 Label 804.2.s Level 804 Weight 2 Character orbit s Rep. character $$\chi_{804}(5,\cdot)$$ Character field $$\Q(\zeta_{22})$$ Dimension 220 Newform subspaces 2 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.s (of order $$22$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$201$$ Character field: $$\Q(\zeta_{22})$$ Newform subspaces: $$2$$ 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 1420 220 1200
Cusp forms 1300 220 1080
Eisenstein series 120 0 120

## Trace form

 $$220q - 4q^{9} + O(q^{10})$$ $$220q - 4q^{9} + 2q^{15} + 22q^{19} - 22q^{21} - 10q^{25} - 44q^{31} - 5q^{33} - 20q^{37} + 54q^{39} - 22q^{43} - 22q^{45} - 6q^{49} + 36q^{55} + 176q^{61} + 30q^{67} + 64q^{73} - 165q^{75} + 24q^{81} - 66q^{87} + 28q^{91} + 48q^{93} - 55q^{99} + O(q^{100})$$

## 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.s.a $$20$$ $$6.420$$ $$\Q(\zeta_{33})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{33}^{13}q^{3}+(-2\zeta_{33}^{7}-2\zeta_{33}^{8}+\cdots)q^{7}+\cdots$$
804.2.s.b $$200$$ $$6.420$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

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