# Properties

 Label 804.2.o Level 804 Weight 2 Character orbit o Rep. character $$\chi_{804}(365,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 46 Newform subspaces 4 Sturm bound 272 Trace bound 3

# Related objects

## Defining parameters

 Level: $$N$$ = $$804 = 2^{2} \cdot 3 \cdot 67$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 804.o (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$201$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$272$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 284 46 238
Cusp forms 260 46 214
Eisenstein series 24 0 24

## Trace form

 $$46q + 6q^{7} - 10q^{9} + O(q^{10})$$ $$46q + 6q^{7} - 10q^{9} - 9q^{13} + 2q^{15} - 4q^{19} - 6q^{21} + 58q^{25} - 3q^{31} + 12q^{37} - 12q^{39} + 23q^{49} + 6q^{51} + 28q^{55} + 42q^{57} - 15q^{61} - 6q^{63} + 45q^{67} - 33q^{69} + 11q^{73} + 15q^{79} - 50q^{81} + 6q^{85} - 9q^{87} + 40q^{91} + 12q^{93} - 45q^{97} - 33q^{99} + O(q^{100})$$

## 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.o.a $$2$$ $$6.420$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$-6$$ $$q+(-1+2\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{7}+\cdots$$
804.2.o.b $$4$$ $$6.420$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$-4$$ $$8$$ $$6$$ $$q+(-1-\beta _{3})q^{3}+2q^{5}+(2+2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$$
804.2.o.c $$4$$ $$6.420$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$4$$ $$-8$$ $$6$$ $$q+(1+\beta _{3})q^{3}-2q^{5}+(2-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$$
804.2.o.d $$36$$ $$6.420$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

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