# Properties

 Label 804.2.q Level 804 Weight 2 Character orbit q Rep. character $$\chi_{804}(25,\cdot)$$ Character field $$\Q(\zeta_{11})$$ Dimension 120 Newforms 2 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.q (of order $$11$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$67$$ Character field: $$\Q(\zeta_{11})$$ Newforms: $$2$$ 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 1420 120 1300
Cusp forms 1300 120 1180
Eisenstein series 120 0 120

## Trace form

 $$120q - 12q^{9} + O(q^{10})$$ $$120q - 12q^{9} - 4q^{11} - 4q^{13} + 18q^{15} + 2q^{17} + 12q^{19} - 4q^{21} - 6q^{23} - 20q^{25} + 20q^{29} - 52q^{31} - 4q^{33} - 4q^{35} + 4q^{37} + 42q^{41} + 42q^{43} + 68q^{47} - 36q^{49} + 4q^{51} + 18q^{53} + 22q^{55} + 14q^{57} + 94q^{59} + 88q^{61} + 76q^{65} + 20q^{67} + 14q^{69} + 92q^{71} + 18q^{73} + 52q^{75} - 84q^{77} + 2q^{79} - 12q^{81} + 34q^{83} - 24q^{85} + 12q^{87} + 36q^{89} - 16q^{91} - 4q^{93} + 74q^{95} - 92q^{97} - 4q^{99} + O(q^{100})$$

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

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
804.2.q.a $$60$$ $$6.420$$ None $$0$$ $$-6$$ $$-2$$ $$-2$$
804.2.q.b $$60$$ $$6.420$$ None $$0$$ $$6$$ $$2$$ $$2$$

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

$$S_{2}^{\mathrm{old}}(804, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(67, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(134, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(201, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(268, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(402, [\chi])$$$$^{\oplus 2}$$