# Properties

 Label 804.2.c Level 804 Weight 2 Character orbit c Rep. character $$\chi_{804}(671,\cdot)$$ Character field $$\Q$$ Dimension 132 Newforms 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.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$12$$ Character field: $$\Q$$ Newforms: $$2$$ 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 140 132 8
Cusp forms 132 132 0
Eisenstein series 8 0 8

## Trace form

 $$132q - 4q^{4} - 6q^{6} + O(q^{10})$$ $$132q - 4q^{4} - 6q^{6} + 4q^{10} + 4q^{12} + 12q^{16} + 2q^{18} - 8q^{22} - 24q^{24} - 124q^{25} + 14q^{30} + 32q^{34} + 26q^{36} - 16q^{37} - 12q^{42} - 28q^{46} - 22q^{48} - 140q^{49} - 8q^{52} - 16q^{54} - 16q^{57} - 52q^{58} - 14q^{60} - 16q^{61} - 16q^{64} - 18q^{66} + 16q^{69} - 4q^{70} + 24q^{72} - 8q^{73} - 36q^{76} + 40q^{78} + 16q^{81} + 52q^{82} + 30q^{84} + 32q^{85} - 28q^{88} - 6q^{90} + 32q^{93} - 8q^{96} + 40q^{97} + O(q^{100})$$

## 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.c.a $$4$$ $$6.420$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{3})q^{3}-2q^{4}-\zeta_{8}^{2}q^{5}+\cdots$$
804.2.c.b $$128$$ $$6.420$$ None $$0$$ $$0$$ $$0$$ $$0$$