# Properties

 Label 806.2.bf Level 806 Weight 2 Character orbit bf Rep. character $$\chi_{806}(57,\cdot)$$ Character field $$\Q(\zeta_{12})$$ Dimension 144 Newforms 1 Sturm bound 224 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$806 = 2 \cdot 13 \cdot 31$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 806.bf (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$403$$ Character field: $$\Q(\zeta_{12})$$ Newforms: $$1$$ Sturm bound: $$224$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(806, [\chi])$$.

Total New Old
Modular forms 464 144 320
Cusp forms 432 144 288
Eisenstein series 32 0 32

## Trace form

 $$144q - 4q^{7} + 64q^{9} + O(q^{10})$$ $$144q - 4q^{7} + 64q^{9} + 12q^{11} + 4q^{14} - 144q^{16} + 16q^{18} + 48q^{21} - 12q^{22} + 12q^{26} - 4q^{28} - 16q^{31} - 8q^{33} - 24q^{34} + 8q^{35} - 60q^{37} + 48q^{39} + 36q^{42} + 12q^{44} + 36q^{45} - 8q^{47} - 12q^{53} + 36q^{57} + 24q^{59} - 112q^{63} - 144q^{65} + 32q^{66} + 48q^{70} + 20q^{71} - 16q^{72} + 48q^{73} - 48q^{74} - 120q^{78} - 96q^{79} - 56q^{81} - 96q^{83} + 48q^{84} + 84q^{86} - 128q^{87} + 56q^{93} + 16q^{94} - 48q^{97} - 8q^{98} + 60q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(806, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
806.2.bf.a $$144$$ $$6.436$$ None $$0$$ $$0$$ $$0$$ $$-4$$

## Decomposition of $$S_{2}^{\mathrm{old}}(806, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(806, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(403, [\chi])$$$$^{\oplus 2}$$