# Properties

 Label 847.2.v Level 847 Weight 2 Character orbit v Rep. character $$\chi_{847}(15,\cdot)$$ Character field $$\Q(\zeta_{55})$$ Dimension 2640 Newform subspaces 2 Sturm bound 176 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$847 = 7 \cdot 11^{2}$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 847.v (of order $$55$$ and degree $$40$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$121$$ Character field: $$\Q(\zeta_{55})$$ Newform subspaces: $$2$$ Sturm bound: $$176$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(847, [\chi])$$.

Total New Old
Modular forms 3600 2640 960
Cusp forms 3440 2640 800
Eisenstein series 160 0 160

## Trace form

 $$2640q + 4q^{2} + 4q^{3} + 68q^{4} - 6q^{6} + 2q^{7} + 2q^{8} - 654q^{9} + O(q^{10})$$ $$2640q + 4q^{2} + 4q^{3} + 68q^{4} - 6q^{6} + 2q^{7} + 2q^{8} - 654q^{9} + 16q^{10} - 2q^{11} - 38q^{12} - 64q^{13} - 3q^{14} - 20q^{15} + 46q^{16} + 16q^{17} - 15q^{18} - 10q^{19} - 30q^{20} - 12q^{21} - 10q^{22} - 14q^{23} - 162q^{24} + 42q^{25} + 2q^{26} - 2q^{27} - 11q^{28} + 6q^{29} - 12q^{30} - 36q^{31} - 12q^{32} + 16q^{33} + 48q^{34} + 8q^{35} + 2q^{36} - 16q^{37} - 166q^{38} - 6q^{39} + 26q^{40} + 32q^{41} - 8q^{43} - 2q^{44} + 24q^{45} + 13q^{46} + 4q^{47} + 12q^{48} + 66q^{49} - 282q^{50} - 216q^{51} - 230q^{52} - 26q^{53} - 64q^{54} - 190q^{55} - 59q^{56} - 140q^{57} - 140q^{58} - 44q^{59} + 28q^{60} - 184q^{62} + 10q^{63} - 70q^{64} - 82q^{65} - 48q^{66} + 26q^{67} - 6q^{68} - 48q^{69} - 36q^{70} - 74q^{71} - 3q^{72} - 12q^{73} + 38q^{74} - 34q^{75} - 308q^{76} + 8q^{77} - 64q^{78} - 94q^{79} - 250q^{80} - 648q^{81} - 158q^{82} - 28q^{83} - 12q^{84} - 106q^{85} + 37q^{86} + 60q^{87} - 268q^{88} + 48q^{89} - 164q^{90} - 84q^{91} + 49q^{92} - 70q^{93} - 122q^{94} - 144q^{95} + 32q^{96} - 68q^{97} - 17q^{98} - 16q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(847, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
847.2.v.a $$1280$$ $$6.763$$ None $$1$$ $$25$$ $$-4$$ $$-32$$
847.2.v.b $$1360$$ $$6.763$$ None $$3$$ $$-21$$ $$4$$ $$34$$

## Decomposition of $$S_{2}^{\mathrm{old}}(847, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(847, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(121, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database