# Properties

 Label 847.2.ba Level $847$ Weight $2$ Character orbit 847.ba Rep. character $\chi_{847}(6,\cdot)$ Character field $\Q(\zeta_{110})$ Dimension $3440$ 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.ba (of order $$110$$ and degree $$40$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$847$$ Character field: $$\Q(\zeta_{110})$$ 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 3600 0
Cusp forms 3440 3440 0
Eisenstein series 160 160 0

## Trace form

 $$3440q - 78q^{2} - 168q^{4} - 34q^{7} - 88q^{8} + 754q^{9} + O(q^{10})$$ $$3440q - 78q^{2} - 168q^{4} - 34q^{7} - 88q^{8} + 754q^{9} - 64q^{11} - 13q^{14} - 176q^{15} - 10q^{16} - 75q^{18} - 77q^{21} - 160q^{22} - 118q^{23} - 128q^{25} - 69q^{28} - 98q^{29} - 114q^{30} - 88q^{32} - 84q^{35} - 16q^{36} - 132q^{37} - 184q^{39} - 121q^{42} - 88q^{43} - 92q^{44} - 93q^{46} - 16q^{49} - 28q^{50} - 232q^{51} - 78q^{53} + 26q^{56} - 64q^{57} - 164q^{58} - 262q^{60} - 35q^{63} - 178q^{64} - 88q^{65} - 88q^{67} - 56q^{70} + 67q^{72} - 178q^{74} + 100q^{77} - 198q^{78} - 10q^{79} - 862q^{81} - 7q^{84} - 278q^{85} - 117q^{86} - 16q^{88} - 55q^{91} - 597q^{92} - 56q^{93} - 116q^{95} - 132q^{98} - 150q^{99} + O(q^{100})$$

## 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.ba.a $$80$$ $$6.763$$ $$\Q(\sqrt{-7})$$ $$0$$ $$0$$ $$0$$ $$0$$
847.2.ba.b $$3360$$ $$6.763$$ None $$-78$$ $$0$$ $$0$$ $$-34$$