# Properties

 Label 805.2.bs Level $805$ Weight $2$ Character orbit 805.bs Rep. character $\chi_{805}(37,\cdot)$ Character field $\Q(\zeta_{132})$ Dimension $3680$ Newform subspaces $1$ Sturm bound $192$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$805 = 5 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 805.bs (of order $$132$$ and degree $$40$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$805$$ Character field: $$\Q(\zeta_{132})$$ Newform subspaces: $$1$$ Sturm bound: $$192$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(805, [\chi])$$.

Total New Old
Modular forms 4000 4000 0
Cusp forms 3680 3680 0
Eisenstein series 320 320 0

## Trace form

 $$3680q - 18q^{2} - 18q^{3} - 22q^{5} - 160q^{6} - 44q^{7} - 56q^{8} + O(q^{10})$$ $$3680q - 18q^{2} - 18q^{3} - 22q^{5} - 160q^{6} - 44q^{7} - 56q^{8} - 22q^{10} - 44q^{11} + 14q^{12} - 72q^{13} - 88q^{15} - 196q^{16} - 22q^{17} - 62q^{18} - 88q^{20} - 88q^{21} - 44q^{23} - 30q^{25} - 28q^{26} - 48q^{27} + 132q^{28} - 22q^{30} - 40q^{31} - 50q^{32} - 22q^{33} - 40q^{35} - 416q^{36} - 110q^{37} - 22q^{38} - 22q^{40} - 192q^{41} - 264q^{42} - 88q^{43} - 44q^{47} + 24q^{48} - 44q^{51} - 374q^{52} - 22q^{53} - 32q^{55} - 220q^{56} + 88q^{57} - 58q^{58} - 22q^{60} - 220q^{61} + 8q^{62} - 44q^{63} - 22q^{65} - 44q^{66} - 22q^{67} - 96q^{70} - 136q^{71} - 46q^{72} + 18q^{73} - 34q^{75} - 176q^{76} - 116q^{77} + 80q^{78} + 176q^{80} - 236q^{81} - 2q^{82} - 88q^{83} - 448q^{85} - 86q^{87} - 110q^{88} - 88q^{90} - 228q^{92} + 4q^{93} - 236q^{95} - 332q^{96} - 88q^{97} + 84q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(805, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
805.2.bs.a $$3680$$ $$6.428$$ None $$-18$$ $$-18$$ $$-22$$ $$-44$$