# Properties

 Label 368.2.x Level $368$ Weight $2$ Character orbit 368.x Rep. character $\chi_{368}(11,\cdot)$ Character field $\Q(\zeta_{44})$ Dimension $920$ Newform subspaces $1$ Sturm bound $96$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$368 = 2^{4} \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 368.x (of order $$44$$ and degree $$20$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$368$$ Character field: $$\Q(\zeta_{44})$$ Newform subspaces: $$1$$ Sturm bound: $$96$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(368, [\chi])$$.

Total New Old
Modular forms 1000 1000 0
Cusp forms 920 920 0
Eisenstein series 80 80 0

## Trace form

 $$920q - 18q^{2} - 18q^{3} - 22q^{4} - 22q^{5} - 12q^{6} - 44q^{7} - 18q^{8} + O(q^{10})$$ $$920q - 18q^{2} - 18q^{3} - 22q^{4} - 22q^{5} - 12q^{6} - 44q^{7} - 18q^{8} - 22q^{10} - 22q^{11} - 12q^{12} - 18q^{13} - 22q^{14} - 6q^{16} - 44q^{17} - 46q^{18} - 22q^{19} - 22q^{20} - 22q^{21} - 48q^{23} - 48q^{24} + 2q^{26} - 42q^{27} - 22q^{28} - 2q^{29} - 22q^{30} + 2q^{32} - 44q^{33} - 66q^{34} - 38q^{35} - 60q^{36} - 22q^{37} + 88q^{38} - 12q^{39} - 22q^{40} - 242q^{42} - 22q^{43} - 22q^{44} + 170q^{46} - 78q^{48} + 32q^{49} - 184q^{50} - 22q^{51} + 50q^{52} - 22q^{53} + 102q^{54} - 36q^{55} - 22q^{56} - 58q^{58} - 30q^{59} - 22q^{60} - 22q^{61} - 20q^{62} - 64q^{64} - 44q^{65} - 22q^{66} - 22q^{67} + 2q^{69} - 32q^{70} - 36q^{71} + 44q^{72} - 22q^{74} - 10q^{75} - 22q^{76} + 26q^{77} - 56q^{78} - 22q^{80} + 24q^{81} - 88q^{82} - 22q^{83} - 22q^{84} - 6q^{85} - 22q^{86} - 36q^{87} - 22q^{88} - 22q^{90} - 26q^{92} - 292q^{93} + 82q^{94} - 46q^{96} - 44q^{97} + 66q^{98} - 22q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(368, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
368.2.x.a $$920$$ $$2.938$$ None $$-18$$ $$-18$$ $$-22$$ $$-44$$