# Properties

 Label 288.2.bf Level $288$ Weight $2$ Character orbit 288.bf Rep. character $\chi_{288}(11,\cdot)$ Character field $\Q(\zeta_{24})$ Dimension $368$ Newform subspaces $1$ Sturm bound $96$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$288 = 2^{5} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 288.bf (of order $$24$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$288$$ Character field: $$\Q(\zeta_{24})$$ Newform subspaces: $$1$$ Sturm bound: $$96$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(288, [\chi])$$.

Total New Old
Modular forms 400 400 0
Cusp forms 368 368 0
Eisenstein series 32 32 0

## Trace form

 $$368q - 12q^{2} - 8q^{3} - 4q^{4} - 12q^{5} - 8q^{6} - 4q^{7} - 8q^{9} + O(q^{10})$$ $$368q - 12q^{2} - 8q^{3} - 4q^{4} - 12q^{5} - 8q^{6} - 4q^{7} - 8q^{9} - 16q^{10} - 12q^{11} - 8q^{12} - 4q^{13} - 12q^{14} - 16q^{15} - 4q^{16} - 8q^{18} - 16q^{19} - 12q^{20} - 8q^{21} - 4q^{22} - 12q^{23} + 32q^{24} - 4q^{25} + 16q^{27} - 16q^{28} - 12q^{29} - 56q^{30} - 12q^{32} - 16q^{33} - 12q^{34} - 60q^{36} - 16q^{37} - 12q^{38} + 16q^{39} - 4q^{40} - 12q^{41} - 8q^{42} - 4q^{43} - 8q^{45} - 16q^{46} - 24q^{47} - 60q^{48} - 168q^{50} - 32q^{51} - 4q^{52} - 52q^{54} - 16q^{55} - 12q^{56} - 8q^{57} + 32q^{58} - 12q^{59} - 20q^{60} - 4q^{61} - 16q^{64} - 24q^{65} - 80q^{66} - 4q^{67} - 60q^{68} - 8q^{69} - 4q^{70} + 52q^{72} - 16q^{73} - 12q^{74} - 28q^{75} - 28q^{76} - 12q^{77} + 80q^{78} - 8q^{79} - 16q^{82} - 132q^{83} - 104q^{84} - 24q^{85} - 12q^{86} - 64q^{87} - 4q^{88} + 124q^{90} - 16q^{91} + 216q^{92} - 20q^{93} - 20q^{94} + 92q^{96} - 8q^{97} - 72q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(288, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
288.2.bf.a $$368$$ $$2.300$$ None $$-12$$ $$-8$$ $$-12$$ $$-4$$