# Properties

 Label 864.2.bt Level 864 Weight 2 Character orbit bt Rep. character $$\chi_{864}(11,\cdot)$$ Character field $$\Q(\zeta_{72})$$ Dimension 3408 Newform subspaces 1 Sturm bound 288 Trace bound 0

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## Defining parameters

 Level: $$N$$ = $$864 = 2^{5} \cdot 3^{3}$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 864.bt (of order $$72$$ and degree $$24$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$864$$ Character field: $$\Q(\zeta_{72})$$ Newform subspaces: $$1$$ Sturm bound: $$288$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(864, [\chi])$$.

Total New Old
Modular forms 3504 3504 0
Cusp forms 3408 3408 0
Eisenstein series 96 96 0

## Trace form

 $$3408q - 24q^{2} - 24q^{3} - 24q^{4} - 24q^{5} - 24q^{6} - 24q^{7} - 36q^{8} - 24q^{9} + O(q^{10})$$ $$3408q - 24q^{2} - 24q^{3} - 24q^{4} - 24q^{5} - 24q^{6} - 24q^{7} - 36q^{8} - 24q^{9} - 12q^{10} - 24q^{11} - 24q^{12} - 24q^{13} - 24q^{14} - 48q^{15} - 24q^{16} - 24q^{18} - 12q^{19} - 24q^{20} - 24q^{21} - 24q^{22} - 24q^{23} - 84q^{24} - 24q^{25} - 24q^{27} - 48q^{28} - 24q^{29} - 24q^{30} - 24q^{32} - 48q^{33} - 36q^{35} - 24q^{36} - 12q^{37} - 24q^{38} - 24q^{39} - 24q^{40} - 24q^{41} + 96q^{42} - 24q^{43} - 36q^{44} - 24q^{45} - 12q^{46} - 48q^{47} - 24q^{48} - 336q^{50} + 12q^{51} - 24q^{52} - 24q^{54} - 48q^{55} - 24q^{56} - 24q^{57} - 132q^{58} - 24q^{59} - 24q^{60} - 24q^{61} - 36q^{62} - 12q^{64} - 48q^{65} - 216q^{66} - 24q^{67} + 24q^{68} - 24q^{69} - 24q^{70} - 36q^{71} - 24q^{72} - 12q^{73} - 24q^{74} - 24q^{75} - 24q^{76} - 24q^{77} - 24q^{78} - 48q^{79} - 48q^{82} + 96q^{83} + 204q^{84} + 36q^{85} - 24q^{86} - 24q^{87} - 24q^{88} - 36q^{89} - 24q^{90} - 12q^{91} - 252q^{92} - 24q^{93} - 24q^{94} - 24q^{96} - 48q^{97} - 36q^{98} - 24q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(864, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
864.2.bt.a $$3408$$ $$6.899$$ None $$-24$$ $$-24$$ $$-24$$ $$-24$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database