# Properties

 Label 54.3.f Level 54 Weight 3 Character orbit f Rep. character $$\chi_{54}(5,\cdot)$$ Character field $$\Q(\zeta_{18})$$ Dimension 36 Newform subspaces 1 Sturm bound 27 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$54 = 2 \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 54.f (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$27$$ Character field: $$\Q(\zeta_{18})$$ Newform subspaces: $$1$$ Sturm bound: $$27$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(54, [\chi])$$.

Total New Old
Modular forms 120 36 84
Cusp forms 96 36 60
Eisenstein series 24 0 24

## Trace form

 $$36q + 18q^{5} + 12q^{6} - 12q^{9} + O(q^{10})$$ $$36q + 18q^{5} + 12q^{6} - 12q^{9} - 18q^{11} - 12q^{12} - 36q^{14} - 18q^{15} - 48q^{18} - 72q^{20} - 228q^{21} + 36q^{22} - 180q^{23} + 18q^{25} + 54q^{27} + 144q^{29} + 144q^{30} - 90q^{31} + 324q^{33} - 72q^{34} + 486q^{35} + 168q^{36} + 180q^{38} + 102q^{39} - 90q^{41} + 48q^{42} + 90q^{43} - 378q^{45} - 378q^{47} - 24q^{48} + 72q^{49} - 54q^{51} - 36q^{54} - 72q^{56} + 72q^{57} + 252q^{59} + 36q^{60} - 144q^{61} + 318q^{63} + 144q^{64} + 18q^{65} - 432q^{66} - 594q^{67} - 180q^{68} - 522q^{69} - 360q^{70} - 648q^{71} - 192q^{72} + 126q^{73} - 504q^{74} - 438q^{75} - 72q^{76} - 342q^{77} - 288q^{78} - 72q^{79} + 324q^{81} + 594q^{83} + 216q^{84} + 360q^{85} + 540q^{86} + 1062q^{87} + 144q^{88} + 648q^{89} + 720q^{90} - 198q^{91} + 396q^{92} + 462q^{93} + 504q^{94} + 252q^{95} + 96q^{96} + 702q^{97} + 648q^{98} + 126q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(54, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
54.3.f.a $$36$$ $$1.471$$ None $$0$$ $$0$$ $$18$$ $$0$$

## Decomposition of $$S_{3}^{\mathrm{old}}(54, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(54, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(27, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database