# Properties

 Label 54.2.e Level $54$ Weight $2$ Character orbit 54.e Rep. character $\chi_{54}(7,\cdot)$ Character field $\Q(\zeta_{9})$ Dimension $18$ Newform subspaces $2$ Sturm bound $18$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$54 = 2 \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 54.e (of order $$9$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$27$$ Character field: $$\Q(\zeta_{9})$$ Newform subspaces: $$2$$ Sturm bound: $$18$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(54, [\chi])$$.

Total New Old
Modular forms 66 18 48
Cusp forms 42 18 24
Eisenstein series 24 0 24

## Trace form

 $$18 q - 6 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} + O(q^{10})$$ $$18 q - 6 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 15 q^{11} - 3 q^{12} - 6 q^{14} - 18 q^{15} - 12 q^{17} + 6 q^{18} + 12 q^{20} + 24 q^{21} - 9 q^{22} + 24 q^{23} - 18 q^{25} + 36 q^{26} + 27 q^{27} + 30 q^{29} + 36 q^{30} - 18 q^{31} + 27 q^{33} - 9 q^{34} + 6 q^{35} + 6 q^{36} - 12 q^{38} - 42 q^{39} - 15 q^{41} - 24 q^{42} - 9 q^{43} - 6 q^{44} - 6 q^{48} - 18 q^{49} - 36 q^{50} - 24 q^{53} - 36 q^{54} - 6 q^{56} - 9 q^{57} + 6 q^{59} - 18 q^{60} - 18 q^{61} - 24 q^{62} - 6 q^{63} - 9 q^{64} + 6 q^{65} + 27 q^{67} - 12 q^{68} + 18 q^{69} + 36 q^{70} + 24 q^{71} + 24 q^{72} - 18 q^{73} + 30 q^{74} + 12 q^{75} + 18 q^{76} + 42 q^{77} + 36 q^{78} + 72 q^{79} + 12 q^{80} + 72 q^{85} + 27 q^{86} + 36 q^{87} + 18 q^{88} - 3 q^{89} + 18 q^{90} - 18 q^{91} + 6 q^{92} - 6 q^{93} + 36 q^{94} + 6 q^{95} + 6 q^{96} + 27 q^{97} - 15 q^{98} - 36 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(54, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
54.2.e.a $6$ $0.431$ $$\Q(\zeta_{18})$$ None $$0$$ $$0$$ $$-3$$ $$3$$ $$q+\zeta_{18}q^{2}+(-\zeta_{18}^{2}+2\zeta_{18}^{5})q^{3}+\cdots$$
54.2.e.b $12$ $0.431$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$-3$$ $$-3$$ $$q+(-\beta _{4}+\beta _{6})q^{2}-\beta _{11}q^{3}+\beta _{3}q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(54, [\chi])$$ into lower level spaces

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