# Properties

 Label 81.2.c Level $81$ Weight $2$ Character orbit 81.c Rep. character $\chi_{81}(28,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $6$ Newform subspaces $2$ Sturm bound $18$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$81 = 3^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 81.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$2$$ Sturm bound: $$18$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(81, [\chi])$$.

Total New Old
Modular forms 30 10 20
Cusp forms 6 6 0
Eisenstein series 24 4 20

## Trace form

 $$6 q - 3 q^{7} + O(q^{10})$$ $$6 q - 3 q^{7} - 12 q^{10} - 3 q^{13} + 6 q^{16} - 6 q^{19} + 12 q^{22} + 9 q^{25} + 12 q^{28} - 12 q^{31} - 18 q^{34} - 6 q^{37} - 6 q^{40} - 12 q^{43} + 24 q^{46} + 12 q^{49} + 12 q^{52} + 24 q^{55} - 6 q^{58} + 15 q^{61} - 12 q^{64} + 15 q^{67} + 12 q^{70} - 42 q^{73} - 18 q^{76} - 21 q^{79} - 48 q^{82} + 18 q^{85} - 12 q^{88} - 18 q^{91} - 24 q^{94} + 15 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(81, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
81.2.c.a $2$ $0.647$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$1$$ $$q+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{7}-5\zeta_{6}q^{13}+\cdots$$
81.2.c.b $4$ $0.647$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}+(-\zeta_{12}^{2}+\cdots)q^{5}+\cdots$$