# Properties

 Label 729.2.c Level $729$ Weight $2$ Character orbit 729.c Rep. character $\chi_{729}(244,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $60$ Newform subspaces $5$ Sturm bound $162$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$729 = 3^{6}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 729.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$5$$ Sturm bound: $$162$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(729, [\chi])$$.

Total New Old
Modular forms 198 84 114
Cusp forms 126 60 66
Eisenstein series 72 24 48

## Trace form

 $$60 q - 24 q^{4} + O(q^{10})$$ $$60 q - 24 q^{4} + 12 q^{10} - 12 q^{16} + 12 q^{19} - 12 q^{22} - 6 q^{25} - 24 q^{28} + 12 q^{37} - 12 q^{40} + 12 q^{46} + 6 q^{49} - 24 q^{52} - 24 q^{55} + 24 q^{58} - 18 q^{61} - 12 q^{64} - 18 q^{67} - 30 q^{70} + 48 q^{73} - 12 q^{76} - 132 q^{82} + 54 q^{85} - 24 q^{88} + 48 q^{91} - 12 q^{94} + 54 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(729, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
729.2.c.a $12$ $5.821$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$-3$$ $$0$$ $$3$$ $$-6$$ $$q+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{6})q^{2}+(-1+\cdots)q^{4}+\cdots$$
729.2.c.b $12$ $5.821$ 12.0.$$\cdots$$.1 None $$-3$$ $$0$$ $$-6$$ $$0$$ $$q+(\beta _{6}+\beta _{8}-\beta _{10})q^{2}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$$
729.2.c.c $12$ $5.821$ $$\Q(\zeta_{36})$$ None $$0$$ $$0$$ $$0$$ $$12$$ $$q+(-\zeta_{36}^{7}-\zeta_{36}^{8}+\zeta_{36}^{10})q^{2}-\zeta_{36}^{11}q^{4}+\cdots$$
729.2.c.d $12$ $5.821$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$3$$ $$0$$ $$-3$$ $$-6$$ $$q+(\beta _{2}-\beta _{3}+\beta _{5}-\beta _{6}+\beta _{9})q^{2}+(-1+\cdots)q^{4}+\cdots$$
729.2.c.e $12$ $5.821$ 12.0.$$\cdots$$.1 None $$3$$ $$0$$ $$6$$ $$0$$ $$q+(-\beta _{6}-\beta _{8}+\beta _{10})q^{2}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(729, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(729, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(81, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(243, [\chi])$$$$^{\oplus 2}$$