# Properties

 Label 144.2.s Level $144$ Weight $2$ Character orbit 144.s Rep. character $\chi_{144}(47,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $12$ Newform subspaces $5$ Sturm bound $48$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$144 = 2^{4} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 144.s (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$36$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$48$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(144, [\chi])$$.

Total New Old
Modular forms 60 12 48
Cusp forms 36 12 24
Eisenstein series 24 0 24

## Trace form

 $$12 q + 6 q^{9} + O(q^{10})$$ $$12 q + 6 q^{9} - 12 q^{21} + 6 q^{25} - 36 q^{29} - 18 q^{33} - 18 q^{41} - 36 q^{45} + 6 q^{49} + 30 q^{57} + 72 q^{65} + 72 q^{69} - 36 q^{73} + 72 q^{77} + 54 q^{81} - 18 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(144, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
144.2.s.a $2$ $1.150$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$-6$$ $$-6$$ $$q+(-1-\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots$$
144.2.s.b $2$ $1.150$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$-3$$ $$q+(1-2\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(-1-\zeta_{6})q^{7}+\cdots$$
144.2.s.c $2$ $1.150$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$3$$ $$q+(-1+2\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(1+\zeta_{6})q^{7}+\cdots$$
144.2.s.d $2$ $1.150$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$-6$$ $$6$$ $$q+(1+\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(2+2\zeta_{6})q^{7}+\cdots$$
144.2.s.e $4$ $1.150$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$6$$ $$0$$ $$q-\zeta_{12}^{3}q^{3}+(1+\zeta_{12})q^{5}+(-\zeta_{12}^{2}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(144, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(144, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 3}$$