# Properties

 Label 576.2.i Level $576$ Weight $2$ Character orbit 576.i Rep. character $\chi_{576}(193,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $44$ Newform subspaces $14$ Sturm bound $192$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$576 = 2^{6} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 576.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$14$$ Sturm bound: $$192$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(576, [\chi])$$.

Total New Old
Modular forms 216 52 164
Cusp forms 168 44 124
Eisenstein series 48 8 40

## Trace form

 $$44 q + 2 q^{5} - 4 q^{9} + O(q^{10})$$ $$44 q + 2 q^{5} - 4 q^{9} + 2 q^{13} - 8 q^{17} - 2 q^{21} - 16 q^{25} + 2 q^{29} + 18 q^{33} + 8 q^{37} + 6 q^{41} + 18 q^{45} - 12 q^{49} + 56 q^{53} - 24 q^{57} + 2 q^{61} + 18 q^{65} + 22 q^{69} - 8 q^{73} - 26 q^{77} - 28 q^{81} + 12 q^{85} - 40 q^{89} - 74 q^{93} - 2 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(576, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
576.2.i.a $2$ $4.599$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$0$$ $$2$$ $$q+(-1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$$
576.2.i.b $2$ $4.599$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$4$$ $$2$$ $$q+(-1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots$$
576.2.i.c $2$ $4.599$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$-3$$ $$q+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+\cdots$$
576.2.i.d $2$ $4.599$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-1$$ $$3$$ $$q+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots$$
576.2.i.e $2$ $4.599$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$-1$$ $$q+(-1+2\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots$$
576.2.i.f $2$ $4.599$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$3$$ $$1$$ $$q+(1-2\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots$$
576.2.i.g $2$ $4.599$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$0$$ $$-2$$ $$q+(1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$$
576.2.i.h $2$ $4.599$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$4$$ $$-2$$ $$q+(1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots$$
576.2.i.i $4$ $4.599$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$-4$$ $$-2$$ $$-2$$ $$q+(-1+\beta _{3})q^{3}-\beta _{2}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$$
576.2.i.j $4$ $4.599$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$-1$$ $$-1$$ $$-3$$ $$q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots$$
576.2.i.k $4$ $4.599$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q-\zeta_{12}^{3}q^{3}+(-1+\zeta_{12})q^{5}-\zeta_{12}^{2}q^{7}+\cdots$$
576.2.i.l $4$ $4.599$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$1$$ $$-1$$ $$3$$ $$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots$$
576.2.i.m $4$ $4.599$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$0$$ $$4$$ $$-2$$ $$2$$ $$q+(1-\beta _{3})q^{3}+(-1+\beta _{2})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$$
576.2.i.n $8$ $4.599$ 8.0.170772624.1 None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-\beta _{1}+\beta _{5})q^{3}+(-1+\beta _{4}-\beta _{7})q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(576, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(576, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(72, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 2}$$