# Properties

 Label 576.2.bb Level $576$ Weight $2$ Character orbit 576.bb Rep. character $\chi_{576}(49,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $88$ Newform subspaces $5$ Sturm bound $192$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$576 = 2^{6} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 576.bb (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$144$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$5$$ Sturm bound: $$192$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 416 104 312
Cusp forms 352 88 264
Eisenstein series 64 16 48

## Trace form

 $$88 q + 4 q^{3} - 2 q^{5} + O(q^{10})$$ $$88 q + 4 q^{3} - 2 q^{5} + 2 q^{11} - 2 q^{13} + 8 q^{15} - 16 q^{17} + 8 q^{19} - 10 q^{21} - 8 q^{27} - 2 q^{29} + 4 q^{31} - 8 q^{33} + 28 q^{35} - 8 q^{37} + 2 q^{43} - 14 q^{45} + 44 q^{47} + 16 q^{49} + 36 q^{51} - 8 q^{53} - 10 q^{59} - 2 q^{61} + 36 q^{63} - 4 q^{65} + 2 q^{67} - 10 q^{69} - 56 q^{75} - 30 q^{77} + 4 q^{79} - 8 q^{81} + 22 q^{83} - 12 q^{85} + 36 q^{91} - 22 q^{93} - 60 q^{95} - 4 q^{97} - 10 q^{99} + O(q^{100})$$

## 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.bb.a $4$ $4.599$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-4$$ $$-12$$ $$q+(-2\zeta_{12}+\zeta_{12}^{3})q^{3}+(-1-\zeta_{12}+\cdots)q^{5}+\cdots$$
576.2.bb.b $4$ $4.599$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$2$$ $$12$$ $$q+(1-2\zeta_{12}^{2})q^{3}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+\cdots$$
576.2.bb.c $4$ $4.599$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$4$$ $$-6$$ $$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(2\zeta_{12}^{2}-2\zeta_{12}^{3})q^{5}+\cdots$$
576.2.bb.d $4$ $4.599$ $$\Q(\zeta_{12})$$ None $$0$$ $$6$$ $$-8$$ $$6$$ $$q+(2-\zeta_{12}^{2})q^{3}+(-2-2\zeta_{12}+2\zeta_{12}^{3})q^{5}+\cdots$$
576.2.bb.e $72$ $4.599$ None $$0$$ $$-2$$ $$4$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(576, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 3}$$