# Properties

 Label 432.2.u Level $432$ Weight $2$ Character orbit 432.u Rep. character $\chi_{432}(49,\cdot)$ Character field $\Q(\zeta_{9})$ Dimension $102$ Newform subspaces $6$ Sturm bound $144$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$432 = 2^{4} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 432.u (of order $$9$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$27$$ Character field: $$\Q(\zeta_{9})$$ Newform subspaces: $$6$$ Sturm bound: $$144$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(432, [\chi])$$.

Total New Old
Modular forms 468 114 354
Cusp forms 396 102 294
Eisenstein series 72 12 60

## Trace form

 $$102 q + 6 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{9} + O(q^{10})$$ $$102 q + 6 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{9} + 6 q^{11} - 6 q^{13} + 6 q^{15} - 3 q^{17} + 3 q^{19} - 6 q^{21} + 6 q^{23} - 6 q^{25} + 24 q^{27} - 18 q^{29} + 6 q^{31} + 39 q^{35} - 3 q^{37} + 42 q^{39} + 6 q^{43} - 18 q^{45} + 24 q^{47} - 6 q^{49} - 3 q^{51} - 12 q^{53} + 12 q^{55} - 3 q^{57} - 12 q^{59} - 6 q^{61} - 24 q^{63} - 30 q^{65} + 6 q^{67} - 30 q^{69} - 39 q^{71} - 3 q^{73} - 36 q^{75} - 30 q^{77} + 6 q^{79} - 30 q^{81} - 24 q^{83} + 9 q^{85} - 12 q^{87} + 3 q^{89} + 3 q^{91} - 6 q^{93} - 117 q^{95} - 24 q^{97} - 102 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(432, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
432.2.u.a $6$ $3.450$ $$\Q(\zeta_{18})$$ None $$0$$ $$0$$ $$-3$$ $$-3$$ $$q+(-2\zeta_{18}^{2}+\zeta_{18}^{5})q^{3}+(-\zeta_{18}^{2}+\cdots)q^{5}+\cdots$$
432.2.u.b $12$ $3.450$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$-3$$ $$3$$ $$q+(\beta _{3}-\beta _{4}-\beta _{11})q^{3}+(-\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots$$
432.2.u.c $12$ $3.450$ 12.0.$$\cdots$$.1 None $$0$$ $$6$$ $$-3$$ $$6$$ $$q+(-\beta _{2}+\beta _{6}+\beta _{7}-\beta _{9})q^{3}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$$
432.2.u.d $18$ $3.450$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$0$$ $$0$$ $$3$$ $$0$$ $$q-\beta _{12}q^{3}+(-1+\beta _{1}-\beta _{4}-\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots$$
432.2.u.e $24$ $3.450$ None $$0$$ $$0$$ $$0$$ $$3$$
432.2.u.f $30$ $3.450$ None $$0$$ $$0$$ $$0$$ $$-3$$

## Decomposition of $$S_{2}^{\mathrm{old}}(432, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(432, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(27, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(108, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(216, [\chi])$$$$^{\oplus 2}$$