# Properties

 Label 585.2.i Level $585$ Weight $2$ Character orbit 585.i Rep. character $\chi_{585}(196,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $96$ Newform subspaces $8$ Sturm bound $168$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$585 = 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 585.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$8$$ Sturm bound: $$168$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(585, [\chi])$$.

Total New Old
Modular forms 176 96 80
Cusp forms 160 96 64
Eisenstein series 16 0 16

## Trace form

 $$96 q + 4 q^{2} + 4 q^{3} - 48 q^{4} + 4 q^{5} - 4 q^{6} - 24 q^{8} + 16 q^{9} + O(q^{10})$$ $$96 q + 4 q^{2} + 4 q^{3} - 48 q^{4} + 4 q^{5} - 4 q^{6} - 24 q^{8} + 16 q^{9} - 4 q^{11} - 4 q^{12} - 24 q^{14} - 48 q^{16} + 24 q^{17} + 12 q^{18} + 24 q^{19} + 12 q^{20} + 28 q^{21} - 12 q^{22} - 12 q^{23} - 16 q^{24} - 48 q^{25} + 4 q^{27} - 12 q^{29} + 4 q^{30} + 68 q^{32} - 68 q^{33} - 36 q^{36} - 24 q^{38} + 12 q^{40} - 8 q^{41} + 24 q^{42} - 12 q^{43} + 112 q^{44} - 24 q^{45} + 40 q^{47} - 60 q^{49} + 4 q^{50} + 28 q^{51} + 32 q^{53} + 16 q^{54} - 40 q^{56} - 8 q^{57} - 24 q^{59} + 28 q^{60} - 12 q^{61} - 176 q^{62} - 32 q^{63} + 72 q^{64} + 8 q^{65} + 64 q^{66} - 12 q^{67} - 48 q^{68} - 28 q^{69} - 12 q^{70} - 64 q^{71} - 24 q^{72} + 72 q^{73} + 48 q^{74} + 4 q^{75} - 24 q^{76} + 28 q^{77} + 20 q^{78} - 56 q^{80} + 24 q^{81} + 24 q^{82} - 36 q^{84} + 4 q^{86} + 24 q^{87} - 36 q^{88} + 8 q^{89} - 16 q^{90} - 68 q^{92} - 4 q^{93} - 12 q^{94} + 108 q^{96} - 36 q^{97} + 152 q^{98} - 68 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(585, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
585.2.i.a $2$ $4.671$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$-1$$ $$4$$ $$q+(2-\zeta_{6})q^{3}+2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots$$
585.2.i.b $2$ $4.671$ $$\Q(\sqrt{-3})$$ None $$1$$ $$0$$ $$1$$ $$-2$$ $$q+(1-\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
585.2.i.c $2$ $4.671$ $$\Q(\sqrt{-3})$$ None $$1$$ $$3$$ $$1$$ $$1$$ $$q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$$
585.2.i.d $2$ $4.671$ $$\Q(\sqrt{-3})$$ None $$2$$ $$-3$$ $$1$$ $$0$$ $$q+(2-2\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$$
585.2.i.e $16$ $4.671$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$-3$$ $$1$$ $$8$$ $$11$$ $$q-\beta _{6}q^{2}+(-\beta _{7}+\beta _{14})q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots$$
585.2.i.f $16$ $4.671$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$1$$ $$-2$$ $$-8$$ $$6$$ $$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3}-\beta _{4}-\beta _{5}-\beta _{6}+\cdots)q^{3}+\cdots$$
585.2.i.g $26$ $4.671$ None $$1$$ $$1$$ $$-13$$ $$-10$$
585.2.i.h $30$ $4.671$ None $$1$$ $$1$$ $$15$$ $$-10$$

## Decomposition of $$S_{2}^{\mathrm{old}}(585, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(585, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(117, [\chi])$$$$^{\oplus 2}$$