# Properties

 Label 585.2.b Level $585$ Weight $2$ Character orbit 585.b Rep. character $\chi_{585}(181,\cdot)$ Character field $\Q$ Dimension $22$ Newform subspaces $7$ Sturm bound $168$ Trace bound $14$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$585 = 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 585.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$168$$ Trace bound: $$14$$ Distinguishing $$T_p$$: $$2$$, $$7$$, $$17$$

## Dimensions

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

Total New Old
Modular forms 92 22 70
Cusp forms 76 22 54
Eisenstein series 16 0 16

## Trace form

 $$22 q - 18 q^{4} + O(q^{10})$$ $$22 q - 18 q^{4} + 2 q^{10} + 8 q^{13} + 8 q^{14} + 2 q^{16} - 8 q^{17} + 24 q^{22} - 8 q^{23} - 22 q^{25} + 2 q^{26} + 12 q^{29} + 12 q^{35} - 4 q^{38} - 6 q^{40} + 24 q^{43} - 54 q^{49} + 36 q^{52} + 4 q^{53} - 4 q^{55} - 8 q^{56} + 12 q^{61} + 22 q^{64} + 6 q^{65} + 64 q^{68} - 60 q^{74} - 92 q^{77} + 16 q^{79} - 92 q^{82} - 20 q^{88} - 40 q^{91} + 100 q^{92} - 72 q^{94} + O(q^{100})$$

## 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.b.a $2$ $4.671$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}+iq^{5}+2iq^{7}+3iq^{8}+\cdots$$
585.2.b.b $2$ $4.671$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}+iq^{5}+4iq^{7}+3iq^{8}+\cdots$$
585.2.b.c $2$ $4.671$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}+iq^{5}-4iq^{7}+3iq^{8}+\cdots$$
585.2.b.d $2$ $4.671$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2q^{4}+iq^{5}-3iq^{7}-3iq^{11}+(2+\cdots)q^{13}+\cdots$$
585.2.b.e $4$ $4.671$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$$
585.2.b.f $4$ $4.671$ $$\Q(i, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-2\beta _{1}q^{2}-2q^{4}+\beta _{1}q^{5}-\beta _{2}q^{7}+\cdots$$
585.2.b.g $6$ $4.671$ 6.0.5089536.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}+(-2+\beta _{3})q^{4}+\beta _{4}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(585, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(117, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(195, [\chi])$$$$^{\oplus 2}$$