# Properties

 Label 585.2.c Level $585$ Weight $2$ Character orbit 585.c Rep. character $\chi_{585}(469,\cdot)$ Character field $\Q$ Dimension $30$ Newform subspaces $4$ Sturm bound $168$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$585 = 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 585.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$168$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 92 30 62
Cusp forms 76 30 46
Eisenstein series 16 0 16

## Trace form

 $$30 q - 26 q^{4} + 4 q^{5} + O(q^{10})$$ $$30 q - 26 q^{4} + 4 q^{5} - 14 q^{10} + 4 q^{11} + 16 q^{14} + 26 q^{16} + 16 q^{19} - 8 q^{20} + 10 q^{25} + 6 q^{26} + 12 q^{29} - 20 q^{31} - 28 q^{34} - 16 q^{35} + 30 q^{40} + 16 q^{41} + 48 q^{46} - 62 q^{49} - 56 q^{50} - 8 q^{55} - 40 q^{56} + 8 q^{59} + 4 q^{61} - 18 q^{64} - 2 q^{65} - 28 q^{70} + 16 q^{71} + 20 q^{74} - 68 q^{76} + 8 q^{79} - 28 q^{80} + 28 q^{85} + 32 q^{86} + 28 q^{89} - 12 q^{91} + 96 q^{94} + 40 q^{95} + O(q^{100})$$

## 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.c.a $2$ $4.671$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+2q^{4}+(1+2i)q^{5}-iq^{7}+q^{11}+\cdots$$
585.2.c.b $6$ $4.671$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2})q^{4}+\cdots$$
585.2.c.c $10$ $4.671$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\beta _{1}q^{2}+(-1-\beta _{4}+\beta _{6}+\beta _{7})q^{4}+\cdots$$
585.2.c.d $12$ $4.671$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{8}q^{2}+(-1-\beta _{9})q^{4}+(-\beta _{5}+\beta _{8}+\cdots)q^{5}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(585, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(65, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(195, [\chi])$$$$^{\oplus 2}$$