# Properties

 Label 585.2.bs Level $585$ Weight $2$ Character orbit 585.bs Rep. character $\chi_{585}(289,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $68$ Newform subspaces $3$ 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.bs (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$65$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ 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 184 76 108
Cusp forms 152 68 84
Eisenstein series 32 8 24

## Trace form

 $$68 q + 32 q^{4} + 2 q^{5} + O(q^{10})$$ $$68 q + 32 q^{4} + 2 q^{5} - 3 q^{10} - 4 q^{11} + 20 q^{14} - 28 q^{16} - 12 q^{19} + 17 q^{20} + 10 q^{25} + 24 q^{26} - 6 q^{29} - 24 q^{34} - 20 q^{35} + 2 q^{40} + 26 q^{41} - 36 q^{44} - 22 q^{46} + 34 q^{49} + 11 q^{50} + 14 q^{55} + 40 q^{56} - 8 q^{59} - 30 q^{61} - 100 q^{64} - 37 q^{65} - 116 q^{70} + 8 q^{71} + 4 q^{74} + 86 q^{76} - 40 q^{79} - 29 q^{80} - 33 q^{85} - 44 q^{86} + 44 q^{89} - 12 q^{91} + 56 q^{94} + 8 q^{95} + O(q^{100})$$

## 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.bs.a $12$ $4.671$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$6$$ $$0$$ $$q-\beta _{4}q^{2}+(-\beta _{2}-\beta _{6}-\beta _{10})q^{4}+(1+\cdots)q^{5}+\cdots$$
585.2.bs.b $24$ $4.671$ None $$0$$ $$0$$ $$-4$$ $$0$$
585.2.bs.c $32$ $4.671$ None $$0$$ $$0$$ $$0$$ $$0$$

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

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