# Properties

 Label 585.2.h Level $585$ Weight $2$ Character orbit 585.h Rep. character $\chi_{585}(64,\cdot)$ Character field $\Q$ Dimension $32$ Newform subspaces $7$ Sturm bound $168$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$585 = 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 585.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$65$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$168$$ Trace bound: $$2$$ 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 36 56
Cusp forms 76 32 44
Eisenstein series 16 4 12

## Trace form

 $$32 q + 24 q^{4} + O(q^{10})$$ $$32 q + 24 q^{4} - 8 q^{10} + 8 q^{14} + 8 q^{16} - 16 q^{25} + 16 q^{26} + 16 q^{35} + 8 q^{40} - 8 q^{49} + 8 q^{55} + 64 q^{56} - 8 q^{61} - 72 q^{64} - 40 q^{65} - 56 q^{74} + 40 q^{79} - 40 q^{91} - 16 q^{94} + O(q^{100})$$

## 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.h.a $2$ $4.671$ $$\Q(\sqrt{-1})$$ None $$-4$$ $$0$$ $$-4$$ $$-6$$ $$q-2q^{2}+2q^{4}+(-2+i)q^{5}-3q^{7}+\cdots$$
585.2.h.b $2$ $4.671$ $$\Q(\sqrt{-1})$$ None $$-2$$ $$0$$ $$-2$$ $$0$$ $$q-q^{2}-q^{4}+(-1-i)q^{5}+3q^{8}+(1+\cdots)q^{10}+\cdots$$
585.2.h.c $2$ $4.671$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$2$$ $$0$$ $$q+q^{2}-q^{4}+(1+i)q^{5}-3q^{8}+(1+i)q^{10}+\cdots$$
585.2.h.d $2$ $4.671$ $$\Q(\sqrt{-1})$$ None $$4$$ $$0$$ $$4$$ $$6$$ $$q+2q^{2}+2q^{4}+(2-i)q^{5}+3q^{7}+(4+\cdots)q^{10}+\cdots$$
585.2.h.e $4$ $4.671$ $$\Q(\sqrt{-5}, \sqrt{13})$$ $$\Q(\sqrt{-195})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-2q^{4}-\beta _{1}q^{5}+\beta _{3}q^{7}+\beta _{1}q^{11}+\cdots$$
585.2.h.f $8$ $4.671$ 8.0.$$\cdots$$.21 $$\Q(\sqrt{-39})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+(2-\beta _{2})q^{4}+\beta _{1}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots$$
585.2.h.g $12$ $4.671$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{10}q^{2}+(1+\beta _{5}-\beta _{11})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$

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

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