# Properties

 Label 570.2.m Level $570$ Weight $2$ Character orbit 570.m Rep. character $\chi_{570}(37,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $40$ Newform subspaces $2$ Sturm bound $240$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.m (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$95$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$240$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(570, [\chi])$$.

Total New Old
Modular forms 256 40 216
Cusp forms 224 40 184
Eisenstein series 32 0 32

## Trace form

 $$40q + 8q^{5} - 8q^{7} + O(q^{10})$$ $$40q + 8q^{5} - 8q^{7} - 16q^{11} - 40q^{16} - 8q^{17} + 40q^{23} - 24q^{25} + 16q^{26} - 8q^{28} - 16q^{30} + 8q^{35} + 40q^{36} - 16q^{38} + 40q^{43} - 40q^{47} + 80q^{55} + 8q^{57} + 32q^{61} - 32q^{62} + 8q^{63} - 8q^{68} - 24q^{73} + 24q^{76} + 64q^{77} - 8q^{80} - 40q^{81} - 32q^{82} - 40q^{83} - 72q^{85} + 16q^{87} - 40q^{92} - 16q^{93} - 56q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(570, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
570.2.m.a $$20$$ $$4.551$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$0$$ $$-4$$ $$-4$$ $$q+\beta _{2}q^{2}+\beta _{11}q^{3}+\beta _{4}q^{4}+\beta _{6}q^{5}+\cdots$$
570.2.m.b $$20$$ $$4.551$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$0$$ $$12$$ $$-4$$ $$q+\beta _{7}q^{2}-\beta _{10}q^{3}+\beta _{2}q^{4}+(1+\beta _{6}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(570, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(570, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(190, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(285, [\chi])$$$$^{\oplus 2}$$