# Properties

 Label 570.2.s Level $570$ Weight $2$ Character orbit 570.s Rep. character $\chi_{570}(221,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $48$ Newform subspaces $2$ Sturm bound $240$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.s (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$57$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$240$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$17$$

## Dimensions

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

Total New Old
Modular forms 256 48 208
Cusp forms 224 48 176
Eisenstein series 32 0 32

## Trace form

 $$48q + 6q^{3} - 24q^{4} + 2q^{6} - 24q^{7} - 2q^{9} + O(q^{10})$$ $$48q + 6q^{3} - 24q^{4} + 2q^{6} - 24q^{7} - 2q^{9} + 36q^{13} - 24q^{16} + 12q^{19} + 36q^{22} + 2q^{24} + 24q^{25} + 12q^{28} - 30q^{33} - 24q^{34} - 2q^{36} + 80q^{39} - 12q^{42} - 44q^{43} + 16q^{45} - 6q^{48} + 24q^{49} - 24q^{51} - 36q^{52} - 28q^{54} - 20q^{57} + 44q^{61} + 36q^{63} + 48q^{64} - 14q^{66} - 96q^{67} - 6q^{72} - 16q^{73} - 24q^{76} - 36q^{78} + 36q^{79} - 18q^{81} + 12q^{82} - 48q^{87} + 24q^{90} + 36q^{91} + 16q^{93} - 4q^{96} + 12q^{97} - 50q^{99} + O(q^{100})$$

## 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.s.a $$24$$ $$4.551$$ None $$-12$$ $$4$$ $$0$$ $$-12$$
570.2.s.b $$24$$ $$4.551$$ None $$12$$ $$2$$ $$0$$ $$-12$$

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

$$S_{2}^{\mathrm{old}}(570, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(285, [\chi])$$$$^{\oplus 2}$$