# Properties

 Label 570.2.i Level $570$ Weight $2$ Character orbit 570.i Rep. character $\chi_{570}(121,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $32$ Newform subspaces $10$ Sturm bound $240$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$10$$ Sturm bound: $$240$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$7$$, $$11$$

## Dimensions

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

Total New Old
Modular forms 256 32 224
Cusp forms 224 32 192
Eisenstein series 32 0 32

## Trace form

 $$32q - 4q^{3} - 16q^{4} - 8q^{7} - 16q^{9} + O(q^{10})$$ $$32q - 4q^{3} - 16q^{4} - 8q^{7} - 16q^{9} - 4q^{10} - 8q^{11} + 8q^{12} - 4q^{13} - 12q^{14} - 16q^{16} + 16q^{17} - 4q^{19} + 4q^{21} - 8q^{23} - 16q^{25} + 8q^{27} + 4q^{28} - 8q^{29} + 24q^{31} - 8q^{33} + 8q^{34} + 4q^{35} - 16q^{36} + 8q^{37} - 24q^{39} - 4q^{40} + 12q^{41} + 8q^{42} + 12q^{43} + 4q^{44} - 24q^{46} + 16q^{47} - 4q^{48} + 64q^{49} - 4q^{52} - 8q^{53} + 24q^{56} - 12q^{57} - 16q^{58} + 4q^{61} - 8q^{62} + 4q^{63} + 32q^{64} + 16q^{65} - 8q^{66} + 4q^{67} - 32q^{68} - 16q^{69} - 8q^{70} - 12q^{73} + 12q^{74} + 8q^{75} - 4q^{76} + 64q^{77} - 8q^{78} - 20q^{79} - 16q^{81} - 16q^{82} - 16q^{83} - 8q^{84} + 24q^{86} - 16q^{87} + 12q^{89} - 4q^{90} + 36q^{91} - 8q^{92} + 20q^{93} - 16q^{94} - 24q^{95} - 16q^{97} + 16q^{98} + 4q^{99} + O(q^{100})$$

## 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.i.a $$2$$ $$4.551$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$1$$ $$-2$$ $$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
570.2.i.b $$2$$ $$4.551$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$1$$ $$-2$$ $$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
570.2.i.c $$2$$ $$4.551$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$1$$ $$6$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
570.2.i.d $$2$$ $$4.551$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$1$$ $$-2$$ $$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
570.2.i.e $$2$$ $$4.551$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$-1$$ $$-10$$ $$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
570.2.i.f $$4$$ $$4.551$$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$-2$$ $$2$$ $$-2$$ $$4$$ $$q+(-1+\beta _{1})q^{2}+(1-\beta _{1})q^{3}-\beta _{1}q^{4}+\cdots$$
570.2.i.g $$4$$ $$4.551$$ $$\Q(\sqrt{-3}, \sqrt{73})$$ None $$2$$ $$-2$$ $$-2$$ $$-4$$ $$q+(1-\beta _{2})q^{2}+(-1+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots$$
570.2.i.h $$4$$ $$4.551$$ $$\Q(\sqrt{-3}, \sqrt{19})$$ None $$2$$ $$-2$$ $$2$$ $$0$$ $$q+(1+\beta _{2})q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots$$
570.2.i.i $$4$$ $$4.551$$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$2$$ $$2$$ $$2$$ $$0$$ $$q+(1+\beta _{2})q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots$$
570.2.i.j $$6$$ $$4.551$$ 6.0.29654208.1 None $$-3$$ $$-3$$ $$-3$$ $$2$$ $$q+(-1+\beta _{1})q^{2}+(-1+\beta _{1})q^{3}-\beta _{1}q^{4}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(570, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(190, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(285, [\chi])$$$$^{\oplus 2}$$