# Properties

 Label 570.2.k Level $570$ Weight $2$ Character orbit 570.k Rep. character $\chi_{570}(77,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $72$ Newform subspaces $2$ Sturm bound $240$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$240$$ Trace bound: $$7$$ 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 72 184
Cusp forms 224 72 152
Eisenstein series 32 0 32

## Trace form

 $$72q + 8q^{3} + 8q^{6} + 8q^{7} + O(q^{10})$$ $$72q + 8q^{3} + 8q^{6} + 8q^{7} - 8q^{10} - 8q^{12} + 16q^{13} + 8q^{15} - 72q^{16} - 16q^{21} - 8q^{22} + 48q^{25} - 16q^{27} + 8q^{28} + 24q^{30} - 16q^{31} + 32q^{33} + 8q^{36} - 32q^{37} - 16q^{40} + 24q^{42} - 32q^{43} - 32q^{46} - 8q^{48} - 16q^{52} - 40q^{55} + 40q^{58} - 8q^{60} + 80q^{61} + 16q^{63} + 80q^{67} - 24q^{70} - 24q^{73} - 32q^{75} - 40q^{78} - 56q^{81} + 32q^{82} - 8q^{88} - 24q^{90} + 64q^{91} - 56q^{93} - 8q^{96} - 56q^{97} + O(q^{100})$$

## 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.k.a $$36$$ $$4.551$$ None $$0$$ $$4$$ $$0$$ $$-12$$
570.2.k.b $$36$$ $$4.551$$ None $$0$$ $$4$$ $$0$$ $$20$$

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

$$S_{2}^{\mathrm{old}}(570, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(285, [\chi])$$$$^{\oplus 2}$$