# Properties

 Label 570.2.c Level $570$ Weight $2$ Character orbit 570.c Rep. character $\chi_{570}(569,\cdot)$ Character field $\Q$ Dimension $40$ Newform subspaces $6$ Sturm bound $240$ Trace bound $15$

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## Defining parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$285$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$240$$ Trace bound: $$15$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$29$$, $$37$$

## Dimensions

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

Total New Old
Modular forms 128 40 88
Cusp forms 112 40 72
Eisenstein series 16 0 16

## Trace form

 $$40q - 40q^{4} + O(q^{10})$$ $$40q - 40q^{4} + 40q^{16} + 16q^{19} + 16q^{25} + 4q^{30} + 60q^{45} - 88q^{49} - 48q^{61} - 40q^{64} + 8q^{66} - 16q^{76} + 16q^{81} + 56q^{85} - 120q^{99} + O(q^{100})$$

## 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.c.a $$4$$ $$4.551$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots$$
570.2.c.b $$4$$ $$4.551$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots$$
570.2.c.c $$8$$ $$4.551$$ 8.0.1499238400.2 None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\beta _{6}q^{2}+(-1-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots$$
570.2.c.d $$8$$ $$4.551$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}q^{2}-\zeta_{24}^{4}q^{3}-q^{4}+(-\zeta_{24}^{2}+\cdots)q^{5}+\cdots$$
570.2.c.e $$8$$ $$4.551$$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}q^{2}+(-\zeta_{24}-\zeta_{24}^{6})q^{3}-q^{4}+\cdots$$
570.2.c.f $$8$$ $$4.551$$ 8.0.1499238400.2 None $$0$$ $$4$$ $$0$$ $$0$$ $$q+\beta _{6}q^{2}+(-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots$$

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

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