# Properties

 Label 570.2.f Level $570$ Weight $2$ Character orbit 570.f Rep. character $\chi_{570}(341,\cdot)$ Character field $\Q$ Dimension $24$ Newform subspaces $4$ 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.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$57$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$240$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$7$$, $$29$$

## Dimensions

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

Total New Old
Modular forms 128 24 104
Cusp forms 112 24 88
Eisenstein series 16 0 16

## Trace form

 $$24 q + 24 q^{4} + 4 q^{6} + 24 q^{7} - 4 q^{9} + O(q^{10})$$ $$24 q + 24 q^{4} + 4 q^{6} + 24 q^{7} - 4 q^{9} + 24 q^{16} + 24 q^{19} + 4 q^{24} - 24 q^{25} + 24 q^{28} - 4 q^{36} + 4 q^{39} + 12 q^{42} - 16 q^{43} - 16 q^{45} - 8 q^{54} - 4 q^{57} - 24 q^{58} + 64 q^{61} - 84 q^{63} + 24 q^{64} - 16 q^{66} - 56 q^{73} + 24 q^{76} + 12 q^{81} + 36 q^{87} - 16 q^{93} + 4 q^{96} - 64 q^{99} + O(q^{100})$$

## 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.f.a $4$ $4.551$ $$\Q(\zeta_{8})$$ None $$-4$$ $$-4$$ $$0$$ $$8$$ $$q-q^{2}+(-1-\zeta_{8}^{2})q^{3}+q^{4}+\zeta_{8}q^{5}+\cdots$$
570.2.f.b $4$ $4.551$ $$\Q(\zeta_{8})$$ None $$4$$ $$4$$ $$0$$ $$8$$ $$q+q^{2}+(1+\zeta_{8}^{2})q^{3}+q^{4}+\zeta_{8}q^{5}+\cdots$$
570.2.f.c $8$ $4.551$ 8.0.7278137344.1 None $$-8$$ $$2$$ $$0$$ $$4$$ $$q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots$$
570.2.f.d $8$ $4.551$ 8.0.7278137344.1 None $$8$$ $$-2$$ $$0$$ $$4$$ $$q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots$$

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

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