# Properties

 Label 570.2.u Level $570$ Weight $2$ Character orbit 570.u Rep. character $\chi_{570}(61,\cdot)$ Character field $\Q(\zeta_{9})$ Dimension $72$ Newform subspaces $10$ Sturm bound $240$ Trace bound $12$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.u (of order $$9$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{9})$$ Newform subspaces: $$10$$ Sturm bound: $$240$$ Trace bound: $$12$$ 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 768 72 696
Cusp forms 672 72 600
Eisenstein series 96 0 96

## Trace form

 $$72 q + O(q^{10})$$ $$72 q + 24 q^{14} + 24 q^{17} - 24 q^{22} + 48 q^{23} + 12 q^{26} + 48 q^{29} + 24 q^{31} - 24 q^{34} - 12 q^{35} - 24 q^{38} + 36 q^{41} - 24 q^{42} - 24 q^{43} - 12 q^{44} + 24 q^{47} + 12 q^{49} - 24 q^{53} - 48 q^{56} + 48 q^{58} - 24 q^{59} - 24 q^{61} - 24 q^{62} - 36 q^{64} + 12 q^{65} + 48 q^{67} + 24 q^{71} - 24 q^{73} - 36 q^{74} - 12 q^{76} - 144 q^{77} - 72 q^{79} - 24 q^{82} + 24 q^{83} - 24 q^{88} - 96 q^{89} + 24 q^{91} - 24 q^{92} - 72 q^{93} - 24 q^{94} - 48 q^{97} - 48 q^{98} - 12 q^{99} + O(q^{100})$$

## 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.u.a $6$ $4.551$ $$\Q(\zeta_{18})$$ None $$0$$ $$0$$ $$0$$ $$-6$$ $$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$$
570.2.u.b $6$ $4.551$ $$\Q(\zeta_{18})$$ None $$0$$ $$0$$ $$0$$ $$-6$$ $$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$$
570.2.u.c $6$ $4.551$ $$\Q(\zeta_{18})$$ None $$0$$ $$0$$ $$0$$ $$-3$$ $$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$$
570.2.u.d $6$ $4.551$ $$\Q(\zeta_{18})$$ None $$0$$ $$0$$ $$0$$ $$-3$$ $$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$$
570.2.u.e $6$ $4.551$ $$\Q(\zeta_{18})$$ None $$0$$ $$0$$ $$0$$ $$3$$ $$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$$
570.2.u.f $6$ $4.551$ $$\Q(\zeta_{18})$$ None $$0$$ $$0$$ $$0$$ $$3$$ $$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$$
570.2.u.g $6$ $4.551$ $$\Q(\zeta_{18})$$ None $$0$$ $$0$$ $$0$$ $$3$$ $$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$$
570.2.u.h $6$ $4.551$ $$\Q(\zeta_{18})$$ None $$0$$ $$0$$ $$0$$ $$9$$ $$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$$
570.2.u.i $12$ $4.551$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-3$$ $$q+(-\beta _{1}+\beta _{4})q^{2}-\beta _{4}q^{3}-\beta _{2}q^{4}+\cdots$$
570.2.u.j $12$ $4.551$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$3$$ $$q+(-\beta _{4}+\beta _{6})q^{2}-\beta _{4}q^{3}+\beta _{3}q^{4}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(570, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(114, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(190, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(285, [\chi])$$$$^{\oplus 2}$$