# Properties

 Label 570.2.d Level $570$ Weight $2$ Character orbit 570.d Rep. character $\chi_{570}(229,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $4$ Sturm bound $240$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$240$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$13$$

## Dimensions

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

Total New Old
Modular forms 128 16 112
Cusp forms 112 16 96
Eisenstein series 16 0 16

## Trace form

 $$16 q - 16 q^{4} + 4 q^{5} - 4 q^{6} - 16 q^{9} + O(q^{10})$$ $$16 q - 16 q^{4} + 4 q^{5} - 4 q^{6} - 16 q^{9} + 4 q^{10} - 8 q^{11} + 4 q^{15} + 16 q^{16} + 4 q^{19} - 4 q^{20} + 4 q^{24} + 16 q^{26} - 32 q^{29} + 16 q^{31} - 24 q^{34} + 24 q^{35} + 16 q^{36} - 8 q^{39} - 4 q^{40} - 16 q^{41} + 8 q^{44} - 4 q^{45} + 8 q^{46} - 16 q^{49} - 16 q^{50} + 16 q^{51} + 4 q^{54} + 16 q^{55} - 32 q^{59} - 4 q^{60} + 16 q^{61} - 16 q^{64} + 32 q^{65} - 8 q^{66} - 16 q^{69} + 40 q^{70} + 32 q^{71} + 16 q^{74} - 4 q^{76} + 4 q^{80} + 16 q^{81} - 8 q^{85} - 32 q^{86} - 48 q^{89} - 4 q^{90} - 112 q^{91} - 24 q^{94} + 4 q^{95} - 4 q^{96} + 8 q^{99} + O(q^{100})$$

## 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.d.a $2$ $4.551$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}+(-1-2i)q^{5}+\cdots$$
570.2.d.b $2$ $4.551$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{2}+iq^{3}-q^{4}+(2+i)q^{5}-q^{6}+\cdots$$
570.2.d.c $6$ $4.551$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{3}q^{5}-q^{6}+\cdots$$
570.2.d.d $6$ $4.551$ 6.0.350464.1 None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}-\beta _{5}q^{5}+q^{6}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(570, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(95, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(190, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(285, [\chi])$$$$^{\oplus 2}$$