# Properties

 Label 574.2.e Level $574$ Weight $2$ Character orbit 574.e Rep. character $\chi_{574}(165,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $56$ Newform subspaces $8$ Sturm bound $168$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$574 = 2 \cdot 7 \cdot 41$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 574.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$8$$ Sturm bound: $$168$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$, $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(574, [\chi])$$.

Total New Old
Modular forms 176 56 120
Cusp forms 160 56 104
Eisenstein series 16 0 16

## Trace form

 $$56q - 28q^{4} - 4q^{5} - 8q^{6} - 24q^{9} + O(q^{10})$$ $$56q - 28q^{4} - 4q^{5} - 8q^{6} - 24q^{9} - 4q^{10} + 4q^{11} + 4q^{14} - 24q^{15} - 28q^{16} + 12q^{17} + 4q^{19} + 8q^{20} + 16q^{21} + 16q^{22} + 4q^{23} + 4q^{24} - 44q^{25} + 4q^{26} + 24q^{27} - 8q^{29} - 4q^{30} + 8q^{31} - 12q^{33} - 16q^{34} - 20q^{35} + 48q^{36} + 12q^{37} + 20q^{39} - 4q^{40} - 16q^{41} + 8q^{42} + 32q^{43} + 4q^{44} - 28q^{45} - 16q^{47} + 28q^{49} + 16q^{50} + 4q^{51} - 12q^{53} + 4q^{54} - 56q^{55} + 4q^{56} + 8q^{57} - 16q^{58} - 28q^{59} + 12q^{60} - 32q^{61} + 8q^{62} + 32q^{63} + 56q^{64} + 32q^{65} + 8q^{66} + 16q^{67} + 12q^{68} - 96q^{69} - 4q^{70} - 64q^{71} + 4q^{73} - 4q^{74} - 8q^{75} - 8q^{76} + 60q^{77} + 16q^{78} + 20q^{79} - 4q^{80} - 44q^{81} + 4q^{82} - 16q^{83} - 32q^{84} + 48q^{85} + 4q^{86} + 40q^{87} - 8q^{88} + 8q^{89} + 72q^{90} + 12q^{91} - 8q^{92} - 32q^{93} - 4q^{94} - 36q^{95} + 4q^{96} - 64q^{97} - 16q^{98} + 64q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(574, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
574.2.e.a $$2$$ $$4.583$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-2$$ $$2$$ $$5$$ $$q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
574.2.e.b $$2$$ $$4.583$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$1$$ $$5$$ $$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
574.2.e.c $$2$$ $$4.583$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$3$$ $$1$$ $$-1$$ $$q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
574.2.e.d $$4$$ $$4.583$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$2$$ $$-1$$ $$1$$ $$-10$$ $$q+(1-\beta _{1})q^{2}-\beta _{3}q^{3}-\beta _{1}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$$
574.2.e.e $$6$$ $$4.583$$ 6.0.309123.1 None $$-3$$ $$3$$ $$-4$$ $$-4$$ $$q+(-1+\beta _{4})q^{2}+\beta _{4}q^{3}-\beta _{4}q^{4}+(-1+\cdots)q^{5}+\cdots$$
574.2.e.f $$8$$ $$4.583$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$4$$ $$-4$$ $$-3$$ $$5$$ $$q+\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$$
574.2.e.g $$12$$ $$4.583$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$6$$ $$-1$$ $$0$$ $$-1$$ $$q-\beta _{8}q^{2}+\beta _{2}q^{3}+(-1-\beta _{8})q^{4}+\beta _{10}q^{5}+\cdots$$
574.2.e.h $$20$$ $$4.583$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$-10$$ $$1$$ $$-2$$ $$1$$ $$q+\beta _{10}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{10}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(574, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(574, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(287, [\chi])$$$$^{\oplus 2}$$