# Properties

 Label 490.2.e Level $490$ Weight $2$ Character orbit 490.e Rep. character $\chi_{490}(361,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $24$ Newform subspaces $10$ Sturm bound $168$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$490 = 2 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 490.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$10$$ Sturm bound: $$168$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$3$$, $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(490, [\chi])$$.

Total New Old
Modular forms 200 24 176
Cusp forms 136 24 112
Eisenstein series 64 0 64

## Trace form

 $$24q - 12q^{4} - 2q^{5} - 4q^{6} - 14q^{9} + O(q^{10})$$ $$24q - 12q^{4} - 2q^{5} - 4q^{6} - 14q^{9} - 2q^{10} - 6q^{11} + 16q^{15} - 12q^{16} - 4q^{17} + 8q^{18} - 6q^{19} + 4q^{20} - 8q^{22} + 12q^{23} + 2q^{24} - 12q^{25} + 10q^{26} - 24q^{27} - 4q^{29} + 2q^{30} + 8q^{31} - 24q^{33} - 16q^{34} + 28q^{36} + 52q^{37} - 8q^{38} + 36q^{39} - 2q^{40} - 16q^{41} - 56q^{43} - 6q^{44} - 4q^{45} - 8q^{46} + 20q^{47} - 44q^{51} - 12q^{53} + 14q^{54} - 16q^{55} - 56q^{57} - 8q^{58} + 4q^{59} - 8q^{60} + 10q^{61} + 48q^{62} + 24q^{64} - 6q^{65} + 48q^{67} - 4q^{68} + 36q^{69} + 32q^{71} + 8q^{72} - 28q^{73} + 14q^{74} + 12q^{76} + 64q^{78} + 32q^{79} - 2q^{80} - 76q^{81} - 16q^{82} + 32q^{83} + 40q^{85} - 30q^{86} + 24q^{87} + 4q^{88} - 2q^{89} + 20q^{90} - 24q^{92} + 12q^{93} + 2q^{94} + 2q^{96} - 64q^{97} - 132q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(490, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
490.2.e.a $$2$$ $$3.913$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-2$$ $$-1$$ $$0$$ $$q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
490.2.e.b $$2$$ $$3.913$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-2$$ $$-1$$ $$0$$ $$q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
490.2.e.c $$2$$ $$3.913$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$-1$$ $$0$$ $$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+q^{8}+\cdots$$
490.2.e.d $$2$$ $$3.913$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$0$$ $$1$$ $$0$$ $$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+q^{8}+\cdots$$
490.2.e.e $$2$$ $$3.913$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$2$$ $$1$$ $$0$$ $$q-\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
490.2.e.f $$2$$ $$3.913$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$3$$ $$-1$$ $$0$$ $$q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
490.2.e.g $$2$$ $$3.913$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-2$$ $$1$$ $$0$$ $$q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
490.2.e.h $$2$$ $$3.913$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$-1$$ $$0$$ $$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
490.2.e.i $$4$$ $$3.913$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$2$$ $$-4$$ $$-2$$ $$0$$ $$q+(1+\beta _{2})q^{2}+(\beta _{1}+2\beta _{2}+\beta _{3})q^{3}+\cdots$$
490.2.e.j $$4$$ $$3.913$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$2$$ $$4$$ $$2$$ $$0$$ $$q-\beta _{2}q^{2}+(2+\beta _{1}+2\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(490, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(490, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(98, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(245, [\chi])$$$$^{\oplus 2}$$