# Properties

 Label 490.2.i Level $490$ Weight $2$ Character orbit 490.i Rep. character $\chi_{490}(79,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $40$ Newform subspaces $6$ Sturm bound $168$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$490 = 2 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 490.i (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$6$$ Sturm bound: $$168$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$, $$11$$, $$19$$

## Dimensions

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

Total New Old
Modular forms 200 40 160
Cusp forms 136 40 96
Eisenstein series 64 0 64

## Trace form

 $$40 q + 20 q^{4} - 2 q^{5} + 12 q^{6} + 14 q^{9} + O(q^{10})$$ $$40 q + 20 q^{4} - 2 q^{5} + 12 q^{6} + 14 q^{9} - 2 q^{10} + 10 q^{11} + 32 q^{15} - 20 q^{16} + 14 q^{19} - 4 q^{20} + 6 q^{24} - 14 q^{26} - 28 q^{29} - 6 q^{30} + 16 q^{31} - 16 q^{34} + 28 q^{36} - 12 q^{39} + 2 q^{40} - 10 q^{44} - 24 q^{45} - 24 q^{46} + 20 q^{51} + 18 q^{54} + 24 q^{55} + 4 q^{59} + 16 q^{60} - 6 q^{61} - 40 q^{64} + 30 q^{65} + 12 q^{69} + 16 q^{71} - 30 q^{74} - 24 q^{75} + 28 q^{76} - 16 q^{79} - 2 q^{80} + 20 q^{81} - 64 q^{85} + 18 q^{86} + 10 q^{89} - 60 q^{90} - 2 q^{94} - 28 q^{95} - 6 q^{96} - 60 q^{99} + O(q^{100})$$

## 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.i.a $4$ $3.913$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2+\zeta_{12}+\cdots)q^{5}+\cdots$$
490.2.i.b $4$ $3.913$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+\zeta_{12}q^{2}+(3\zeta_{12}-3\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$$
490.2.i.c $8$ $3.913$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-\zeta_{24}+\zeta_{24}^{4})q^{2}+(-\zeta_{24}^{5}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots$$
490.2.i.d $8$ $3.913$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{2}q^{2}+\zeta_{24}^{4}q^{4}+(\zeta_{24}^{3}+2\zeta_{24}^{5}+\cdots)q^{5}+\cdots$$
490.2.i.e $8$ $3.913$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{24}^{2}q^{2}+(-\zeta_{24}+\zeta_{24}^{7})q^{3}+\zeta_{24}^{4}q^{4}+\cdots$$
490.2.i.f $8$ $3.913$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(-\zeta_{24}+\zeta_{24}^{4})q^{2}+(-\zeta_{24}^{5}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots$$

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

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