# Properties

 Label 490.4.c Level $490$ Weight $4$ Character orbit 490.c Rep. character $\chi_{490}(99,\cdot)$ Character field $\Q$ Dimension $62$ Newform subspaces $7$ Sturm bound $336$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$490 = 2 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 490.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$336$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(490, [\chi])$$.

Total New Old
Modular forms 268 62 206
Cusp forms 236 62 174
Eisenstein series 32 0 32

## Trace form

 $$62 q - 248 q^{4} + 6 q^{5} - 8 q^{6} - 530 q^{9} + O(q^{10})$$ $$62 q - 248 q^{4} + 6 q^{5} - 8 q^{6} - 530 q^{9} + 16 q^{10} + 100 q^{11} - 44 q^{15} + 992 q^{16} - 24 q^{19} - 24 q^{20} + 32 q^{24} - 514 q^{25} - 416 q^{26} + 104 q^{29} + 352 q^{30} + 184 q^{31} + 528 q^{34} + 2120 q^{36} + 680 q^{39} - 64 q^{40} - 884 q^{41} - 400 q^{44} - 1318 q^{45} + 744 q^{46} + 1240 q^{50} + 544 q^{51} + 1616 q^{54} - 1176 q^{55} + 1136 q^{59} + 176 q^{60} + 92 q^{61} - 3968 q^{64} + 208 q^{65} - 192 q^{66} + 5248 q^{69} - 864 q^{71} - 56 q^{74} + 2960 q^{75} + 96 q^{76} - 4120 q^{79} + 96 q^{80} + 2038 q^{81} - 384 q^{85} + 1008 q^{86} - 3516 q^{89} - 3968 q^{90} + 72 q^{94} - 1236 q^{95} - 128 q^{96} - 3068 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(490, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
490.4.c.a $2$ $28.911$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-20$$ $$0$$ $$q-2iq^{2}+7iq^{3}-4q^{4}+(-10+5i)q^{5}+\cdots$$
490.4.c.b $2$ $28.911$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$10$$ $$0$$ $$q+iq^{2}+iq^{3}-4q^{4}+(5+5i)q^{5}+\cdots$$
490.4.c.c $6$ $28.911$ 6.0.$$\cdots$$.1 None $$0$$ $$0$$ $$16$$ $$0$$ $$q+2\beta _{3}q^{2}+(2\beta _{3}-\beta _{5})q^{3}-4q^{4}+(3+\cdots)q^{5}+\cdots$$
490.4.c.d $8$ $28.911$ 8.0.$$\cdots$$.6 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{6}q^{3}-4q^{4}+(-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$$
490.4.c.e $12$ $28.911$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$-8$$ $$0$$ $$q+\beta _{7}q^{2}+(\beta _{4}+\beta _{7})q^{3}-4q^{4}+(-1+\cdots)q^{5}+\cdots$$
490.4.c.f $12$ $28.911$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$8$$ $$0$$ $$q-\beta _{7}q^{2}+(\beta _{4}+\beta _{7})q^{3}-4q^{4}+(1-\beta _{5}+\cdots)q^{5}+\cdots$$
490.4.c.g $20$ $28.911$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{2}+\beta _{5}q^{3}-4q^{4}+\beta _{8}q^{5}-\beta _{2}q^{6}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(490, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(490, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(10, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(245, [\chi])$$$$^{\oplus 2}$$