# Properties

 Label 980.2.e Level $980$ Weight $2$ Character orbit 980.e Rep. character $\chi_{980}(589,\cdot)$ Character field $\Q$ Dimension $20$ Newform subspaces $6$ Sturm bound $336$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$980 = 2^{2} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 980.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$336$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$3$$, $$11$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(980, [\chi])$$.

Total New Old
Modular forms 192 20 172
Cusp forms 144 20 124
Eisenstein series 48 0 48

## Trace form

 $$20 q + 2 q^{5} - 20 q^{9} + O(q^{10})$$ $$20 q + 2 q^{5} - 20 q^{9} - 4 q^{11} + 10 q^{15} - 8 q^{19} - 6 q^{25} + 4 q^{29} + 20 q^{31} - 30 q^{45} + 28 q^{51} + 12 q^{55} - 28 q^{59} + 12 q^{61} - 36 q^{65} + 12 q^{69} - 40 q^{71} - 24 q^{75} - 20 q^{79} + 4 q^{81} + 10 q^{85} - 4 q^{89} + 34 q^{95} + 48 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(980, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
980.2.e.a $2$ $7.825$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1-i)q^{5}+3q^{9}+2iq^{13}-2iq^{17}+\cdots$$
980.2.e.b $2$ $7.825$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+3iq^{3}+(2+i)q^{5}-6q^{9}+3q^{11}+\cdots$$
980.2.e.c $4$ $7.825$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$0$$ $$-1$$ $$0$$ $$q-\beta _{2}q^{3}+\beta _{1}q^{5}+(-2-\beta _{1}-\beta _{3})q^{11}+\cdots$$
980.2.e.d $4$ $7.825$ $$\Q(\sqrt{-5}, \sqrt{-21})$$ $$\Q(\sqrt{-35})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-4+\beta _{3})q^{9}+(1+\cdots)q^{11}+\cdots$$
980.2.e.e $4$ $7.825$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}-q^{11}-\beta _{2}q^{13}+\cdots$$
980.2.e.f $4$ $7.825$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$0$$ $$1$$ $$0$$ $$q-\beta _{2}q^{3}-\beta _{3}q^{5}+(-2-\beta _{1}-\beta _{3})q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(980, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(980, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(245, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(490, [\chi])$$$$^{\oplus 2}$$