Properties

 Label 980.2.q Level $980$ Weight $2$ Character orbit 980.q Rep. character $\chi_{980}(569,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $40$ Newform subspaces $9$ Sturm bound $336$ Trace bound $5$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$980 = 2^{2} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 980.q (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$35$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$9$$ Sturm bound: $$336$$ Trace bound: $$5$$ 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 384 40 344
Cusp forms 288 40 248
Eisenstein series 96 0 96

Trace form

 $$40 q + q^{5} + 26 q^{9} + O(q^{10})$$ $$40 q + q^{5} + 26 q^{9} - 8 q^{11} + 14 q^{15} + 2 q^{19} + 15 q^{25} + 8 q^{29} - 2 q^{31} + 18 q^{39} + 60 q^{41} + 20 q^{51} - 54 q^{55} - 2 q^{59} - 24 q^{61} + 6 q^{65} - 48 q^{69} - 56 q^{71} + 27 q^{75} - 16 q^{79} - 76 q^{81} - 22 q^{85} + 28 q^{89} + 35 q^{95} + 24 q^{99} + O(q^{100})$$

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.q.a $4$ $7.825$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$-6$$ $$-6$$ $$0$$ $$q+(-2-\beta _{2})q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots$$
980.2.q.b $4$ $7.825$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$-6$$ $$2$$ $$0$$ $$q+(-2+\beta _{2})q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+\cdots$$
980.2.q.c $4$ $7.825$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+3\zeta_{12}q^{3}+(-\zeta_{12}-2\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots$$
980.2.q.d $4$ $7.825$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}-3\zeta_{12}^{2}q^{9}+\cdots$$
980.2.q.e $4$ $7.825$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}-3\zeta_{12}^{2}q^{9}+\cdots$$
980.2.q.f $4$ $7.825$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+3\zeta_{12}q^{3}+(-\zeta_{12}+2\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots$$
980.2.q.g $4$ $7.825$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$6$$ $$-1$$ $$0$$ $$q+(2-\beta _{2})q^{3}+\beta _{3}q^{5}+(1-2\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$$
980.2.q.h $4$ $7.825$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$6$$ $$6$$ $$0$$ $$q+(1-\beta _{2})q^{3}+(2+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots$$
980.2.q.i $8$ $7.825$ 8.0.$$\cdots$$.2 $$\Q(\sqrt{-35})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{2}-\beta _{7})q^{3}+(-\beta _{3}-\beta _{7})q^{5}+(4+\cdots)q^{9}+\cdots$$

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

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