Properties

 Label 980.2.i Level $980$ Weight $2$ Character orbit 980.i Rep. character $\chi_{980}(361,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $28$ Newform subspaces $12$ Sturm bound $336$ Trace bound $11$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$980 = 2^{2} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 980.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$12$$ Sturm bound: $$336$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$3$$, $$11$$

Dimensions

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

Total New Old
Modular forms 384 28 356
Cusp forms 288 28 260
Eisenstein series 96 0 96

Trace form

 $$28 q - 2 q^{3} - 2 q^{5} - 10 q^{9} + O(q^{10})$$ $$28 q - 2 q^{3} - 2 q^{5} - 10 q^{9} + 6 q^{11} + 8 q^{13} - 8 q^{15} - 4 q^{17} + 8 q^{19} - 6 q^{23} - 14 q^{25} + 28 q^{27} - 16 q^{29} + 4 q^{31} + 12 q^{33} - 12 q^{37} - 10 q^{39} - 4 q^{41} + 60 q^{43} - 4 q^{45} + 8 q^{47} - 14 q^{51} + 24 q^{53} + 8 q^{55} + 24 q^{57} - 8 q^{59} + 6 q^{61} + 6 q^{65} - 46 q^{67} - 60 q^{69} - 16 q^{71} + 4 q^{73} - 2 q^{75} - 26 q^{79} - 6 q^{81} - 4 q^{83} - 20 q^{85} - 6 q^{87} + 10 q^{89} - 40 q^{93} - 12 q^{95} + 40 q^{97} - 120 q^{99} + O(q^{100})$$

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.i.a $2$ $7.825$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$-1$$ $$0$$ $$q+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots$$
980.2.i.b $2$ $7.825$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-3$$ $$1$$ $$0$$ $$q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots$$
980.2.i.c $2$ $7.825$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$-1$$ $$0$$ $$q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$$
980.2.i.d $2$ $7.825$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-1$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots$$
980.2.i.e $2$ $7.825$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$1$$ $$0$$ $$q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots$$
980.2.i.f $2$ $7.825$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-1$$ $$0$$ $$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-6+\cdots)q^{11}+\cdots$$
980.2.i.g $2$ $7.825$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-1$$ $$0$$ $$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots$$
980.2.i.h $2$ $7.825$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$1$$ $$0$$ $$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots$$
980.2.i.i $2$ $7.825$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$1$$ $$0$$ $$q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+2q^{13}+\cdots$$
980.2.i.j $2$ $7.825$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$-1$$ $$0$$ $$q+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+(5+\cdots)q^{11}+\cdots$$
980.2.i.k $4$ $7.825$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$-2$$ $$2$$ $$0$$ $$q+(-1+\beta _{1}-\beta _{2})q^{3}-\beta _{2}q^{5}+(-2\beta _{1}+\cdots)q^{9}+\cdots$$
980.2.i.l $4$ $7.825$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$2$$ $$-2$$ $$0$$ $$q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(2\beta _{1}+2\beta _{3})q^{9}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(980, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(98, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(196, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(245, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(490, [\chi])$$$$^{\oplus 2}$$