# Properties

 Label 980.2.c Level $980$ Weight $2$ Character orbit 980.c Rep. character $\chi_{980}(979,\cdot)$ Character field $\Q$ Dimension $112$ Newform subspaces $5$ Sturm bound $336$ Trace bound $4$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$980 = 2^{2} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 980.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$140$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$336$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 184 128 56
Cusp forms 152 112 40
Eisenstein series 32 16 16

## Trace form

 $$112q + 4q^{4} - 88q^{9} + O(q^{10})$$ $$112q + 4q^{4} - 88q^{9} - 4q^{16} + 12q^{25} - 24q^{29} - 28q^{30} + 36q^{36} + 4q^{44} + 4q^{46} - 4q^{50} - 96q^{60} - 44q^{64} + 40q^{65} - 76q^{74} + 24q^{81} + 52q^{85} + 24q^{86} + O(q^{100})$$

## 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.c.a $$8$$ $$7.825$$ $$\Q(\zeta_{16})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{16}^{2}q^{2}-2q^{4}-\zeta_{16}^{4}q^{5}+2\zeta_{16}^{2}q^{8}+\cdots$$
980.2.c.b $$8$$ $$7.825$$ 8.0.3317760000.3 $$\Q(\sqrt{-5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{2}+\beta _{3}q^{3}+2q^{4}+\beta _{6}q^{5}+(-\beta _{5}+\cdots)q^{6}+\cdots$$
980.2.c.c $$16$$ $$7.825$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+(-\beta _{8}-\beta _{10}-\beta _{12})q^{3}+\cdots$$
980.2.c.d $$32$$ $$7.825$$ None $$0$$ $$0$$ $$0$$ $$0$$
980.2.c.e $$48$$ $$7.825$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(980, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 2}$$