# Properties

 Label 980.1.p Level $980$ Weight $1$ Character orbit 980.p Rep. character $\chi_{980}(79,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $12$ Newform subspaces $3$ Sturm bound $168$ Trace bound $2$

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## Defining parameters

 Level: $$N$$ $$=$$ $$980 = 2^{2} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 980.p (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$140$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$168$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(980, [\chi])$$.

Total New Old
Modular forms 52 28 24
Cusp forms 20 12 8
Eisenstein series 32 16 16

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 12 0 0 0

## Trace form

 $$12 q + 2 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{9} + O(q^{10})$$ $$12 q + 2 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{9} - 6 q^{16} - 4 q^{20} - 2 q^{24} - 2 q^{25} - 4 q^{29} + 2 q^{30} + 8 q^{36} + 4 q^{41} + 2 q^{46} - 8 q^{50} + 2 q^{54} - 2 q^{61} - 4 q^{64} + 4 q^{65} - 4 q^{69} - 8 q^{74} + 2 q^{80} - 2 q^{81} - 8 q^{85} + 2 q^{86} - 2 q^{89} + 4 q^{94} - 2 q^{96} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(980, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
980.1.p.a $2$ $0.489$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-5})$$ None $$-1$$ $$-1$$ $$1$$ $$0$$ $$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$$
980.1.p.b $2$ $0.489$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-5})$$ None $$1$$ $$1$$ $$1$$ $$0$$ $$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$$
980.1.p.c $8$ $0.489$ $$\Q(\zeta_{24})$$ $D_{4}$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}-\zeta_{24}^{7}q^{5}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(980, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(980, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 2}$$