# Properties

 Label 1984.1.e Level $1984$ Weight $1$ Character orbit 1984.e Rep. character $\chi_{1984}(1921,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $2$ Sturm bound $256$ Trace bound $7$

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## Defining parameters

 Level: $$N$$ $$=$$ $$1984 = 2^{6} \cdot 31$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1984.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$31$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$256$$ Trace bound: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(1984, [\chi])$$.

Total New Old
Modular forms 24 4 20
Cusp forms 12 2 10
Eisenstein series 12 2 10

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2 q + 2 q^{5} + 2 q^{9} + O(q^{10})$$ $$2 q + 2 q^{5} + 2 q^{9} - 2 q^{41} + 2 q^{45} + 2 q^{81} - 2 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(1984, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1984.1.e.a $1$ $0.990$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-31})$$ None $$0$$ $$0$$ $$1$$ $$-1$$ $$q+q^{5}-q^{7}+q^{9}+q^{19}+q^{31}-q^{35}+\cdots$$
1984.1.e.b $1$ $0.990$ $$\Q$$ $D_{3}$ $$\Q(\sqrt{-31})$$ None $$0$$ $$0$$ $$1$$ $$1$$ $$q+q^{5}+q^{7}+q^{9}-q^{19}-q^{31}+q^{35}+\cdots$$

## Decomposition of $$S_{1}^{\mathrm{old}}(1984, [\chi])$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(1984, [\chi]) \cong$$ $$S_{1}^{\mathrm{new}}(31, [\chi])$$$$^{\oplus 7}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(496, [\chi])$$$$^{\oplus 3}$$