# Properties

 Label 1280.2.f Level $1280$ Weight $2$ Character orbit 1280.f Rep. character $\chi_{1280}(129,\cdot)$ Character field $\Q$ Dimension $44$ Newform subspaces $12$ Sturm bound $384$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1280 = 2^{8} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1280.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$40$$ Character field: $$\Q$$ Newform subspaces: $$12$$ Sturm bound: $$384$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$3$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1280, [\chi])$$.

Total New Old
Modular forms 216 52 164
Cusp forms 168 44 124
Eisenstein series 48 8 40

## Trace form

 $$44 q + 44 q^{9} + O(q^{10})$$ $$44 q + 44 q^{9} + 4 q^{25} + 8 q^{41} - 28 q^{49} + 28 q^{81} - 24 q^{89} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1280, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1280.2.f.a $2$ $10.221$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-4$$ $$-4$$ $$0$$ $$q-2q^{3}+(-2-i)q^{5}-2iq^{7}+q^{9}+\cdots$$
1280.2.f.b $2$ $10.221$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-4$$ $$4$$ $$0$$ $$q-2q^{3}+(2-i)q^{5}-2iq^{7}+q^{9}+4iq^{11}+\cdots$$
1280.2.f.c $2$ $10.221$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-2+i)q^{5}-3q^{9}+4q^{13}-8iq^{17}+\cdots$$
1280.2.f.d $2$ $10.221$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2+i)q^{5}-3q^{9}-4q^{13}+8iq^{17}+\cdots$$
1280.2.f.e $2$ $10.221$ $$\Q(\sqrt{-1})$$ None $$0$$ $$4$$ $$-4$$ $$0$$ $$q+2q^{3}+(-2-i)q^{5}+2iq^{7}+q^{9}+\cdots$$
1280.2.f.f $2$ $10.221$ $$\Q(\sqrt{-1})$$ None $$0$$ $$4$$ $$4$$ $$0$$ $$q+2q^{3}+(2-i)q^{5}+2iq^{7}+q^{9}-4iq^{11}+\cdots$$
1280.2.f.g $4$ $10.221$ $$\Q(i, \sqrt{5})$$ $$\Q(\sqrt{-5})$$ $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(-1-\beta _{3})q^{3}-\beta _{2}q^{5}+(3\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$$
1280.2.f.h $4$ $10.221$ $$\Q(i, \sqrt{5})$$ $$\Q(\sqrt{-5})$$ $$0$$ $$4$$ $$0$$ $$0$$ $$q+(1+\beta _{3})q^{3}-\beta _{2}q^{5}+(-3\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$$
1280.2.f.i $6$ $10.221$ 6.0.350464.1 None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(-1-\beta _{1})q^{3}+(\beta _{1}+\beta _{3})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots$$
1280.2.f.j $6$ $10.221$ 6.0.350464.1 None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(-1-\beta _{1})q^{3}+(-\beta _{1}+\beta _{5})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots$$
1280.2.f.k $6$ $10.221$ 6.0.350464.1 None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(1+\beta _{1})q^{3}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$$
1280.2.f.l $6$ $10.221$ 6.0.350464.1 None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(1+\beta _{1})q^{3}+(-\beta _{1}+\beta _{5})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1280, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1280, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(320, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(640, [\chi])$$$$^{\oplus 2}$$