# Properties

 Label 1280.2.o Level $1280$ Weight $2$ Character orbit 1280.o Rep. character $\chi_{1280}(127,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $88$ Newform subspaces $22$ Sturm bound $384$ Trace bound $13$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1280 = 2^{8} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1280.o (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$40$$ Character field: $$\Q(i)$$ Newform subspaces: $$22$$ Sturm bound: $$384$$ Trace bound: $$13$$ Distinguishing $$T_p$$: $$3$$, $$7$$, $$13$$

## Dimensions

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

Total New Old
Modular forms 432 104 328
Cusp forms 336 88 248
Eisenstein series 96 16 80

## Trace form

 $$88 q + O(q^{10})$$ $$88 q - 8 q^{17} + 8 q^{25} + 16 q^{33} + 16 q^{41} + 32 q^{57} - 8 q^{65} - 24 q^{73} - 40 q^{81} - 8 q^{97} + O(q^{100})$$

## 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.o.a $2$ $10.221$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-4$$ $$-2$$ $$4$$ $$q+(-2+2i)q^{3}+(-1-2i)q^{5}+(2+\cdots)q^{7}+\cdots$$
1280.2.o.b $2$ $10.221$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-4$$ $$2$$ $$-4$$ $$q+(-2+2i)q^{3}+(1+2i)q^{5}+(-2+\cdots)q^{7}+\cdots$$
1280.2.o.c $2$ $10.221$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$-4$$ $$-6$$ $$q+(-1+i)q^{3}+(-2+i)q^{5}+(-3+\cdots)q^{7}+\cdots$$
1280.2.o.d $2$ $10.221$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$-4$$ $$-2$$ $$q+(-1+i)q^{3}+(-2-i)q^{5}+(-1+\cdots)q^{7}+\cdots$$
1280.2.o.e $2$ $10.221$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$4$$ $$2$$ $$q+(-1+i)q^{3}+(2+i)q^{5}+(1-i)q^{7}+\cdots$$
1280.2.o.f $2$ $10.221$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$4$$ $$6$$ $$q+(-1+i)q^{3}+(2-i)q^{5}+(3-3i)q^{7}+\cdots$$
1280.2.o.g $2$ $10.221$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1-2i)q^{5}+3iq^{9}+(1+i)q^{13}+\cdots$$
1280.2.o.h $2$ $10.221$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1+2i)q^{5}+3iq^{9}+(5+5i)q^{13}+\cdots$$
1280.2.o.i $2$ $10.221$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1-2i)q^{5}+3iq^{9}+(-5-5i)q^{13}+\cdots$$
1280.2.o.j $2$ $10.221$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1+2i)q^{5}+3iq^{9}+(-1-i)q^{13}+\cdots$$
1280.2.o.k $2$ $10.221$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$-4$$ $$2$$ $$q+(1-i)q^{3}+(-2-i)q^{5}+(1-i)q^{7}+\cdots$$
1280.2.o.l $2$ $10.221$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$-4$$ $$6$$ $$q+(1-i)q^{3}+(-2+i)q^{5}+(3-3i)q^{7}+\cdots$$
1280.2.o.m $2$ $10.221$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$4$$ $$-6$$ $$q+(1-i)q^{3}+(2-i)q^{5}+(-3+3i)q^{7}+\cdots$$
1280.2.o.n $2$ $10.221$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$4$$ $$-2$$ $$q+(1-i)q^{3}+(2+i)q^{5}+(-1+i)q^{7}+\cdots$$
1280.2.o.o $2$ $10.221$ $$\Q(\sqrt{-1})$$ None $$0$$ $$4$$ $$-2$$ $$-4$$ $$q+(2-2i)q^{3}+(-1-2i)q^{5}+(-2+\cdots)q^{7}+\cdots$$
1280.2.o.p $2$ $10.221$ $$\Q(\sqrt{-1})$$ None $$0$$ $$4$$ $$2$$ $$4$$ $$q+(2-2i)q^{3}+(1+2i)q^{5}+(2-2i)q^{7}+\cdots$$
1280.2.o.q $4$ $10.221$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-8$$ $$0$$ $$q-\zeta_{12}^{2}q^{3}+(-2-\zeta_{12})q^{5}+\zeta_{12}^{2}q^{7}+\cdots$$
1280.2.o.r $4$ $10.221$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$8$$ $$0$$ $$q-\zeta_{12}^{2}q^{3}+(2+\zeta_{12})q^{5}-\zeta_{12}^{2}q^{7}+\cdots$$
1280.2.o.s $12$ $10.221$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$-4$$ $$-8$$ $$q-\beta _{2}q^{3}-\beta _{7}q^{5}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots$$
1280.2.o.t $12$ $10.221$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$-4$$ $$8$$ $$q+\beta _{3}q^{3}-\beta _{6}q^{5}+(1+\beta _{3}+\beta _{5}-\beta _{7}+\cdots)q^{7}+\cdots$$
1280.2.o.u $12$ $10.221$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$4$$ $$-8$$ $$q+\beta _{3}q^{3}+\beta _{6}q^{5}+(-1-\beta _{3}-\beta _{5}+\cdots)q^{7}+\cdots$$
1280.2.o.v $12$ $10.221$ 12.0.$$\cdots$$.1 None $$0$$ $$0$$ $$4$$ $$8$$ $$q-\beta _{2}q^{3}+\beta _{7}q^{5}+(1+\beta _{2}-\beta _{4}-\beta _{6}+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1280, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(320, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(640, [\chi])$$$$^{\oplus 2}$$