# Properties

 Label 1280.2.d Level $1280$ Weight $2$ Character orbit 1280.d Rep. character $\chi_{1280}(641,\cdot)$ Character field $\Q$ Dimension $32$ Newform subspaces $13$ Sturm bound $384$ Trace bound $15$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1280 = 2^{8} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1280.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$8$$ Character field: $$\Q$$ Newform subspaces: $$13$$ Sturm bound: $$384$$ Trace bound: $$15$$ Distinguishing $$T_p$$: $$3$$, $$7$$, $$11$$, $$31$$

## Dimensions

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

Total New Old
Modular forms 216 32 184
Cusp forms 168 32 136
Eisenstein series 48 0 48

## Trace form

 $$32q - 32q^{9} + O(q^{10})$$ $$32q - 32q^{9} - 32q^{25} - 32q^{49} + 64q^{57} + 64q^{73} + 32q^{81} - 64q^{97} + O(q^{100})$$

## 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.d.a $$2$$ $$10.221$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+iq^{5}-4q^{7}+3q^{9}-4iq^{11}+2iq^{13}+\cdots$$
1280.2.d.b $$2$$ $$10.221$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+2iq^{3}+iq^{5}-2q^{7}-q^{9}-4iq^{11}+\cdots$$
1280.2.d.c $$2$$ $$10.221$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+2iq^{3}-iq^{5}-2q^{7}-q^{9}-2iq^{13}+\cdots$$
1280.2.d.d $$2$$ $$10.221$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q-iq^{5}-2q^{7}+3q^{9}-6iq^{11}+2iq^{13}+\cdots$$
1280.2.d.e $$2$$ $$10.221$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{3}+iq^{5}-q^{9}-2iq^{11}+2iq^{13}+\cdots$$
1280.2.d.f $$2$$ $$10.221$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{3}-iq^{5}-q^{9}-2iq^{11}-2iq^{13}+\cdots$$
1280.2.d.g $$2$$ $$10.221$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+2iq^{3}+iq^{5}+2q^{7}-q^{9}+2iq^{13}+\cdots$$
1280.2.d.h $$2$$ $$10.221$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+2iq^{3}-iq^{5}+2q^{7}-q^{9}-4iq^{11}+\cdots$$
1280.2.d.i $$2$$ $$10.221$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+iq^{5}+2q^{7}+3q^{9}-6iq^{11}-2iq^{13}+\cdots$$
1280.2.d.j $$2$$ $$10.221$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q+iq^{5}+4q^{7}+3q^{9}+4iq^{11}+2iq^{13}+\cdots$$
1280.2.d.k $$4$$ $$10.221$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+(-\beta _{1}+\beta _{2})q^{3}-\beta _{1}q^{5}+(-1-\beta _{3})q^{7}+\cdots$$
1280.2.d.l $$4$$ $$10.221$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}^{2}q^{3}+\zeta_{8}q^{5}-\zeta_{8}^{3}q^{7}-5q^{9}+\cdots$$
1280.2.d.m $$4$$ $$10.221$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{1}q^{5}+(1+\beta _{3})q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1280, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(64, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(128, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(256, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(320, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(640, [\chi])$$$$^{\oplus 2}$$