Properties

 Label 1280.2.n Level $1280$ Weight $2$ Character orbit 1280.n Rep. character $\chi_{1280}(767,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $88$ Newform subspaces $19$ Sturm bound $384$ Trace bound $13$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1280 = 2^{8} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1280.n (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$20$$ Character field: $$\Q(i)$$ Newform subspaces: $$19$$ 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

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

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.n.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.n.b $$2$$ $$10.221$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-4$$ $$2$$ $$4$$ $$q+(-2-2i)q^{3}+(1+2i)q^{5}+(2-2i)q^{7}+\cdots$$
1280.2.n.c $$2$$ $$10.221$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$-4$$ $$2$$ $$q+(-1-i)q^{3}+(-2+i)q^{5}+(1-i)q^{7}+\cdots$$
1280.2.n.d $$2$$ $$10.221$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$4$$ $$-2$$ $$q+(-1-i)q^{3}+(2-i)q^{5}+(-1+i)q^{7}+\cdots$$
1280.2.n.e $$2$$ $$10.221$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1-2i)q^{5}-3iq^{9}+(-5+5i)q^{13}+\cdots$$
1280.2.n.f $$2$$ $$10.221$$ $$\Q(\sqrt{-1})$$ $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1+2i)q^{5}-3iq^{9}+(-1+i)q^{13}+\cdots$$
1280.2.n.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.n.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.n.i $$2$$ $$10.221$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$-4$$ $$-2$$ $$q+(1+i)q^{3}+(-2+i)q^{5}+(-1+i)q^{7}+\cdots$$
1280.2.n.j $$2$$ $$10.221$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$4$$ $$2$$ $$q+(1+i)q^{3}+(2-i)q^{5}+(1-i)q^{7}+\cdots$$
1280.2.n.k $$2$$ $$10.221$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$4$$ $$-2$$ $$4$$ $$q+(2+2i)q^{3}+(-1-2i)q^{5}+(2-2i)q^{7}+\cdots$$
1280.2.n.l $$2$$ $$10.221$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$4$$ $$2$$ $$-4$$ $$q+(2+2i)q^{3}+(1+2i)q^{5}+(-2+2i)q^{7}+\cdots$$
1280.2.n.m $$8$$ $$10.221$$ $$\Q(\zeta_{20})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(-1+\zeta_{20}^{2})q^{3}+(-\zeta_{20}^{4}+\zeta_{20}^{6}+\cdots)q^{5}+\cdots$$
1280.2.n.n $$8$$ $$10.221$$ 8.0.49787136.1 None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+(-\beta _{2}-\beta _{7})q^{3}+(\beta _{2}+\beta _{4}+\beta _{7})q^{5}+\cdots$$
1280.2.n.o $$8$$ $$10.221$$ 8.0.40960000.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{6}q^{3}-\beta _{4}q^{5}-\beta _{2}q^{7}-\beta _{3}q^{9}+\cdots$$
1280.2.n.p $$8$$ $$10.221$$ 8.0.49787136.1 None $$0$$ $$0$$ $$0$$ $$4$$ $$q+(-\beta _{2}-\beta _{7})q^{3}+(-\beta _{2}-\beta _{4}-\beta _{7})q^{5}+\cdots$$
1280.2.n.q $$8$$ $$10.221$$ $$\Q(\zeta_{20})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(1-\zeta_{20}^{2})q^{3}+(\zeta_{20}^{4}-\zeta_{20}^{6})q^{5}+\cdots$$
1280.2.n.r $$12$$ $$10.221$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{2}q^{3}+\beta _{7}q^{5}+\beta _{6}q^{7}+(\beta _{5}+\beta _{7}+\cdots)q^{9}+\cdots$$
1280.2.n.s $$12$$ $$10.221$$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+\beta _{2}q^{3}-\beta _{7}q^{5}-\beta _{6}q^{7}+(\beta _{5}+\beta _{7}+\cdots)q^{9}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1280, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(320, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(640, [\chi])$$$$^{\oplus 2}$$