Space of modular forms of level 1280, weight 2, and Character 1280.f

• 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: $13$

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

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

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1280.2.f.a	$1280$	$2$	1280.f	40.f	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-1})$	None					40.2.c.a	$2$	$1$	$0$	$-4$	$-4$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2 q^{3}+(-i-2)q^{5}-2 i q^{7}+q^{9}+\cdots$
1280.2.f.b	$1280$	$2$	1280.f	40.f	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-1})$	None					40.2.c.a	$2$	$0$	$0$	$-4$	$4$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2 q^{3}+(-i+2)q^{5}-2 i q^{7}+q^{9}+\cdots$
1280.2.f.c	$1280$	$2$	1280.f	40.f	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-1})$	$\Q(\sqrt{-1})$					160.2.c.a	$4$	$0$	$0$	$0$	$-4$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+(i-2)q^{5}-3 q^{9}+4 q^{13}-8 i q^{17}+\cdots$
1280.2.f.d	$1280$	$2$	1280.f	40.f	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-1})$	$\Q(\sqrt{-1})$					160.2.c.a	$4$	$0$	$0$	$0$	$4$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+(i+2)q^{5}-3 q^{9}-4 q^{13}+8 i q^{17}+\cdots$
1280.2.f.e	$1280$	$2$	1280.f	40.f	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-1})$	None					40.2.c.a	$2$	$0$	$0$	$4$	$-4$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 q^{3}+(-i-2)q^{5}+2 i q^{7}+q^{9}+\cdots$
1280.2.f.f	$1280$	$2$	1280.f	40.f	$2$	$2$	$2$	$10.221$	$\Q(\sqrt{-1})$	None					40.2.c.a	$2$	$0$	$0$	$4$	$4$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 q^{3}+(-i+2)q^{5}+2 i q^{7}+q^{9}+\cdots$
1280.2.f.g	$1280$	$2$	1280.f	40.f	$2$	$4$	$4$	$10.221$	$\Q(i, \sqrt{5})$	$\Q(\sqrt{-5})$					160.2.c.b	$4$	$0$	$0$	$-4$	$0$	$0$	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(-1-\beta _{3})q^{3}-\beta _{2}q^{5}+(3\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
1280.2.f.h	$1280$	$2$	1280.f	40.f	$2$	$4$	$4$	$10.221$	$\Q(i, \sqrt{5})$	$\Q(\sqrt{-5})$					160.2.c.b	$4$	$0$	$0$	$4$	$0$	$0$	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(1+\beta _{3})q^{3}-\beta _{2}q^{5}+(-3\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
1280.2.f.i	$1280$	$2$	1280.f	40.f	$2$	$6$	$6$	$10.221$	6.0.350464.1	None					640.2.c.a	$2$	$0$	$0$	$-4$	$0$	$0$	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1})q^{3}+(\beta _{1}+\beta _{3})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots$
1280.2.f.j	$1280$	$2$	1280.f	40.f	$2$	$6$	$6$	$10.221$	6.0.350464.1	None					640.2.c.a	$2$	$0$	$0$	$-4$	$0$	$0$	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1})q^{3}+(-\beta _{1}+\beta _{5})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots$
1280.2.f.k	$1280$	$2$	1280.f	40.f	$2$	$6$	$6$	$10.221$	6.0.350464.1	None					640.2.c.a	$2$	$0$	$0$	$4$	$0$	$0$	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{3}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
1280.2.f.l	$1280$	$2$	1280.f	40.f	$2$	$6$	$6$	$10.221$	6.0.350464.1	None					640.2.c.a	$2$	$0$	$0$	$4$	$0$	$0$	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{3}+(-\beta _{1}+\beta _{5})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$

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

$S_{2}^{\mathrm{old}}(1280, [\chi]) \simeq$ $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}$