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

• 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: $15$

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

\( 32 q - 32 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1280.2.d.a	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}-4q^{7}+3q^{9}-4iq^{11}+2iq^{13}+\cdots\)
1280.2.d.b	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}+iq^{5}-2q^{7}-q^{9}-4iq^{11}+\cdots\)
1280.2.d.c	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}-iq^{5}-2q^{7}-q^{9}-2iq^{13}+\cdots\)
1280.2.d.d	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{5}-2q^{7}+3q^{9}-6iq^{11}+2iq^{13}+\cdots\)
1280.2.d.e	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}+iq^{5}-q^{9}-2iq^{11}+2iq^{13}+\cdots\)
1280.2.d.f	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}-iq^{5}-q^{9}-2iq^{11}-2iq^{13}+\cdots\)
1280.2.d.g	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}+iq^{5}+2q^{7}-q^{9}+2iq^{13}+\cdots\)
1280.2.d.h	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}-iq^{5}+2q^{7}-q^{9}-4iq^{11}+\cdots\)
1280.2.d.i	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}+2q^{7}+3q^{9}-6iq^{11}-2iq^{13}+\cdots\)
1280.2.d.j	$1280$	$2$	1280.d	8.b	$2$	$2$	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}+4q^{7}+3q^{9}+4iq^{11}+2iq^{13}+\cdots\)
1280.2.d.k	$1280$	$2$	1280.d	8.b	$2$	$4$	$4$	$10.221$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{3}-\beta _{1}q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
1280.2.d.l	$1280$	$2$	1280.d	8.b	$2$	$4$	$4$	$10.221$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{3}+\zeta_{8}q^{5}-\zeta_{8}^{3}q^{7}-5q^{9}+\cdots\)
1280.2.d.m	$1280$	$2$	1280.d	8.b	$2$	$4$	$4$	$10.221$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{1}q^{5}+(1+\beta _{3})q^{7}+\cdots\)

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

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