Space of modular forms of level 1280, weight 1, and Character 1280.e

• Label: 1280.1.e
• Level: $1280$
• Weight: $1$
• Character orbit: 1280.e
• Rep. character: $\chi_{1280}(639,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1280.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1280, [\chi])\).

	Total	New	Old
Modular forms	38	6	32
Cusp forms	14	2	12
Eisenstein series	24	4	20

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + 2 q^{9} - 2 q^{25} + 4 q^{41} - 2 q^{49} + 2 q^{81} - 4 q^{89}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1280, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1280.1.e.a	$1280$	$1$	1280.e	40.e	$2$	$2$	$2$	$0.639$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{5}) \)			✓	✓	80.1.h.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-i q^{5}+q^{9}-q^{25}-2 i q^{29}+2 q^{41}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1280, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1280, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)