Space of modular forms of level 640, weight 1, and Character 640.m

• Label: 640.1.m
• Level: $640$
• Weight: $1$
• Character orbit: 640.m
• Rep. character: $\chi_{640}(193,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	640.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(640, [\chi])\).

	Total	New	Old
Modular forms	36	4	32
Cusp forms	4	4	0
Eisenstein series	32	0	32

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(640, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
640.1.m.a	$640$	$1$	640.m	40.i	$4$	$2$	$1$	$0.319$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{5}-iq^{9}+(-1-i)q^{13}+(1+i+\cdots)q^{17}+\cdots\)
640.1.m.b	$640$	$1$	640.m	40.i	$4$	$2$	$1$	$0.319$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+iq^{5}-iq^{9}+(1+i)q^{13}+(1+i+\cdots)q^{17}+\cdots\)