Space of modular forms of level 643, weight 1, and Character 643.b

• Label: 643.1.b
• Level: $643$
• Weight: $1$
• Character orbit: 643.b
• Rep. character: $\chi_{643}(642,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $53$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 643 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	643.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 643 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(53\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(643, [\chi])\).

	Total	New	Old
Modular forms	4	4	0
Cusp forms	3	3	0
Eisenstein series	1	1	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	1	0	2	0

Trace form

\( 3 q - q^{4} - 4 q^{6} + q^{7} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(643, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
643.1.b.a	$643$	$1$	643.b	643.b	$2$	$1$	$1$	$0.321$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-643}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+q^{4}-q^{7}+q^{9}+q^{16}-q^{23}+q^{25}+\cdots\)
643.1.b.b	$643$	$1$	643.b	643.b	$2$	$2$	$2$	$0.321$	\(\Q(\sqrt{-2}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q-\beta q^{2}-\beta q^{3}-q^{4}-2q^{6}+q^{7}-q^{9}+\cdots\)