Space of modular forms of level 563, weight 1, and Character 563.b

• Label: 563.1.b
• Level: $563$
• Weight: $1$
• Character orbit: 563.b
• Rep. character: $\chi_{563}(562,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $47$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 563 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	563.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 563 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(47\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(563, [\chi])\).

	Total	New	Old
Modular forms	7	7	0
Cusp forms	6	6	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	4	0	2	0

Trace form

\( 6 q - 3 q^{3} + 2 q^{4} + q^{7} + 3 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(563, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
563.1.b.a	$563$	$1$	563.b	563.b	$2$	$1$	$1$	$0.281$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-563}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q-q^{3}+q^{4}-q^{7}+2q^{11}-q^{12}+2q^{13}+\cdots\)
563.1.b.b	$563$	$1$	563.b	563.b	$2$	$2$	$2$	$0.281$	\(\Q(\sqrt{-2}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)	$1$		\(q-\beta q^{2}-q^{3}-q^{4}-\beta q^{5}+\beta q^{6}+q^{7}+\cdots\)
563.1.b.c	$563$	$1$	563.b	563.b	$2$	$3$	$3$	$0.281$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-563}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{7}+(1+\beta _{2})q^{9}+\cdots\)