Space of modular forms of level 2563, weight 1, and Character 2563.b

• Label: 2563.1.b
• Level: $2563$
• Weight: $1$
• Character orbit: 2563.b
• Rep. character: $\chi_{2563}(2562,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $4$
• Sturm bound: $234$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2563 = 11 \cdot 233 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2563.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2563 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(234\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2563, [\chi])\).

	Total	New	Old
Modular forms	8	8	0
Cusp forms	6	6	0
Eisenstein series	2	2	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	4	0

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(2563, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2563.1.b.a	$2563$	$1$	2563.b	2563.b	$2$	$1$	$1$	$1.279$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-2563}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{4}+q^{9}-q^{11}+q^{16}+q^{17}-q^{23}+\cdots\)
2563.1.b.b	$2563$	$1$	2563.b	2563.b	$2$	$1$	$1$	$1.279$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-2563}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{4}+q^{9}+q^{11}+q^{16}-q^{17}-q^{23}+\cdots\)
2563.1.b.c	$2563$	$1$	2563.b	2563.b	$2$	$2$	$2$	$1.279$	\(\Q(\sqrt{-2}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}-\beta q^{3}-q^{4}+\beta q^{5}-2q^{6}+\cdots\)
2563.1.b.d	$2563$	$1$	2563.b	2563.b	$2$	$2$	$2$	$1.279$	\(\Q(\sqrt{-2}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}+\beta q^{3}-q^{4}-\beta q^{5}+2q^{6}+\cdots\)