Space of modular forms of level 1023, weight 1, and Character 1023.g

• Label: 1023.1.g
• Level: $1023$
• Weight: $1$
• Character orbit: 1023.g
• Rep. character: $\chi_{1023}(1022,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $4$
• Sturm bound: $128$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1023 = 3 \cdot 11 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1023.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1023 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(128\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1023, [\chi])\).

	Total	New	Old
Modular forms	10	10	0
Cusp forms	6	6	0
Eisenstein series	4	4	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(1023, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1023.1.g.a	$1023$	$1$	1023.g	1023.g	$2$	$1$	$1$	$0.511$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-1023}) \)	\(\Q(\sqrt{93}) \)	✓	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$		\(q-q^{3}-q^{4}+q^{9}-q^{11}+q^{12}+q^{16}+\cdots\)
1023.1.g.b	$1023$	$1$	1023.g	1023.g	$2$	$1$	$1$	$0.511$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-1023}) \)	\(\Q(\sqrt{93}) \)	✓	$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q+q^{3}-q^{4}+q^{9}+q^{11}-q^{12}+q^{16}+\cdots\)
1023.1.g.c	$1023$	$1$	1023.g	1023.g	$2$	$2$	$2$	$0.511$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-1023}) \)	None	✓	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}-q^{3}+q^{4}+\beta q^{6}+q^{9}+q^{11}+\cdots\)
1023.1.g.d	$1023$	$1$	1023.g	1023.g	$2$	$2$	$2$	$0.511$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-1023}) \)	None	✓	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}+q^{3}+q^{4}-\beta q^{6}+q^{9}-q^{11}+\cdots\)