Space of modular forms of level 1027, weight 1, and Character 1027.x

• Label: 1027.1.x
• Level: $1027$
• Weight: $1$
• Character orbit: 1027.x
• Rep. character: $\chi_{1027}(213,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $93$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1027 = 13 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1027.x (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1027 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(93\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1027, [\chi])\).

	Total	New	Old
Modular forms	12	12	0
Cusp forms	4	4	0
Eisenstein series	8	8	0

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

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

Trace form

\( 4 q - 2 q^{3} + 2 q^{5} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1027, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1027.1.x.a	$1027$	$1$	1027.x	1027.x	$12$	$4$	$1$	$0.513$	\(\Q(\zeta_{12})\)	$S_{4}$	None	None		$4$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)	$1$		\(q+\zeta_{12}^{4}q^{3}-\zeta_{12}^{5}q^{4}+(\zeta_{12}^{2}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots\)