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 - 2 * q^13 - 4 * q^15 + 2 * q^16 - 2 * q^19 + 2 * q^20 - 4 * q^27 - 2 * q^29 - 2 * q^39 + 2 * q^48 + 2 * q^53 + 4 * q^57 + 2 * q^60 - 4 * q^61 - 4 * q^65 - 4 * q^67 - 2 * q^68 + 4 * q^71 + 2 * q^73 - 2 * q^76 + 2 * q^79 + 4 * q^80 + 2 * q^81 + 2 * q^83 - 2 * q^85 + 4 * q^87

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	Twist minimal	Largest	Maximal	Minimal twist	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		✓	✓	✓	1027.1.x.a	$4$	$0$	$0$	$-2$	$2$	$0$	$1$		$q+\zeta_{12}^{4}q^{3}-\zeta_{12}^{5}q^{4}+(\zeta_{12}^{2}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots$