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

• Label: 1027.1.s
• Level: $1027$
• Weight: $1$
• Character orbit: 1027.s
• Rep. character: $\chi_{1027}(394,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $93$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1027 = 13 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1027.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1027 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(93\)
Trace bound:			\(1\)

Dimensions

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

	Total	New	Old
Modular forms	14	14	0
Cusp forms	10	10	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	10	0	0	0

Trace form

\( 10 q + 5 q^{4} - 5 q^{9} + O(q^{10}) \)

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.s.a	$1027$	$1$	1027.s	1027.s	$6$	$2$	$1$	$0.513$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-79}) \)	None		$4$	$0$	\(3\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(1-\zeta_{6}^{2})q^{2}+(1-\zeta_{6}-\zeta_{6}^{2})q^{4}+\cdots\)
1027.1.s.b	$1027$	$1$	1027.s	1027.s	$6$	$8$	$4$	$0.513$	\(\Q(\zeta_{15})\)	$D_{30}$	\(\Q(\sqrt{-79}) \)	None		$4$	$0$	\(-3\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}+(-\zeta_{30}+\zeta_{30}^{5}+\cdots)q^{4}+\cdots\)