Space of modular forms of level 1127, weight 1, and Character 1127.x

• Label: 1127.1.x
• Level: $1127$
• Weight: $1$
• Character orbit: 1127.x
• Rep. character: $\chi_{1127}(30,\cdot)$
• Character field: $\Q(\zeta_{66})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1127 = 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1127.x (of order \(66\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q(\zeta_{66})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(112\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1127, [\chi])\).

	Total	New	Old
Modular forms	180	100	80
Cusp forms	20	20	0
Eisenstein series	160	80	80

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	20	0	0	0

Trace form

\( 20 q - 2 q^{2} + 3 q^{4} + 8 q^{8} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1127, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1127.1.x.a	$1127$	$1$	1127.x	161.p	$66$	$20$	$1$	$0.562$	\(\Q(\zeta_{33})\)	$D_{22}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{66}^{5}+\zeta_{66}^{29})q^{2}+(-\zeta_{66}+\zeta_{66}^{10}+\cdots)q^{4}+\cdots\)