Space of modular forms of level 1067, weight 1, and Character 1067.bg

• Label: 1067.1.bg
• Level: $1067$
• Weight: $1$
• Character orbit: 1067.bg
• Rep. character: $\chi_{1067}(32,\cdot)$
• Character field: $\Q(\zeta_{48})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $98$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1067 = 11 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1067.bg (of order \(48\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1067 \)
Character field:			\(\Q(\zeta_{48})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(98\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1067, [\chi])\).

	Total	New	Old
Modular forms	48	48	0
Cusp forms	16	16	0
Eisenstein series	32	32	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1067, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1067.1.bg.a	$1067$	$1$	1067.bg	1067.ag	$48$	$16$	$1$	$0.533$	\(\Q(\zeta_{48})\)	$D_{48}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{48}^{5}-\zeta_{48}^{9})q^{3}+\zeta_{48}^{2}q^{4}+(-\zeta_{48}^{3}+\cdots)q^{5}+\cdots\)