Space of modular forms of level 867, weight 1, and Character 867.g

• Label: 867.1.g
• Level: $867$
• Weight: $1$
• Character orbit: 867.g
• Rep. character: $\chi_{867}(110,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $102$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	867.g (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 51 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(102\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(867, [\chi])\).

	Total	New	Old
Modular forms	80	64	16
Cusp forms	8	8	0
Eisenstein series	72	56	16

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(867, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
867.1.g.a	$867$	$1$	867.g	51.g	$8$	$8$	$2$	$0.433$	\(\Q(\zeta_{16})\)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	867.1.b.a	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{16}^{7}q^{3}+\zeta_{16}^{4}q^{4}-\zeta_{16}^{5}q^{7}+\cdots\)