Space of modular forms of level 1156, weight 1, and Character 1156.g

• Label: 1156.1.g
• Level: $1156$
• Weight: $1$
• Character orbit: 1156.g
• Rep. character: $\chi_{1156}(155,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $153$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1156 = 2^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1156.g (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 68 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(153\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1156, [\chi])\).

	Total	New	Old
Modular forms	84	68	16
Cusp forms	12	12	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	12	0	0	0

Trace form

\( 12 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1156, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1156.1.g.a	$1156$	$1$	1156.g	68.g	$8$	$4$	$1$	$0.577$	\(\Q(\zeta_{8})\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \)	\(\Q(\sqrt{17}) \)					68.1.d.a	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{8}-\zeta_{8}q^{9}+\cdots\)
1156.1.g.b	$1156$	$1$	1156.g	68.g	$8$	$8$	$2$	$0.577$	\(\Q(\zeta_{16})\)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None			✓		68.1.f.a	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$		\(q+\zeta_{16}^{6}q^{2}-\zeta_{16}^{4}q^{4}+(-\zeta_{16}^{3}-\zeta_{16}^{7}+\cdots)q^{5}+\cdots\)