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

• Label: 1156.1.l
• Level: $1156$
• Weight: $1$
• Character orbit: 1156.l
• Rep. character: $\chi_{1156}(67,\cdot)$
• Character field: $\Q(\zeta_{34})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $153$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1156 = 2^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1156.l (of order \(34\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1156 \)
Character field:			\(\Q(\zeta_{34})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(153\)
Trace bound:			\(0\)

Dimensions

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

	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

\( 16 q + q^{2} - q^{4} - 17 q^{5} + q^{8} + q^{9} + O(q^{10}) \)

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.l.a	$1156$	$1$	1156.l	1156.l	$34$	$16$	$1$	$0.577$	\(\Q(\zeta_{34})\)	$D_{34}$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	1156.1.l.a	$4$	$0$	\(1\)	\(0\)	\(-17\)	\(0\)	$1$		\(q-\zeta_{34}^{10}q^{2}-\zeta_{34}^{3}q^{4}+(-1+\zeta_{34}^{8}+\cdots)q^{5}+\cdots\)