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

• Label: 1156.1.c
• Level: $1156$
• Weight: $1$
• Character orbit: 1156.c
• Rep. character: $\chi_{1156}(579,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• 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.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
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	21	18	3
Cusp forms	3	3	0
Eisenstein series	18	15	3

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	3	0	0	0

Trace form

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

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.c.a	$1156$	$1$	1156.c	4.b	$2$	$1$	$1$	$0.577$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \)	\(\Q(\sqrt{17}) \)	✓				68.1.d.a	$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{4}+q^{8}+q^{9}-2q^{13}+q^{16}+\cdots\)
1156.1.c.b	$1156$	$1$	1156.c	4.b	$2$	$2$	$2$	$0.577$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None	✓		✓		68.1.f.a	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}+q^{4}-\beta q^{5}-q^{8}+q^{9}+\beta q^{10}+\cdots\)