Space of modular forms of level 1183, weight 1, and Character 1183.b

• Label: 1183.1.b
• Level: $1183$
• Weight: $1$
• Character orbit: 1183.b
• Rep. character: $\chi_{1183}(1182,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $121$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1183.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(121\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1183, [\chi])\).

	Total	New	Old
Modular forms	20	16	4
Cusp forms	6	6	0
Eisenstein series	14	10	4

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q - 4 q^{4} + 6 q^{9} - 2 q^{14} + 2 q^{16} - 4 q^{22} + 2 q^{23} - 6 q^{25} - 2 q^{29} - 4 q^{36} + 2 q^{43} - 6 q^{49} - 2 q^{53} + 4 q^{56} - 4 q^{74} + 2 q^{77} - 2 q^{79} + 6 q^{81} + 8 q^{88} - 6 q^{92}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1183, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1183.1.b.a	$1183$	$1$	1183.b	91.b	$2$	$6$	$6$	$0.590$	6.0.153664.1	$D_{7}$	\(\Q(\sqrt{-7}) \)	None		✓	✓	✓	1183.1.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{5}q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)