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

• Label: 1183.1.t
• Level: $1183$
• Weight: $1$
• Character orbit: 1183.t
• Rep. character: $\chi_{1183}(699,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• 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.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{6})\)
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	40	32	8
Cusp forms	12	12	0
Eisenstein series	28	20	8

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

\( 12 q + 4 q^{4} - 6 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1183.1.t.a	$1183$	$1$	1183.t	91.t	$6$	$12$	$6$	$0.590$	12.0.\(\cdots\).1	$D_{7}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\beta _{1}+\beta _{2}-\beta _{6})q^{2}+(-1+\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)