Space of modular forms of level 1161, weight 1, and Character 1161.i

• Label: 1161.1.i
• Level: $1161$
• Weight: $1$
• Character orbit: 1161.i
• Rep. character: $\chi_{1161}(350,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $14$
• Newform subspaces: $3$
• Sturm bound: $132$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1161 = 3^{3} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1161.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 129 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(132\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1161, [\chi])\).

	Total	New	Old
Modular forms	26	14	12
Cusp forms	14	14	0
Eisenstein series	12	0	12

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	4	8

Trace form

\( 14 q - 2 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1161, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1161.1.i.a	$1161$	$1$	1161.i	129.f	$6$	$2$	$1$	$0.579$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+q^{4}-\zeta_{6}q^{7}+\zeta_{6}q^{13}+q^{16}-\zeta_{6}^{2}q^{19}+\cdots\)
1161.1.i.b	$1161$	$1$	1161.i	129.f	$6$	$4$	$2$	$0.579$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$S_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{3}q^{2}-q^{4}-\beta _{1}q^{5}+(-2+2\beta _{2}+\cdots)q^{10}+\cdots\)
1161.1.i.c	$1161$	$1$	1161.i	129.f	$6$	$8$	$4$	$0.579$	8.0.12960000.1	$A_{5}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q+\beta _{7}q^{2}+(-\beta _{3}-\beta _{6}-\beta _{7})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)