Space of modular forms of level 1176, weight 1, and Character 1176.bj

• Label: 1176.1.bj
• Level: $1176$
• Weight: $1$
• Character orbit: 1176.bj
• Rep. character: $\chi_{1176}(29,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $224$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1176.bj (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1176 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(224\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1176, [\chi])\).

	Total	New	Old
Modular forms	36	36	0
Cusp forms	12	12	0
Eisenstein series	24	24	0

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

\( 12 q - 2 q^{4} - 2 q^{6} - 2 q^{7} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1176, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1176.1.bj.a	$1176$	$1$	1176.bj	1176.aj	$14$	$6$	$1$	$0.587$	\(\Q(\zeta_{14})\)	$D_{7}$	\(\Q(\sqrt{-6}) \)	None		$4$	$0$	\(-1\)	\(-1\)	\(-2\)	\(-1\)	$1$		\(q-\zeta_{14}^{3}q^{2}+\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}+\cdots\)
1176.1.bj.b	$1176$	$1$	1176.bj	1176.aj	$14$	$6$	$1$	$0.587$	\(\Q(\zeta_{14})\)	$D_{7}$	\(\Q(\sqrt{-6}) \)	None		$4$	$0$	\(1\)	\(1\)	\(2\)	\(-1\)	$1$		\(q+\zeta_{14}^{3}q^{2}-\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}+\cdots\)