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

• Label: 1176.1.n
• Level: $1176$
• Weight: $1$
• Character orbit: 1176.n
• Rep. character: $\chi_{1176}(197,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $5$
• Sturm bound: $224$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1176.n (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(224\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	24	18	6
Cusp forms	8	8	0
Eisenstein series	16	10	6

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

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

Trace form

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

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.n.a	$1176$	$1$	1176.n	24.h	$2$	$1$	$1$	$0.587$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-6}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(1\)	\(0\)	$1$		\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
1176.1.n.b	$1176$	$1$	1176.n	24.h	$2$	$1$	$1$	$0.587$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-6}) \)	None	✓	$2$	$0$	\(-1\)	\(1\)	\(-1\)	\(0\)	$1$		\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
1176.1.n.c	$1176$	$1$	1176.n	24.h	$2$	$1$	$1$	$0.587$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-6}) \)	None	✓	$2$	$0$	\(1\)	\(-1\)	\(1\)	\(0\)	$1$		\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
1176.1.n.d	$1176$	$1$	1176.n	24.h	$2$	$1$	$1$	$0.587$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-6}) \)	None	✓	$2$	$0$	\(1\)	\(1\)	\(-1\)	\(0\)	$1$		\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
1176.1.n.e	$1176$	$1$	1176.n	24.h	$2$	$4$	$4$	$0.587$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-14}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+(\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{5}+\cdots\)