Space of modular forms of level 1116, weight 1, and Character 1116.b

• Label: 1116.1.b
• Level: $1116$
• Weight: $1$
• Character orbit: 1116.b
• Rep. character: $\chi_{1116}(1115,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1116 = 2^{2} \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1116.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 372 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1116, [\chi])\).

	Total	New	Old
Modular forms	20	12	8
Cusp forms	12	12	0
Eisenstein series	8	0	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

\( 12 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1116, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1116.1.b.a	$1116$	$1$	1116.b	372.b	$2$	$4$	$4$	$0.557$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-31}) \)	None		✓	1116.1.b.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
1116.1.b.b	$1116$	$1$	1116.b	372.b	$2$	$8$	$8$	$0.557$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-31}) \)	None		✓	1116.1.b.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(\zeta_{24}^{5}+\zeta_{24}^{7}+\cdots)q^{5}+\cdots\)