Space of modular forms of level 1113, weight 1, and Character 1113.n

• Label: 1113.1.n
• Level: $1113$
• Weight: $1$
• Character orbit: 1113.n
• Rep. character: $\chi_{1113}(158,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $20$
• Newform subspaces: $4$
• Sturm bound: $144$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1113 = 3 \cdot 7 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1113.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1113 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(144\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1113, [\chi])\).

	Total	New	Old
Modular forms	28	28	0
Cusp forms	20	20	0
Eisenstein series	8	8	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	20	0	0	0

Trace form

\( 20 q - 10 q^{4} - 10 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1113, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1113.1.n.a	$1113$	$1$	1113.n	1113.n	$6$	$2$	$1$	$0.555$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-159}) \)	None		✓	1113.1.n.a	$4$	$0$	\(-1\)	\(1\)	\(-1\)	\(-1\)	$1$		\(q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{5}-q^{6}+\zeta_{6}^{2}q^{7}+\cdots\)
1113.1.n.b	$1113$	$1$	1113.n	1113.n	$6$	$2$	$1$	$0.555$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-159}) \)	None		✓	1113.1.n.a	$4$	$0$	\(1\)	\(-1\)	\(1\)	\(-1\)	$1$		\(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}-q^{6}+\zeta_{6}^{2}q^{7}+\cdots\)
1113.1.n.c	$1113$	$1$	1113.n	1113.n	$6$	$8$	$4$	$0.555$	\(\Q(\zeta_{15})\)	$D_{15}$	\(\Q(\sqrt{-159}) \)	None		✓	1113.1.n.c	$4$	$0$	\(-1\)	\(-4\)	\(-1\)	\(1\)	$1$		\(q+(\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}-\zeta_{30}^{5}q^{3}+(-\zeta_{30}+\cdots)q^{4}+\cdots\)
1113.1.n.d	$1113$	$1$	1113.n	1113.n	$6$	$8$	$4$	$0.555$	\(\Q(\zeta_{15})\)	$D_{15}$	\(\Q(\sqrt{-159}) \)	None		✓	1113.1.n.c	$4$	$0$	\(1\)	\(4\)	\(1\)	\(1\)	$1$		\(q+(-\zeta_{30}^{6}-\zeta_{30}^{14})q^{2}+\zeta_{30}^{5}q^{3}+\cdots\)