Space of modular forms of level 2916, weight 1, and Character 2916.j

• Label: 2916.1.j
• Level: $2916$
• Weight: $1$
• Character orbit: 2916.j
• Rep. character: $\chi_{2916}(163,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $48$
• Newform subspaces: $8$
• Sturm bound: $486$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2916 = 2^{2} \cdot 3^{6} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2916.j (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 108 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(486\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2916, [\chi])\).

	Total	New	Old
Modular forms	264	84	180
Cusp forms	48	48	0
Eisenstein series	216	36	180

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	48	0	0	0

Trace form

\( 48 q + 6 q^{10} + 6 q^{37} - 24 q^{64} + 6 q^{73} - 12 q^{82}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2916, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2916.1.j.a	$2916$	$1$	2916.j	108.j	$18$	$6$	$1$	$1.455$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-1}) \)	None		✓			2916.1.d.a	$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$		\(q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+(-1-\zeta_{18}^{4}+\cdots)q^{5}+\cdots\)
2916.1.j.b	$2916$	$1$	2916.j	108.j	$18$	$6$	$1$	$1.455$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-1}) \)	None		✓			2916.1.d.a	$4$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$		\(q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+(\zeta_{18}^{6}-\zeta_{18}^{7}+\cdots)q^{5}+\cdots\)
2916.1.j.c	$2916$	$1$	2916.j	108.j	$18$	$6$	$1$	$1.455$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-1}) \)	None		✓			2916.1.d.a	$4$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$		\(q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+(-\zeta_{18}-\zeta_{18}^{3}+\cdots)q^{5}+\cdots\)
2916.1.j.d	$2916$	$1$	2916.j	108.j	$18$	$6$	$1$	$1.455$	\(\Q(\zeta_{18})\)	$D_{3}$	\(\Q(\sqrt{-1}) \)	None					324.1.d.a	$12$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}-\zeta_{18}^{2}q^{5}+\cdots\)
2916.1.j.e	$2916$	$1$	2916.j	108.j	$18$	$6$	$1$	$1.455$	\(\Q(\zeta_{18})\)	$D_{3}$	\(\Q(\sqrt{-1}) \)	None					324.1.d.a	$12$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{2}q^{5}+\cdots\)
2916.1.j.f	$2916$	$1$	2916.j	108.j	$18$	$6$	$1$	$1.455$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-1}) \)	None		✓			2916.1.d.a	$4$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$		\(q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+(-\zeta_{18}^{6}+\zeta_{18}^{7}+\cdots)q^{5}+\cdots\)
2916.1.j.g	$2916$	$1$	2916.j	108.j	$18$	$6$	$1$	$1.455$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-1}) \)	None		✓			2916.1.d.a	$4$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$		\(q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+(\zeta_{18}+\zeta_{18}^{3}+\cdots)q^{5}+\cdots\)
2916.1.j.h	$2916$	$1$	2916.j	108.j	$18$	$6$	$1$	$1.455$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-1}) \)	None		✓			2916.1.d.a	$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$1$		\(q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+(1+\zeta_{18}^{4}+\cdots)q^{5}+\cdots\)