Space of modular forms of level 2717, weight 1, and Character 2717.db

• Label: 2717.1.db
• Level: $2717$
• Weight: $1$
• Character orbit: 2717.db
• Rep. character: $\chi_{2717}(142,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $60$
• Newform subspaces: $4$
• Sturm bound: $280$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2717 = 11 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2717.db (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2717 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(280\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2717, [\chi])\).

	Total	New	Old
Modular forms	84	84	0
Cusp forms	60	60	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	60	0	0	0

Trace form

\( 60 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2717, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2717.1.db.a	$2717$	$1$	2717.db	2717.cb	$18$	$6$	$1$	$1.356$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-143}) \)	None		$4$	$0$	\(-3\)	\(-3\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{18}^{3}+\zeta_{18}^{8})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{6}+\cdots)q^{3}+\cdots\)
2717.1.db.b	$2717$	$1$	2717.db	2717.cb	$18$	$6$	$1$	$1.356$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-143}) \)	None		$4$	$0$	\(3\)	\(-3\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{18}^{3}-\zeta_{18}^{8})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{6}+\cdots)q^{3}+\cdots\)
2717.1.db.c	$2717$	$1$	2717.db	2717.cb	$18$	$24$	$4$	$1.356$	\(\Q(\zeta_{45})\)	$D_{45}$	\(\Q(\sqrt{-143}) \)	None		$4$	$0$	\(-3\)	\(3\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{90}^{11}+\zeta_{90}^{39})q^{2}+(\zeta_{90}^{6}+\zeta_{90}^{14}+\cdots)q^{3}+\cdots\)
2717.1.db.d	$2717$	$1$	2717.db	2717.cb	$18$	$24$	$4$	$1.356$	\(\Q(\zeta_{45})\)	$D_{45}$	\(\Q(\sqrt{-143}) \)	None		$4$	$0$	\(3\)	\(3\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{90}^{11}-\zeta_{90}^{39})q^{2}+(\zeta_{90}^{6}+\zeta_{90}^{14}+\cdots)q^{3}+\cdots\)