Space of modular forms of level 2627, weight 1, and Character 2627.x

• Label: 2627.1.x
• Level: $2627$
• Weight: $1$
• Character orbit: 2627.x
• Rep. character: $\chi_{2627}(141,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $42$
• Newform subspaces: $2$
• Sturm bound: $228$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2627 = 37 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2627.x (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2627 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(228\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2627, [\chi])\).

	Total	New	Old
Modular forms	54	54	0
Cusp forms	42	42	0
Eisenstein series	12	12	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	42	0	0	0

Trace form

\( 42 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2627, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2627.1.x.a	$2627$	$1$	2627.x	2627.x	$18$	$6$	$1$	$1.311$	\(\Q(\zeta_{18})\)	$D_{18}$	\(\Q(\sqrt{-71}) \)	None		✓			2627.1.x.a	$4$	$0$	\(0\)	\(-6\)	\(-3\)	\(0\)	$1$		\(q+(-1-\zeta_{18}^{4})q^{3}-\zeta_{18}^{5}q^{4}+(-\zeta_{18}^{3}+\cdots)q^{5}+\cdots\)
2627.1.x.b	$2627$	$1$	2627.x	2627.x	$18$	$36$	$6$	$1.311$	\(\Q(\zeta_{63})\)	$D_{126}$	\(\Q(\sqrt{-71}) \)	None		✓	✓		2627.1.x.b	$4$	$0$	\(0\)	\(6\)	\(3\)	\(0\)	$1$		\(q+(-\zeta_{126}^{13}-\zeta_{126}^{22})q^{2}+(-\zeta_{126}^{10}+\cdots)q^{3}+\cdots\)