Space of modular forms of level 648, weight 1, and Character 648.j

• Label: 648.1.j
• Level: $648$
• Weight: $1$
• Character orbit: 648.j
• Rep. character: $\chi_{648}(53,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $108$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	648.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 72 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(108\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(648, [\chi])\).

	Total	New	Old
Modular forms	28	8	20
Cusp forms	4	4	0
Eisenstein series	24	4	20

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q - 2 q^{4} + 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(648, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
648.1.j.a	$648$	$1$	648.j	72.j	$6$	$2$	$1$	$0.323$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-6}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(1\)	\(1\)	$1$		\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\cdots\)
648.1.j.b	$648$	$1$	648.j	72.j	$6$	$2$	$1$	$0.323$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-6}) \)	None		$4$	$0$	\(1\)	\(0\)	\(-1\)	\(1\)	$1$		\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\cdots\)