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

• Label: 648.1.r
• Level: $648$
• Weight: $1$
• Character orbit: 648.r
• Rep. character: $\chi_{648}(19,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $108$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	648.r (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 216 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(108\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	54	18	36
Cusp forms	18	6	12
Eisenstein series	36	12	24

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q + 3 q^{8} + O(q^{10}) \)

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.r.a	$648$	$1$	648.r	216.r	$18$	$6$	$1$	$0.323$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{3}q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(648, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(648, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)