Space of modular forms of level 648, weight 2, and Character 648.bb

• Label: 648.2.bb
• Level: $648$
• Weight: $2$
• Character orbit: 648.bb
• Rep. character: $\chi_{648}(11,\cdot)$
• Character field: $\Q(\zeta_{54})$
• Dimension: $1908$
• Newform subspaces: $2$
• Sturm bound: $216$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.bb (of order \(54\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 648 \)
Character field:			\(\Q(\zeta_{54})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(216\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(648, [\chi])\).

	Total	New	Old
Modular forms	1980	1980	0
Cusp forms	1908	1908	0
Eisenstein series	72	72	0

Trace form

\( 1908 q - 18 q^{2} - 36 q^{3} - 18 q^{4} - 18 q^{6} - 18 q^{8} - 36 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(648, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
648.2.bb.a	$648$	$2$	648.bb	648.ab	$54$	$36$	$2$	$5.174$		\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{54}]$
648.2.bb.b	$648$	$2$	648.bb	648.ab	$54$	$1872$	$104$	$5.174$		None		$4$	$0$	\(-18\)	\(-36\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{54}]$