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

• Label: 648.2.q
• Level: $648$
• Weight: $2$
• Character orbit: 648.q
• Rep. character: $\chi_{648}(73,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $54$
• 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.q (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{9})\)
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	720	54	666
Cusp forms	576	54	522
Eisenstein series	144	0	144

Trace form

\( 54 q + O(q^{10}) \)

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.q.a	$648$	$2$	648.q	27.e	$9$	$24$	$4$	$5.174$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)		$\mathrm{SU}(2)[C_{9}]$
648.2.q.b	$648$	$2$	648.q	27.e	$9$	$30$	$5$	$5.174$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(3\)		$\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(648, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(648, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 2}\)