Space of modular forms of level 644, weight 2, and Character 644.z

• Label: 644.2.z
• Level: $644$
• Weight: $2$
• Character orbit: 644.z
• Rep. character: $\chi_{644}(11,\cdot)$
• Character field: $\Q(\zeta_{66})$
• Dimension: $1840$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.z (of order \(66\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 644 \)
Character field:			\(\Q(\zeta_{66})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(644, [\chi])\).

	Total	New	Old
Modular forms	2000	2000	0
Cusp forms	1840	1840	0
Eisenstein series	160	160	0

Trace form

\( 1840 q - 11 q^{2} - 11 q^{4} - 22 q^{5} - 28 q^{6} - 32 q^{8} - 102 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(644, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
644.2.z.a	$644$	$2$	644.z	644.z	$66$	$1840$	$92$	$5.142$		None		$8$	$0$	\(-11\)	\(0\)	\(-22\)	\(0\)		$\mathrm{SU}(2)[C_{66}]$