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

• Label: 644.2.v
• Level: $644$
• Weight: $2$
• Character orbit: 644.v
• Rep. character: $\chi_{644}(97,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $160$
• 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.v (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q(\zeta_{22})\)
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	1020	160	860
Cusp forms	900	160	740
Eisenstein series	120	0	120

Trace form

\( 160 q + 8 q^{9} + O(q^{10}) \)

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.v.a	$644$	$2$	644.v	161.k	$22$	$160$	$16$	$5.142$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{2}^{\mathrm{old}}(644, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(644, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 2}\)