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

• Label: 644.2.w
• Level: $644$
• Weight: $2$
• Character orbit: 644.w
• Rep. character: $\chi_{644}(15,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $720$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.w (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 92 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	1000	720	280
Cusp forms	920	720	200
Eisenstein series	80	0	80

Trace form

\( 720 q - 2 q^{2} + 6 q^{4} - 2 q^{6} + 4 q^{8} + 72 q^{9} + O(q^{10}) \)

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.w.a	$644$	$2$	644.w	92.h	$22$	$360$	$36$	$5.142$		None		$2$	$0$	\(-1\)	\(0\)	\(0\)	\(-36\)		$\mathrm{SU}(2)[C_{22}]$
644.2.w.b	$644$	$2$	644.w	92.h	$22$	$360$	$36$	$5.142$		None		$2$	$0$	\(-1\)	\(0\)	\(0\)	\(36\)		$\mathrm{SU}(2)[C_{22}]$

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

\( S_{2}^{\mathrm{old}}(644, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 2}\)