Space of modular forms of level 644, weight 4, and Character 644.i

• Label: 644.4.i
• Level: $644$
• Weight: $4$
• Character orbit: 644.i
• Rep. character: $\chi_{644}(93,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $88$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	644.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(644, [\chi])\).

	Total	New	Old
Modular forms	588	88	500
Cusp forms	564	88	476
Eisenstein series	24	0	24

Trace form

\( 88 q - 44 q^{7} - 364 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(644, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
644.4.i.a	$644$	$4$	644.i	7.c	$3$	$44$	$22$	$37.997$		None		✓			644.4.i.a	$2$	$0$	\(0\)	\(-12\)	\(-10\)	\(-38\)		$\mathrm{SU}(2)[C_{3}]$
644.4.i.b	$644$	$4$	644.i	7.c	$3$	$44$	$22$	$37.997$		None		✓			644.4.i.b	$2$	$0$	\(0\)	\(12\)	\(10\)	\(-6\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{4}^{\mathrm{old}}(644, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(644, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 2}\)