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

• Label: 644.2.c
• Level: $644$
• Weight: $2$
• Character orbit: 644.c
• Rep. character: $\chi_{644}(183,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• 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.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 92 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(11\)

Dimensions

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

	Total	New	Old
Modular forms	100	72	28
Cusp forms	92	72	20
Eisenstein series	8	0	8

Trace form

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

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

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

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