Space of modular forms of level 669, weight 2, and Character 669.c

• Label: 669.2.c
• Level: $669$
• Weight: $2$
• Character orbit: 669.c
• Rep. character: $\chi_{669}(668,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $1$
• Sturm bound: $149$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 669 = 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	669.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 669 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(149\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(669, [\chi])\).

	Total	New	Old
Modular forms	76	76	0
Cusp forms	72	72	0
Eisenstein series	4	4	0

Trace form

\( 72 q - 72 q^{4} + 8 q^{7} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(669, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
669.2.c.a	$669$	$2$	669.c	669.c	$2$	$72$	$72$	$5.342$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{2}]$