Space of modular forms of level 504, weight 2, and Character 504.w

• Label: 504.2.w
• Level: $504$
• Weight: $2$
• Character orbit: 504.w
• Rep. character: $\chi_{504}(205,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $184$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.w (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 504 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(504, [\chi])\).

	Total	New	Old
Modular forms	200	200	0
Cusp forms	184	184	0
Eisenstein series	16	16	0

Trace form

\( 184 q + q^{2} + q^{4} - 2 q^{6} - 2 q^{7} - 8 q^{8} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(504, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
504.2.w.a	$504$	$2$	504.w	504.w	$6$	$184$	$92$	$4.024$		None		✓	✓	✓	504.2.w.a	$4$	$0$	\(1\)	\(0\)	\(0\)	\(-2\)		$\mathrm{SU}(2)[C_{6}]$