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

• Label: 504.2.bf
• Level: $504$
• Weight: $2$
• Character orbit: 504.bf
• Rep. character: $\chi_{504}(115,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $184$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bf (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 504 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

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

\( 184 q - 2 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} - 8 q^{8} - 2 q^{9} + O(q^{10}) \)

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.bf.a	$504$	$2$	504.bf	504.af	$6$	$4$	$2$	$4.024$	\(\Q(\zeta_{12})\)	None		✓			504.2.bf.a	$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{12}^{3})q^{2}+(1-2\zeta_{12}^{2})q^{3}+2\zeta_{12}^{3}q^{4}+\cdots\)
504.2.bf.b	$504$	$2$	504.bf	504.af	$6$	$180$	$90$	$4.024$		None		✓	✓		504.2.bf.b	$4$	$0$	\(-6\)	\(-6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$