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

• Label: 504.2.cs
• Level: $504$
• Weight: $2$
• Character orbit: 504.cs
• Rep. character: $\chi_{504}(85,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $144$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cs (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 72 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(6\)
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	144	56
Cusp forms	184	144	40
Eisenstein series	16	0	16

Trace form

\( 144 q - 6 q^{6} + 12 q^{8} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
504.2.cs.a	$504$	$2$	504.cs	72.n	$6$	$72$	$36$	$4.024$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(36\)		$\mathrm{SU}(2)[C_{6}]$
504.2.cs.b	$504$	$2$	504.cs	72.n	$6$	$72$	$36$	$4.024$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-36\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(504, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(504, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)