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 + 12 * q^12 - 22 * q^18 + 14 * q^20 + 24 * q^23 - 2 * q^24 + 72 * q^25 - 56 * q^26 - 56 * q^30 - 10 * q^32 + 16 * q^33 + 12 * q^34 - 28 * q^38 - 24 * q^39 + 12 * q^40 - 8 * q^41 - 20 * q^42 - 64 * q^44 + 24 * q^46 - 24 * q^48 - 72 * q^49 + 46 * q^50 - 18 * q^52 + 42 * q^54 + 8 * q^57 + 18 * q^58 - 16 * q^60 + 48 * q^62 - 60 * q^64 + 118 * q^66 + 78 * q^68 - 112 * q^71 + 34 * q^72 - 12 * q^76 + 8 * q^78 + 88 * q^80 - 8 * q^81 - 36 * q^82 + 14 * q^84 - 42 * q^86 - 104 * q^87 - 24 * q^88 - 160 * q^90 + 66 * q^92 + 6 * q^94 - 64 * q^95 - 24 * q^96

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.cs.a	$504$	$2$	504.cs	72.n	$6$	$72$	$36$	$4.024$		None		✓			504.2.cs.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(36\)		$\mathrm{SU}(2)[C_{6}]$
504.2.cs.b	$504$	$2$	504.cs	72.n	$6$	$72$	$36$	$4.024$		None		✓			504.2.cs.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-36\)		$\mathrm{SU}(2)[C_{6}]$

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

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