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

• Label: 504.2.ch
• Level: $504$
• Weight: $2$
• Character orbit: 504.ch
• Rep. character: $\chi_{504}(269,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• 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.ch (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 168 \)
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	208	64	144
Cusp forms	176	64	112
Eisenstein series	32	0	32

Trace form

\( 64 q + 4 q^{16} - 16 q^{22} + 32 q^{25} + 44 q^{28} + 60 q^{40} - 16 q^{46} + 16 q^{49} + 36 q^{52} - 44 q^{58} - 24 q^{64} - 60 q^{70} + 48 q^{73} + 16 q^{79} - 132 q^{82} + 4 q^{88} - 108 q^{94}+O(q^{100}) \)

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.ch.a	$504$	$2$	504.ch	168.aa	$6$	$8$	$4$	$4.024$	8.0.4857532416.2	None		✓			504.2.ch.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(20\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(2-2\beta _{3})q^{4}-\beta _{5}q^{5}+(3+\cdots)q^{7}+\cdots\)
504.2.ch.b	$504$	$2$	504.ch	168.aa	$6$	$56$	$28$	$4.024$		None		✓	✓		504.2.ch.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-20\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(504, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)