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

• Label: 504.2.i
• Level: $504$
• Weight: $2$
• Character orbit: 504.i
• Rep. character: $\chi_{504}(125,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• 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.i (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 168 \)
Character field:			\(\Q\)
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	104	32	72
Cusp forms	88	32	56
Eisenstein series	16	0	16

Trace form

\( 32 q + O(q^{10}) \)

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.i.a	$504$	$2$	504.i	168.i	$2$	$8$	$8$	$4.024$	8.0.157351936.1	\(\Q(\sqrt{-7}) \)		✓			504.2.i.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{7}+\beta _{3}q^{8}+\cdots\)
504.2.i.b	$504$	$2$	504.i	168.i	$2$	$24$	$24$	$4.024$		None		✓	✓		504.2.i.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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