Space of modular forms of level 504, weight 3, and Character 504.cu

• Label: 504.3.cu
• Level: $504$
• Weight: $3$
• Character orbit: 504.cu
• Rep. character: $\chi_{504}(233,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.cu (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(504, [\chi])\).

	Total	New	Old
Modular forms	416	32	384
Cusp forms	352	32	320
Eisenstein series	64	0	64

Trace form

\( 32 q - 24 q^{7} + 16 q^{13} - 32 q^{19} + 88 q^{25} - 24 q^{31} - 56 q^{37} + 96 q^{43} + 16 q^{49} + 208 q^{55} + 112 q^{61} + 176 q^{67} + 312 q^{73} + 72 q^{79} - 608 q^{85} - 368 q^{91} + 80 q^{97}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(504, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
504.3.cu.a	$504$	$3$	504.cu	21.h	$6$	$16$	$8$	$13.733$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			504.3.cu.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-24\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{4}+\beta _{6})q^{5}+(-2+\beta _{1}+\beta _{3}+\beta _{15})q^{7}+\cdots\)
504.3.cu.b	$504$	$3$	504.cu	21.h	$6$	$16$	$8$	$13.733$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			504.3.cu.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{6}q^{5}+(-1-\beta _{4}-\beta _{9}-\beta _{11})q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(504, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(504, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)