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

• Label: 504.2.q
• Level: $504$
• Weight: $2$
• Character orbit: 504.q
• Rep. character: $\chi_{504}(25,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $192$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(192\)
Trace bound:			\(5\)
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	48	160
Cusp forms	176	48	128
Eisenstein series	32	0	32

Trace form

48 * q + 4 * q^5 + 4 * q^9 - 8 * q^15 + 8 * q^17 - 4 * q^23 - 24 * q^25 - 6 * q^27 - 6 * q^29 - 12 * q^31 + 8 * q^33 + 12 * q^35 - 26 * q^39 + 18 * q^41 + 6 * q^43 - 2 * q^45 - 12 * q^47 - 6 * q^49 + 36 * q^51 + 4 * q^53 + 12 * q^55 - 20 * q^57 + 72 * q^59 - 12 * q^61 + 26 * q^63 - 24 * q^65 - 32 * q^69 - 40 * q^71 + 30 * q^75 + 28 * q^77 + 12 * q^79 - 8 * q^81 - 36 * q^83 - 68 * q^87 + 18 * q^89 - 6 * q^91 + 8 * q^93 + 20 * q^95 - 32 * q^99

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.q.a	$504$	$2$	504.q	63.h	$3$	$2$	$1$	$4.024$	\(\Q(\sqrt{-3}) \)	None		✓			504.2.q.a	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
504.2.q.b	$504$	$2$	504.q	63.h	$3$	$2$	$1$	$4.024$	\(\Q(\sqrt{-3}) \)	None		✓			504.2.q.b	$2$	$0$	\(0\)	\(0\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
504.2.q.c	$504$	$2$	504.q	63.h	$3$	$22$	$11$	$4.024$		None		✓			504.2.q.c	$2$	$0$	\(0\)	\(-2\)	\(1\)	\(5\)		$\mathrm{SU}(2)[C_{3}]$
504.2.q.d	$504$	$2$	504.q	63.h	$3$	$22$	$11$	$4.024$		None		✓			504.2.q.d	$2$	$0$	\(0\)	\(2\)	\(3\)	\(-5\)		$\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(504, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)