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

• Label: 504.2.bf
• Level: $504$
• Weight: $2$
• Character orbit: 504.bf
• Rep. character: $\chi_{504}(115,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $184$
• 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.bf (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 504 \)
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	200	200	0
Cusp forms	184	184	0
Eisenstein series	16	16	0

Trace form

184 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 - 8 * q^8 - 2 * q^9 - 6 * q^10 + 2 * q^11 + 12 * q^12 + 2 * q^14 - 2 * q^16 - 12 * q^17 - 4 * q^18 - 12 * q^19 + 24 * q^20 - 6 * q^22 - 12 * q^24 - 74 * q^25 - 5 * q^30 - 42 * q^32 - 6 * q^33 - 6 * q^34 - 18 * q^35 + 2 * q^36 - 33 * q^38 + 12 * q^40 + 10 * q^42 - 4 * q^43 - 21 * q^44 + 2 * q^46 - 9 * q^48 - 2 * q^49 + 19 * q^50 + 6 * q^51 + 21 * q^52 - 51 * q^54 - 2 * q^56 - 20 * q^57 + 5 * q^58 + 25 * q^60 - 8 * q^64 + 36 * q^65 + 36 * q^66 - 4 * q^67 + 12 * q^68 + 21 * q^70 - 4 * q^72 - 12 * q^73 + 47 * q^74 - 6 * q^75 - 12 * q^76 - 39 * q^78 - 63 * q^80 + 14 * q^81 - 12 * q^82 + 60 * q^83 + 7 * q^84 - 31 * q^86 + 9 * q^88 - 36 * q^89 - 33 * q^90 + 20 * q^91 - 32 * q^92 - 45 * q^96 + 27 * q^98 - 26 * 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.bf.a	$504$	$2$	504.bf	504.af	$6$	$4$	$2$	$4.024$	\(\Q(\zeta_{12})\)	None		✓			504.2.bf.a	$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{12}^{3})q^{2}+(1-2\zeta_{12}^{2})q^{3}+2\zeta_{12}^{3}q^{4}+\cdots\)
504.2.bf.b	$504$	$2$	504.bf	504.af	$6$	$180$	$90$	$4.024$		None		✓	✓		504.2.bf.b	$4$	$0$	\(-6\)	\(-6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$