Space of modular forms of level 288, weight 3, and Character 288.be

• Label: 288.3.be
• Level: $288$
• Weight: $3$
• Character orbit: 288.be
• Rep. character: $\chi_{288}(5,\cdot)$
• Character field: $\Q(\zeta_{24})$
• Dimension: $752$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	288.be (of order \(24\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 288 \)
Character field:			\(\Q(\zeta_{24})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(288, [\chi])\).

	Total	New	Old
Modular forms	784	784	0
Cusp forms	752	752	0
Eisenstein series	32	32	0

Trace form

752 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 - 288 * q^24 - 4 * q^25 - 104 * q^27 - 16 * q^28 - 12 * q^29 + 48 * q^30 - 8 * q^31 - 12 * q^32 - 16 * q^33 - 20 * q^34 - 76 * q^36 - 16 * q^37 - 12 * q^38 + 184 * q^39 - 4 * q^40 - 12 * q^41 + 632 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 60 * q^48 - 480 * q^50 - 80 * q^51 - 4 * q^52 - 316 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 - 184 * q^58 - 12 * q^59 - 436 * q^60 - 4 * q^61 - 16 * q^63 - 16 * q^64 - 24 * q^65 + 808 * q^66 - 4 * q^67 - 204 * q^68 - 8 * q^69 - 4 * q^70 - 428 * q^72 - 16 * q^73 - 12 * q^74 + 92 * q^75 - 316 * q^76 - 12 * q^77 - 288 * q^78 - 16 * q^82 + 1428 * q^83 - 1384 * q^84 - 104 * q^85 - 12 * q^86 + 440 * q^87 - 4 * q^88 + 292 * q^90 - 16 * q^91 - 696 * q^92 + 28 * q^93 + 28 * q^94 - 24 * q^95 + 604 * q^96 - 8 * q^97 - 264 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(288, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
288.3.be.a	$288$	$3$	288.be	288.ae	$24$	$752$	$94$	$7.847$		None		✓	✓	✓	288.3.be.a	$4$	$0$	\(-12\)	\(-8\)	\(-12\)	\(-4\)		$\mathrm{SU}(2)[C_{24}]$