Space of modular forms of level 864, weight 2, and Character 864.bt

• Label: 864.2.bt
• Level: $864$
• Weight: $2$
• Character orbit: 864.bt
• Rep. character: $\chi_{864}(11,\cdot)$
• Character field: $\Q(\zeta_{72})$
• Dimension: $3408$
• Newform subspaces: $1$
• Sturm bound: $288$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bt (of order \(72\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 864 \)
Character field:			\(\Q(\zeta_{72})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(288\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(864, [\chi])\).

	Total	New	Old
Modular forms	3504	3504	0
Cusp forms	3408	3408	0
Eisenstein series	96	96	0

Trace form

3408 * q - 24 * q^2 - 24 * q^3 - 24 * q^4 - 24 * q^5 - 24 * q^6 - 24 * q^7 - 36 * q^8 - 24 * q^9 - 12 * q^10 - 24 * q^11 - 24 * q^12 - 24 * q^13 - 24 * q^14 - 48 * q^15 - 24 * q^16 - 24 * q^18 - 12 * q^19 - 24 * q^20 - 24 * q^21 - 24 * q^22 - 24 * q^23 - 84 * q^24 - 24 * q^25 - 24 * q^27 - 48 * q^28 - 24 * q^29 - 24 * q^30 - 24 * q^32 - 48 * q^33 - 36 * q^35 - 24 * q^36 - 12 * q^37 - 24 * q^38 - 24 * q^39 - 24 * q^40 - 24 * q^41 + 96 * q^42 - 24 * q^43 - 36 * q^44 - 24 * q^45 - 12 * q^46 - 48 * q^47 - 24 * q^48 - 336 * q^50 + 12 * q^51 - 24 * q^52 - 24 * q^54 - 48 * q^55 - 24 * q^56 - 24 * q^57 - 132 * q^58 - 24 * q^59 - 24 * q^60 - 24 * q^61 - 36 * q^62 - 12 * q^64 - 48 * q^65 - 216 * q^66 - 24 * q^67 + 24 * q^68 - 24 * q^69 - 24 * q^70 - 36 * q^71 - 24 * q^72 - 12 * q^73 - 24 * q^74 - 24 * q^75 - 24 * q^76 - 24 * q^77 - 24 * q^78 - 48 * q^79 - 48 * q^82 + 96 * q^83 + 204 * q^84 + 36 * q^85 - 24 * q^86 - 24 * q^87 - 24 * q^88 - 36 * q^89 - 24 * q^90 - 12 * q^91 - 252 * q^92 - 24 * q^93 - 24 * q^94 - 24 * q^96 - 48 * q^97 - 36 * q^98 - 24 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(864, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
864.2.bt.a	$864$	$2$	864.bt	864.at	$72$	$3408$	$142$	$6.899$		None		✓	✓	✓	864.2.bt.a	$4$	$0$	\(-24\)	\(-24\)	\(-24\)	\(-24\)		$\mathrm{SU}(2)[C_{72}]$