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

\( 3408 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 24 q^{6} - 24 q^{7} - 36 q^{8} - 24 q^{9} + O(q^{10}) \)

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	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		$4$	$0$	\(-24\)	\(-24\)	\(-24\)	\(-24\)		$\mathrm{SU}(2)[C_{72}]$