Space of modular forms of level 864, weight 5, and Character 864.t

• Label: 864.5.t
• Level: $864$
• Weight: $5$
• Character orbit: 864.t
• Rep. character: $\chi_{864}(559,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $92$
• Newform subspaces: $2$
• Sturm bound: $720$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	864.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 72 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(720\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(864, [\chi])\).

	Total	New	Old
Modular forms	1200	100	1100
Cusp forms	1104	92	1012
Eisenstein series	96	8	88

Trace form

\( 92 q + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(864, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
864.5.t.a	$864$	$5$	864.t	72.p	$6$	$4$	$2$	$89.312$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)					72.5.p.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{3}$	$\mathrm{U}(1)[D_{6}]$	\(q+(-23\beta _{1}+7\beta _{2})q^{11}+(-287-2\beta _{3})q^{17}+\cdots\)
864.5.t.b	$864$	$5$	864.t	72.p	$6$	$88$	$44$	$89.312$		None			✓		72.5.p.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{5}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(864, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)