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

• Label: 864.2.f
• Level: $864$
• Weight: $2$
• Character orbit: 864.f
• Rep. character: $\chi_{864}(431,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	168	16	152
Cusp forms	120	16	104
Eisenstein series	48	0	48

Trace form

\( 16 q + O(q^{10}) \)

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.f.a	$864$	$2$	864.f	24.f	$2$	$8$	$8$	$6.899$	8.0.\(\cdots\).3	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}-\beta _{4}q^{7}-\beta _{6}q^{11}+(\beta _{4}+\beta _{7})q^{13}+\cdots\)
864.2.f.b	$864$	$2$	864.f	24.f	$2$	$8$	$8$	$6.899$	8.0.170772624.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{6}q^{11}+\beta _{7}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 9}\)