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

• Label: 864.2.v
• Level: $864$
• Weight: $2$
• Character orbit: 864.v
• Rep. character: $\chi_{864}(109,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $256$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.v (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 32 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	600	256	344
Cusp forms	552	256	296
Eisenstein series	48	0	48

Trace form

\( 256 q + 8 q^{10} - 64 q^{16} + 16 q^{22} + 32 q^{40} + 32 q^{46} + 8 q^{52} - 32 q^{55} + 32 q^{58} + 32 q^{61} - 48 q^{64} + 128 q^{67} - 48 q^{70} + 64 q^{76} - 40 q^{82} - 40 q^{88} + 48 q^{91} - 24 q^{94}+O(q^{100}) \)

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.v.a	$864$	$2$	864.v	32.g	$8$	$128$	$32$	$6.899$		None		✓			864.2.v.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
864.2.v.b	$864$	$2$	864.v	32.g	$8$	$128$	$32$	$6.899$		None		✓			864.2.v.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

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

\( S_{2}^{\mathrm{old}}(864, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)