Space of modular forms of level 864, weight 3, and Character 864.g

• Label: 864.3.g
• Level: $864$
• Weight: $3$
• Character orbit: 864.g
• Rep. character: $\chi_{864}(703,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $4$
• Sturm bound: $432$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	864.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(432\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(864, [\chi])\).

	Total	New	Old
Modular forms	312	32	280
Cusp forms	264	32	232
Eisenstein series	48	0	48

Trace form

\( 32 q + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(864, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
864.3.g.a	$864$	$3$	864.g	4.b	$2$	$8$	$8$	$23.542$	8.0.22581504.2	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{14}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{2})q^{5}+\beta _{7}q^{7}+(\beta _{3}+\beta _{6}+\cdots)q^{11}+\cdots\)
864.3.g.b	$864$	$3$	864.g	4.b	$2$	$8$	$8$	$23.542$	8.0.56070144.2	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{12}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{3})q^{5}+(-\beta _{2}-\beta _{6})q^{7}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
864.3.g.c	$864$	$3$	864.g	4.b	$2$	$8$	$8$	$23.542$	8.0.22581504.2	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{14}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{2})q^{5}-\beta _{6}q^{7}+(-\beta _{4}-\beta _{5}+\cdots)q^{11}+\cdots\)
864.3.g.d	$864$	$3$	864.g	4.b	$2$	$8$	$8$	$23.542$	8.0.56070144.2	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{12}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{3})q^{5}+(\beta _{2}+\beta _{6})q^{7}+(-\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)