Space of modular forms of level 864, weight 4, and Character 864.c

• Label: 864.4.c
• Level: $864$
• Weight: $4$
• Character orbit: 864.c
• Rep. character: $\chi_{864}(863,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $576$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	864.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(576\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(864, [\chi])\).

	Total	New	Old
Modular forms	456	48	408
Cusp forms	408	48	360
Eisenstein series	48	0	48

Trace form

\( 48 q + 72 q^{13} - 1032 q^{25} + 1560 q^{37} - 2304 q^{49} + 2328 q^{61} + 768 q^{73} + 2256 q^{85} - 3024 q^{97}+O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(864, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
864.4.c.a	$864$	$4$	864.c	12.b	$2$	$24$	$24$	$50.978$		None		✓			864.4.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
864.4.c.b	$864$	$4$	864.c	12.b	$2$	$24$	$24$	$50.978$		None		✓			864.4.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(864, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)