Space of modular forms of level 288, weight 3, and Character 288.o

• Label: 288.3.o
• Level: $288$
• Weight: $3$
• Character orbit: 288.o
• Rep. character: $\chi_{288}(31,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $48$
• Newform subspaces: $3$
• Sturm bound: $144$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	288.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 36 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(144\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(288, [\chi])\).

	Total	New	Old
Modular forms	208	48	160
Cusp forms	176	48	128
Eisenstein series	32	0	32

Trace form

\( 48 q + 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(288, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
288.3.o.a	$288$	$3$	288.o	36.f	$6$	$4$	$2$	$7.847$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(-14\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+3\zeta_{12}^{3}q^{3}-7\zeta_{12}^{2}q^{5}+5\zeta_{12}q^{7}+\cdots\)
288.3.o.b	$288$	$3$	288.o	36.f	$6$	$20$	$10$	$7.847$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(14\)	\(0\)	$2^{26}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{3}+(\beta _{1}-\beta _{4}+\beta _{7})q^{5}+(\beta _{15}+\cdots)q^{7}+\cdots\)
288.3.o.c	$288$	$3$	288.o	36.f	$6$	$24$	$12$	$7.847$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)