Space of modular forms of level 288, weight 4, and Character 288.c

• Label: 288.4.c
• Level: $288$
• Weight: $4$
• Character orbit: 288.c
• Rep. character: $\chi_{288}(287,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	288.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(288, [\chi])\).

	Total	New	Old
Modular forms	160	12	148
Cusp forms	128	12	116
Eisenstein series	32	0	32

Trace form

\( 12 q - 144 q^{13} - 636 q^{25} - 744 q^{37} - 684 q^{49} - 1848 q^{61} - 1536 q^{73} + 3480 q^{85} + 6048 q^{97}+O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(288, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
288.4.c.a	$288$	$4$	288.c	12.b	$2$	$4$	$4$	$16.993$	\(\Q(\zeta_{8})\)	None		✓			288.4.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{5}-\beta_1 q^{7}-\beta_{3} q^{11}+28 q^{13}+\cdots\)
288.4.c.b	$288$	$4$	288.c	12.b	$2$	$8$	$8$	$16.993$	8.0.\(\cdots\).8	None		✓	✓		288.4.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{20}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{2}+\beta _{5})q^{5}+(\beta _{1}-\beta _{3})q^{7}+(-2\beta _{6}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

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