Space of modular forms of level 288, weight 6, and Character 288.c

• Label: 288.6.c
• Level: $288$
• Weight: $6$
• Character orbit: 288.c
• Rep. character: $\chi_{288}(287,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(288\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(288, [\chi])\).

	Total	New	Old
Modular forms	256	20	236
Cusp forms	224	20	204
Eisenstein series	32	0	32

Trace form

\( 20 q + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(288, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
288.6.c.a	$288$	$6$	288.c	12.b	$2$	$8$	$8$	$46.191$	8.0.\(\cdots\).8	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{20}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(5\beta _{2}-\beta _{6})q^{5}+(-\beta _{1}-\beta _{4})q^{7}+(8\beta _{3}+\cdots)q^{11}+\cdots\)
288.6.c.b	$288$	$6$	288.c	12.b	$2$	$12$	$12$	$46.191$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{55}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-3\beta _{6}+\beta _{7})q^{5}+\beta _{4}q^{7}+(\beta _{9}-\beta _{10}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(288, [\chi]) \cong \)