Space of modular forms of level 288, weight 1, and Character 288.t

• Label: 288.1.t
• Level: $288$
• Weight: $1$
• Character orbit: 288.t
• Rep. character: $\chi_{288}(79,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	288.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 72 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(288, [\chi])\).

	Total	New	Old
Modular forms	24	6	18
Cusp forms	8	2	6
Eisenstein series	16	4	12

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + q^{3} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(288, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
288.1.t.a	$288$	$1$	288.t	72.p	$6$	$2$	$1$	$0.144$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{11}-q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)