Space of modular forms of level 1288, weight 2, and Character 1288.ba

• Label: 1288.2.ba
• Level: $1288$
• Weight: $2$
• Character orbit: 1288.ba
• Rep. character: $\chi_{1288}(689,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1288 = 2^{3} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1288.ba (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1288, [\chi])\).

	Total	New	Old
Modular forms	400	96	304
Cusp forms	368	96	272
Eisenstein series	32	0	32

Trace form

\( 96 q + 44 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1288, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1288.2.ba.a	$1288$	$2$	1288.ba	161.g	$6$	$48$	$24$	$10.285$		None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
1288.2.ba.b	$1288$	$2$	1288.ba	161.g	$6$	$48$	$24$	$10.285$		None		$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1288, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1288, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 3}\)