Space of modular forms of level 144, weight 6, and Character 144.l

• Label: 144.6.l
• Level: $144$
• Weight: $6$
• Character orbit: 144.l
• Rep. character: $\chi_{144}(35,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $80$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	144.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 48 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(144, [\chi])\).

	Total	New	Old
Modular forms	248	80	168
Cusp forms	232	80	152
Eisenstein series	16	0	16

Trace form

\( 80 q + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(144, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
144.6.l.a	$144$	$6$	144.l	48.k	$4$	$80$	$40$	$23.095$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{6}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)