Space of modular forms of level 72, weight 7, and Character 72.j

• Label: 72.7.j
• Level: $72$
• Weight: $7$
• Character orbit: 72.j
• Rep. character: $\chi_{72}(5,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $140$
• Newform subspaces: $1$
• Sturm bound: $84$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	72.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 72 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(84\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(72, [\chi])\).

	Total	New	Old
Modular forms	148	148	0
Cusp forms	140	140	0
Eisenstein series	8	8	0

Trace form

\( 140 q - 3 q^{2} - q^{4} + 317 q^{6} - 2 q^{7} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(72, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
72.7.j.a	$72$	$7$	72.j	72.j	$6$	$140$	$70$	$16.564$		None		$4$	$0$	\(-3\)	\(0\)	\(0\)	\(-2\)		$\mathrm{SU}(2)[C_{6}]$