Space of modular forms of level 72, weight 8, and Character 72.l

• Label: 72.8.l
• Level: $72$
• Weight: $8$
• Character orbit: 72.l
• Rep. character: $\chi_{72}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $164$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	72.l (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 72 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(72, [\chi])\).

	Total	New	Old
Modular forms	172	172	0
Cusp forms	164	164	0
Eisenstein series	8	8	0

Trace form

\( 164 q - 3 q^{2} - 4 q^{3} - q^{4} - 43 q^{6} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(72, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
72.8.l.a	$72$	$8$	72.l	72.l	$6$	$4$	$2$	$22.492$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(86\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(8\beta _{1}-8\beta _{3})q^{2}+(13\beta _{1}+43\beta _{2}-13\beta _{3})q^{3}+\cdots\)
72.8.l.b	$72$	$8$	72.l	72.l	$6$	$160$	$80$	$22.492$		None		$4$	$0$	\(-3\)	\(-90\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$