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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3
3.40.a.a	$3$	$40$	3.a	1.a	$1$	$3$	$3$	$28.902$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(-1107000\)	\(3486784401\)	\(93\!\cdots\!90\)	\(13\!\cdots\!04\)		$-$	$-$	$2^{10}\cdot 3^{6}\cdot 5$	$\mathrm{SU}(2)$	\(q+(-369000-\beta _{1})q^{2}+3^{19}q^{3}+(335300075200+\cdots)q^{4}+\cdots\)
3.40.a.b	$3$	$40$	3.a	1.a	$1$	$3$	$3$	$28.902$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(533574\)	\(-3486784401\)	\(-53\!\cdots\!30\)	\(-15\!\cdots\!28\)		$+$	$+$	$2^{8}\cdot 3^{6}\cdot 5\cdot 7\cdot 13$	$\mathrm{SU}(2)$	\(q+(177858-\beta _{1})q^{2}-3^{19}q^{3}+(319147551244+\cdots)q^{4}+\cdots\)