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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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2
2.38.a.a	$2$	$38$	2.a	1.a	$1$	$2$	$2$	$17.343$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$1$	\(-524288\)	\(423071208\)	\(-13\!\cdots\!40\)	\(31\!\cdots\!56\)		$+$	$+$	$2^{8}\cdot 3^{3}\cdot 5$	$\mathrm{SU}(2)$	\(q-2^{18}q^{2}+(211535604-\beta )q^{3}+2^{36}q^{4}+\cdots\)
2.38.a.b	$2$	$38$	2.a	1.a	$1$	$2$	$2$	$17.343$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$0$	\(524288\)	\(-501686808\)	\(41\!\cdots\!00\)	\(-35\!\cdots\!56\)		$-$	$-$	$2^{8}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+2^{18}q^{2}+(-250843404-\beta )q^{3}+\cdots\)