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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	3	23	29
4002.2.a.bg	$4002$	$2$	4002.a	1.a	$1$	$7$	$7$	$31.956$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-7\)	\(-7\)	\(2\)	\(-5\)		$+$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-\beta _{5}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
4002.2.a.bh	$4002$	$2$	4002.a	1.a	$1$	$7$	$7$	$31.956$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(7\)	\(7\)	\(1\)	\(-2\)		$-$	$-$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+\beta _{3}q^{5}+q^{6}-\beta _{6}q^{7}+\cdots\)