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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	7	11	13
4004.2.a.d	$4004$	$2$	4004.a	1.a	$1$	$4$	$4$	$31.972$	4.4.3981.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(4\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{3})q^{3}+(\beta _{2}+\beta _{3})q^{5}+q^{7}+\cdots\)
4004.2.a.e	$4004$	$2$	4004.a	1.a	$1$	$4$	$4$	$31.972$	\(\Q(\zeta_{15})^+\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-4\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+\cdots\)