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Level	Weight	Analytic conductor	\(Nk^2\)	Dim.

Bad \(p\)	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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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
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	7	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
399.2.a.b	$399$	$2$	399.a	1.a	$1$	$1$	$1$	$3.186$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(4\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+4q^{5}-q^{6}-q^{7}+\cdots\)
399.2.a.e	$399$	$2$	399.a	1.a	$1$	$3$	$3$	$3.186$	3.3.404.1	None	✓	$1$	$0$	\(1\)	\(3\)	\(0\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

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