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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	11	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1045.4.a.a	$1045$	$4$	1045.a	1.a	$1$	$1$	$1$	$61.657$	\(\Q\)	None	✓	$1$	$1$	\(-5\)	\(-1\)	\(-5\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{2}-q^{3}+17q^{4}-5q^{5}+5q^{6}+\cdots\)
1045.4.a.c	$1045$	$4$	1045.a	1.a	$1$	$20$	$20$	$61.657$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(-8\)	\(-100\)	\(49\)		$+$	$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(3+\beta _{2})q^{4}-5q^{5}+\cdots\)

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