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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
1045.2.a.b	$1045$	$2$	1045.a	1.a	$1$	$1$	$1$	$8.344$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-3q^{8}-3q^{9}+q^{10}+\cdots\)
1045.2.a.d	$1045$	$2$	1045.a	1.a	$1$	$5$	$5$	$8.344$	\(\Q(\zeta_{22})^+\)	None	✓	$1$	$1$	\(-3\)	\(-7\)	\(5\)	\(-11\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}-\beta _{4})q^{2}+(-2-\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)

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