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The results below are complete, since the LMFDB contains all newforms with $Nk^2$ at most 4000

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad \(p\)	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
165.1.l.a	$165$	$1$	165.l	165.l	$4$	$2$	$1$	$0.082$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-11}) \)	None		✓			165.1.l.a	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-q^{3}+i q^{4}+i q^{5}+q^{9}-i q^{11}+\cdots\)
165.1.l.b	$165$	$1$	165.l	165.l	$4$	$2$	$1$	$0.082$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-11}) \)	None		✓			165.1.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-i q^{3}+i q^{4}-i q^{5}-q^{9}+i q^{11}+\cdots\)

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