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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
3828.1.f.g	$3828$	$1$	3828.f	3828.f	$2$	$2$	$2$	$1.910$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-87}) \), \(\Q(\sqrt{-33}) \)	\(\Q(\sqrt{319}) \)		✓			3828.1.f.g	$8$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$		\(q-iq^{2}-iq^{3}-q^{4}-q^{6}+q^{7}+iq^{8}+\cdots\)
3828.1.f.h	$3828$	$1$	3828.f	3828.f	$2$	$2$	$2$	$1.910$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-87}) \), \(\Q(\sqrt{-33}) \)	\(\Q(\sqrt{319}) \)		✓			3828.1.f.g	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$		\(q+iq^{2}-iq^{3}-q^{4}+q^{6}-q^{7}-iq^{8}+\cdots\)

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