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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	Image	CM	RM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
2255.1.h.i	$2255$	$1$	2255.h	2255.h	$2$	$4$	$4$	$1.125$	\(\Q(\zeta_{20})^+\)	$D_{10}$	\(\Q(\sqrt{-2255}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$		\(q+\beta _{3}q^{2}-\beta _{1}q^{3}+(1-\beta _{2})q^{4}-q^{5}+\cdots\)
2255.1.h.j	$2255$	$1$	2255.h	2255.h	$2$	$4$	$4$	$1.125$	\(\Q(\zeta_{20})^+\)	$D_{10}$	\(\Q(\sqrt{-2255}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$		\(q-\beta _{3}q^{2}-\beta _{1}q^{3}+(1-\beta _{2})q^{4}-q^{5}+\cdots\)

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