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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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Results (4 matches)

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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
3995.1.e.a	$3995$	$1$	3995.e	3995.e	$2$	$3$	$3$	$1.994$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-3995}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(-1\)	$1$		\(q-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{2}q^{7}+(1+\beta _{2})q^{9}+\cdots\)
3995.1.e.b	$3995$	$1$	3995.e	3995.e	$2$	$3$	$3$	$1.994$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-3995}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(3\)	\(-1\)	$1$		\(q-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{2}q^{7}+(1+\beta _{2})q^{9}+\cdots\)
3995.1.e.c	$3995$	$1$	3995.e	3995.e	$2$	$3$	$3$	$1.994$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-3995}) \)	None	✓	$2$	$0$	\(0\)	\(1\)	\(-3\)	\(1\)	$1$		\(q-\beta _{2}q^{3}+q^{4}-q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
3995.1.e.d	$3995$	$1$	3995.e	3995.e	$2$	$3$	$3$	$1.994$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-3995}) \)	None	✓	$2$	$0$	\(0\)	\(1\)	\(3\)	\(1\)	$1$		\(q+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{2}q^{7}+(1+\beta _{2})q^{9}+\cdots\)

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