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Note: Search results may be incomplete due to uncomputed quantities: atkin_lehner_string (110727 objects)

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 (3 matches)

 

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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	13
507.2.a.e	$507$	$2$	507.a	1.a	$1$	$2$	$2$	$4.048$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+2\beta q^{5}+\beta q^{7}+q^{9}+\cdots\)
507.2.a.f	$507$	$2$	507.a	1.a	$1$	$2$	$2$	$4.048$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+q^{4}-\beta q^{6}+2\beta q^{7}+\cdots\)
507.2.a.l	$507$	$2$	507.a	1.a	$1$	$3$	$3$	$4.048$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$0$	\(3\)	\(-3\)	\(6\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}-\beta _{2})q^{2}-q^{3}+(4-\beta _{1})q^{4}+\cdots\)