↑

Learn more

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

Refine search

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
		Only for weight 1:

				Sort order	Select

Results (displaying both matches)

Download displayed columns for results to

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
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
147.4.a.b	$147$	$4$	147.a	1.a	$1$	$1$	$1$	$8.673$	\(\Q\)	None	✓	$1$	$1$	\(-3\)	\(3\)	\(-3\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}+3q^{3}+q^{4}-3q^{5}-9q^{6}+\cdots\)
147.4.a.k	$147$	$4$	147.a	1.a	$1$	$2$	$2$	$8.673$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(2\)	\(6\)	\(-20\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3q^{3}+(-5+2\beta )q^{4}+\cdots\)

Download displayed columns for results to