↑

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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
684.2.a.c	$684$	$2$	684.a	1.a	$1$	$1$	$1$	$5.462$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+q^{7}+5q^{11}-6q^{13}+5q^{17}+\cdots\)
684.2.a.d	$684$	$2$	684.a	1.a	$1$	$2$	$2$	$5.462$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+(1-\beta )q^{7}+(1+\beta )q^{11}+\cdots\)

Download displayed columns for results to