↑

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	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
16.22.a.e	$16$	$22$	16.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{358549}) \)	None	✓	$1$	$1$	\(0\)	\(105432\)	\(2108140\)	\(-444771792\)		$+$	$+$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(52716-\beta )q^{3}+(1054070-20\beta )q^{5}+\cdots\)
16.22.a.f	$16$	$22$	16.a	1.a	$1$	$3$	$3$	$44.716$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-96764\)	\(-24111774\)	\(-295988280\)		$+$	$+$	$2^{21}\cdot 3\cdot 5\cdot 7$	$\mathrm{SU}(2)$	\(q+(-32255+\beta _{1})q^{3}+(-8037261+\cdots)q^{5}+\cdots\)

Download displayed columns for results to