↑

Learn more

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

Refine search

Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad \(p\)	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

				Sort order	Select

Results (8 matches)

Download displayed columns for results to

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	5	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
800.4.a.a	$800$	$4$	800.a	1.a	$1$	$1$	$1$	$47.202$	\(\Q\)	None	✓				32.4.a.a	$1$	$1$	\(0\)	\(-8\)	\(0\)	\(-16\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-8q^{3}-2^{4}q^{7}+37q^{9}-40q^{11}+\cdots\)
800.4.a.b	$800$	$4$	800.a	1.a	$1$	$1$	$1$	$47.202$	\(\Q\)	None	✓	✓			800.4.a.b	$1$	$1$	\(0\)	\(-5\)	\(0\)	\(10\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{3}+10q^{7}-2q^{9}-15q^{11}+8q^{13}+\cdots\)
800.4.a.f	$800$	$4$	800.a	1.a	$1$	$1$	$1$	$47.202$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓				32.4.a.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-3^{3}q^{9}+18q^{13}+94q^{17}-130q^{29}+\cdots\)
800.4.a.h	$800$	$4$	800.a	1.a	$1$	$1$	$1$	$47.202$	\(\Q\)	None	✓				160.4.a.a	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-6q^{7}-23q^{9}+60q^{11}-50q^{13}+\cdots\)
800.4.a.j	$800$	$4$	800.a	1.a	$1$	$1$	$1$	$47.202$	\(\Q\)	None	✓	✓			800.4.a.b	$1$	$1$	\(0\)	\(5\)	\(0\)	\(-10\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+5q^{3}-10q^{7}-2q^{9}+15q^{11}+8q^{13}+\cdots\)
800.4.a.q	$800$	$4$	800.a	1.a	$1$	$2$	$2$	$47.202$	\(\Q(\sqrt{13}) \)	None	✓				160.4.a.e	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-\beta q^{7}+5^{2}q^{9}+6\beta q^{11}-34q^{13}+\cdots\)
800.4.a.s	$800$	$4$	800.a	1.a	$1$	$2$	$2$	$47.202$	\(\Q(\sqrt{6}) \)	None	✓				160.4.a.c	$1$	$1$	\(0\)	\(8\)	\(0\)	\(8\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(4+\beta )q^{3}+(4-5\beta )q^{7}+(13+8\beta )q^{9}+\cdots\)
800.4.a.u	$800$	$4$	800.a	1.a	$1$	$3$	$3$	$47.202$	3.3.5685.1	None	✓	✓	✓		800.4.a.u	$1$	$1$	\(0\)	\(-5\)	\(0\)	\(2\)		$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{1})q^{3}+(1+\beta _{1}+\beta _{2})q^{7}+\cdots\)

Download displayed columns for results to