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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

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Results (7 matches)

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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.c	$800$	$4$	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.g	$800$	$4$	800.a	1.a	$1$	$1$	$1$	$47.202$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓				160.4.c.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-3^{3}q^{9}+92q^{13}-104q^{17}+130q^{29}+\cdots\)
800.4.a.i	$800$	$4$	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.l	$800$	$4$	800.a	1.a	$1$	$2$	$2$	$47.202$	\(\Q(\sqrt{5}) \)	\(\Q(\sqrt{-5}) \)	✓				160.4.c.c	$2$	$1$	\(0\)	\(-14\)	\(0\)	\(-18\)		$+$	$-$	$-$	$2$	$N(\mathrm{U}(1))$	\(q+(-7-\beta )q^{3}+(-9-11\beta )q^{7}+(3^{3}+\cdots)q^{9}+\cdots\)
800.4.a.r	$800$	$4$	800.a	1.a	$1$	$2$	$2$	$47.202$	\(\Q(\sqrt{29}) \)	None	✓				160.4.c.b	$2$	$1$	\(0\)	\(8\)	\(0\)	\(-8\)		$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+4q^{3}-4q^{7}-11q^{9}-2\beta q^{11}+\beta q^{13}+\cdots\)
800.4.a.w	$800$	$4$	800.a	1.a	$1$	$3$	$3$	$47.202$	3.3.5685.1	None	✓	✓			800.4.a.u	$1$	$1$	\(0\)	\(5\)	\(0\)	\(-2\)		$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(2+\beta _{1})q^{3}+(-1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
800.4.a.y	$800$	$4$	800.a	1.a	$1$	$4$	$4$	$47.202$	4.4.37485.2	None	✓		✓		160.4.c.d	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{7}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{7}+(19-3\beta _{2}+\cdots)q^{9}+\cdots\)

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