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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 (13 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.d	$800$	$4$	800.a	1.a	$1$	$1$	$1$	$47.202$	\(\Q\)	None	✓				160.4.a.a	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+6q^{7}-23q^{9}-60q^{11}-50q^{13}+\cdots\)
800.4.a.e	$800$	$4$	800.a	1.a	$1$	$1$	$1$	$47.202$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓				160.4.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-3^{3}q^{9}-92q^{13}+104q^{17}+130q^{29}+\cdots\)
800.4.a.k	$800$	$4$	800.a	1.a	$1$	$1$	$1$	$47.202$	\(\Q\)	None	✓				32.4.a.a	$1$	$0$	\(0\)	\(8\)	\(0\)	\(16\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+8q^{3}+2^{4}q^{7}+37q^{9}+40q^{11}+\cdots\)
800.4.a.m	$800$	$4$	800.a	1.a	$1$	$2$	$2$	$47.202$	\(\Q(\sqrt{6}) \)	None	✓				160.4.a.c	$1$	$0$	\(0\)	\(-8\)	\(0\)	\(-8\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-4+\beta )q^{3}+(-4-5\beta )q^{7}+(13+\cdots)q^{9}+\cdots\)
800.4.a.n	$800$	$4$	800.a	1.a	$1$	$2$	$2$	$47.202$	\(\Q(\sqrt{29}) \)	None	✓				160.4.c.b	$2$	$0$	\(0\)	\(-8\)	\(0\)	\(8\)		$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-4q^{3}+4q^{7}-11q^{9}+2\beta q^{11}+\beta q^{13}+\cdots\)
800.4.a.o	$800$	$4$	800.a	1.a	$1$	$2$	$2$	$47.202$	\(\Q(\sqrt{5}) \)	None	✓				160.4.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+7\beta q^{7}-7q^{9}-2\beta q^{11}+62q^{13}+\cdots\)
800.4.a.p	$800$	$4$	800.a	1.a	$1$	$2$	$2$	$47.202$	\(\Q(\sqrt{10}) \)	None	✓				160.4.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+3\beta q^{7}+13q^{9}+2\beta q^{11}+\cdots\)
800.4.a.t	$800$	$4$	800.a	1.a	$1$	$2$	$2$	$47.202$	\(\Q(\sqrt{5}) \)	\(\Q(\sqrt{-5}) \)	✓				160.4.c.c	$2$	$0$	\(0\)	\(14\)	\(0\)	\(18\)		$-$	$-$	$+$	$2$	$N(\mathrm{U}(1))$	\(q+(7-\beta )q^{3}+(9-11\beta )q^{7}+(3^{3}-14\beta )q^{9}+\cdots\)
800.4.a.v	$800$	$4$	800.a	1.a	$1$	$3$	$3$	$47.202$	3.3.5685.1	None	✓	✓			800.4.a.u	$1$	$0$	\(0\)	\(-5\)	\(0\)	\(2\)		$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{1})q^{3}+(1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
800.4.a.x	$800$	$4$	800.a	1.a	$1$	$3$	$3$	$47.202$	3.3.5685.1	None	✓	✓			800.4.a.u	$1$	$0$	\(0\)	\(5\)	\(0\)	\(-2\)		$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(2+\beta _{1})q^{3}+(-1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
800.4.a.z	$800$	$4$	800.a	1.a	$1$	$4$	$4$	$47.202$	4.4.37485.2	None	✓				160.4.c.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2^{7}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{7}+(19-3\beta _{2}+\cdots)q^{9}+\cdots\)
800.4.a.ba	$800$	$4$	800.a	1.a	$1$	$4$	$4$	$47.202$	4.4.2106005.1	None	✓	✓			800.4.a.ba	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{7}+(24+\beta _{2})q^{9}+\cdots\)
800.4.a.bb	$800$	$4$	800.a	1.a	$1$	$4$	$4$	$47.202$	4.4.2106005.1	None	✓	✓	✓		800.4.a.ba	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{7}+(24+\beta _{2})q^{9}+\cdots\)

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