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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.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.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.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.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.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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