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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 (8 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
1612.1.b.a	$1612$	$1$	1612.b	403.b	$2$	$1$	$1$	$0.804$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-403}) \)	None	✓	✓			1612.1.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{9}-q^{11}+q^{13}+q^{25}+q^{31}+\cdots\)
1612.1.b.b	$1612$	$1$	1612.b	403.b	$2$	$1$	$1$	$0.804$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-403}) \)	None	✓	✓			1612.1.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{9}+q^{11}-q^{13}+q^{25}-q^{31}+\cdots\)
3627.1.c.a	$3627$	$1$	3627.c	403.b	$2$	$1$	$1$	$1.810$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-403}) \)	\(\Q(\sqrt{1209}) \)	✓	✓			3627.1.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{4}-q^{13}+q^{16}+q^{25}+q^{31}+\cdots\)
3627.1.c.b	$3627$	$1$	3627.c	403.b	$2$	$1$	$1$	$1.810$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-403}) \)	\(\Q(\sqrt{1209}) \)	✓	✓			3627.1.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{4}+q^{13}+q^{16}+q^{25}-q^{31}+\cdots\)
403.3.b.a	$403$	$3$	403.b	403.b	$2$	$1$	$1$	$10.981$	\(\Q\)	$_{}$	\(\Q(\sqrt{-403}) \)	None	✓	✓			403.3.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{4}+9q^{9}-9q^{11}+13q^{13}+2^{4}q^{16}+\cdots\)
403.3.b.b	$403$	$3$	403.b	403.b	$2$	$1$	$1$	$10.981$	\(\Q\)	$_{}$	\(\Q(\sqrt{-403}) \)	None	✓	✓			403.3.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{4}+9q^{9}+9q^{11}-13q^{13}+2^{4}q^{16}+\cdots\)
1612.3.b.c	$1612$	$3$	1612.b	403.b	$2$	$2$	$2$	$43.924$	\(\Q(\sqrt{1209}) \)	$_{}$	\(\Q(\sqrt{-403}) \)	None	✓	✓			1612.3.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+9q^{9}+(-5+\beta )q^{11}-13q^{13}+5^{2}q^{25}+\cdots\)
1612.3.b.d	$1612$	$3$	1612.b	403.b	$2$	$2$	$2$	$43.924$	\(\Q(\sqrt{1209}) \)	$_{}$	\(\Q(\sqrt{-403}) \)	None	✓	✓			1612.3.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+9q^{9}+(5-\beta )q^{11}+13q^{13}+5^{2}q^{25}+\cdots\)

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