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

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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1089.2.a.d	$1089$	$2$	1089.a	1.a	$1$	$1$	$1$	$8.696$	\(\Q\)	None	✓				99.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(4\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+4q^{5}+2q^{7}+3q^{8}-4q^{10}+\cdots\)
1089.2.a.e	$1089$	$2$	1089.a	1.a	$1$	$1$	$1$	$8.696$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			1089.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-5\)		$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}-5q^{7}-2q^{13}+4q^{16}+7q^{19}+\cdots\)
1089.2.a.f	$1089$	$2$	1089.a	1.a	$1$	$1$	$1$	$8.696$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			1089.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(5\)		$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+5q^{7}+2q^{13}+4q^{16}-7q^{19}+\cdots\)
1089.2.a.g	$1089$	$2$	1089.a	1.a	$1$	$1$	$1$	$8.696$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓				121.2.a.b	$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+3q^{5}+4q^{16}-6q^{20}+9q^{23}+\cdots\)
1089.2.a.h	$1089$	$2$	1089.a	1.a	$1$	$1$	$1$	$8.696$	\(\Q\)	None	✓				99.2.a.a	$1$	$0$	\(1\)	\(0\)	\(-4\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-4q^{5}+2q^{7}-3q^{8}-4q^{10}+\cdots\)
1089.2.a.m	$1089$	$2$	1089.a	1.a	$1$	$2$	$2$	$8.696$	\(\Q(\sqrt{5}) \)	None	✓				33.2.e.a	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+(2-\beta )q^{5}+3q^{7}+\cdots\)
1089.2.a.o	$1089$	$2$	1089.a	1.a	$1$	$2$	$2$	$8.696$	\(\Q(\sqrt{3}) \)	None	✓				363.2.a.f	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+3q^{5}+2\beta q^{7}-\beta q^{8}+\cdots\)
1089.2.a.p	$1089$	$2$	1089.a	1.a	$1$	$2$	$2$	$8.696$	\(\Q(\sqrt{5}) \)	None	✓				363.2.a.g	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+3q^{4}-2q^{5}-2\beta q^{7}-\beta q^{8}+\cdots\)
1089.2.a.q	$1089$	$2$	1089.a	1.a	$1$	$2$	$2$	$8.696$	\(\Q(\sqrt{7}) \)	None	✓	✓			1089.2.a.q	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+5q^{4}+\beta q^{5}-2q^{7}+3\beta q^{8}+\cdots\)
1089.2.a.r	$1089$	$2$	1089.a	1.a	$1$	$2$	$2$	$8.696$	\(\Q(\sqrt{7}) \)	None	✓	✓			1089.2.a.q	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+5q^{4}-\beta q^{5}+2q^{7}+3\beta q^{8}+\cdots\)
1089.2.a.t	$1089$	$2$	1089.a	1.a	$1$	$2$	$2$	$8.696$	\(\Q(\sqrt{5}) \)	None	✓				33.2.e.b	$1$	$0$	\(3\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3\beta q^{4}+(-1+\beta )q^{5}+\cdots\)
1089.2.a.u	$1089$	$2$	1089.a	1.a	$1$	$4$	$4$	$8.696$	\(\Q(\sqrt{3}, \sqrt{11})\)	None	✓		✓		363.2.a.j	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{3})q^{4}+\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1089.2.a.w	$1089$	$2$	1089.a	1.a	$1$	$4$	$4$	$8.696$	4.4.4400.1	None	✓		✓		99.2.f.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{1}q^{5}+(3+2\beta _{2}+\cdots)q^{7}+\cdots\)

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