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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 (1-50 of 263 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	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
38720.2.a.a	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-3$	$-1$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}-3q^{7}+6q^{9}+4q^{13}+\cdots$
38720.2.a.b	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-3$	$-1$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}-q^{7}+6q^{9}-6q^{13}+\cdots$
38720.2.a.c	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-3$	$-1$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}+3q^{7}+6q^{9}-4q^{13}+\cdots$
38720.2.a.d	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-3$	$1$	$-5$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}-5q^{7}+6q^{9}+4q^{13}+\cdots$
38720.2.a.e	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-3$	$1$	$5$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}+5q^{7}+6q^{9}-4q^{13}+\cdots$
38720.2.a.f	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-2$	$-1$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}-4q^{7}+q^{9}-4q^{13}+\cdots$
38720.2.a.g	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-2$	$-1$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}-4q^{7}+q^{9}+4q^{13}+\cdots$
38720.2.a.h	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-2$	$-1$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+q^{9}+2q^{15}+4q^{17}+\cdots$
38720.2.a.i	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-2$	$-1$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+q^{9}+4q^{13}+2q^{15}+\cdots$
38720.2.a.j	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-2$	$1$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}-2q^{7}+q^{9}-6q^{13}+\cdots$
38720.2.a.k	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-2$	$1$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}-6q^{13}-2q^{15}+\cdots$
38720.2.a.l	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-2$	$1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots$
38720.2.a.m	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-2$	$1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}+2q^{13}-2q^{15}+\cdots$
38720.2.a.n	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-2$	$1$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}+6q^{13}-2q^{15}+\cdots$
38720.2.a.o	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-2$	$1$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+2q^{7}+q^{9}-2q^{13}+\cdots$
38720.2.a.p	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-2$	$1$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots$
38720.2.a.q	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$-1$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-3q^{7}-2q^{9}+q^{15}-8q^{17}+\cdots$
38720.2.a.r	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$-1$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-3q^{7}-2q^{9}+q^{15}+3q^{17}+\cdots$
38720.2.a.s	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$-1$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}-2q^{9}-4q^{13}+q^{15}+\cdots$
38720.2.a.t	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$-1$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}-2q^{9}+4q^{13}+q^{15}+\cdots$
38720.2.a.u	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$-1$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}-2q^{9}-4q^{13}+q^{15}+\cdots$
38720.2.a.v	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$-1$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}-2q^{9}-2q^{13}+q^{15}+\cdots$
38720.2.a.w	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$-1$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}-2q^{9}+4q^{13}+q^{15}+\cdots$
38720.2.a.x	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$-1$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+3q^{7}-2q^{9}-6q^{13}+\cdots$
38720.2.a.y	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$-1$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+3q^{7}-2q^{9}-2q^{13}+\cdots$
38720.2.a.z	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$-1$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+3q^{7}-2q^{9}+q^{15}-3q^{17}+\cdots$
38720.2.a.ba	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$-1$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+3q^{7}-2q^{9}+q^{15}+8q^{17}+\cdots$
38720.2.a.bb	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$1$	$-5$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-5q^{7}-2q^{9}+2q^{13}+\cdots$
38720.2.a.bc	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$1$	$-3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-3q^{7}-2q^{9}-4q^{13}+\cdots$
38720.2.a.bd	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$1$	$-3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-3q^{7}-2q^{9}-2q^{13}+\cdots$
38720.2.a.be	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$1$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-q^{7}-2q^{9}-2q^{13}-q^{15}+\cdots$
38720.2.a.bf	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$1$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-q^{7}-2q^{9}-q^{15}+3q^{17}+\cdots$
38720.2.a.bg	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$1$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}-2q^{9}-q^{15}-3q^{17}+\cdots$
38720.2.a.bh	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$1$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}-2q^{9}+2q^{13}-q^{15}+\cdots$
38720.2.a.bi	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$1$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}-2q^{9}+2q^{13}-q^{15}+\cdots$
38720.2.a.bj	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$1$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+3q^{7}-2q^{9}-2q^{13}+\cdots$
38720.2.a.bk	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$1$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+3q^{7}-2q^{9}+2q^{13}+\cdots$
38720.2.a.bl	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$1$	$3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+3q^{7}-2q^{9}+4q^{13}+\cdots$
38720.2.a.bm	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$0$	$-1$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}-3q^{9}-2q^{13}-2q^{17}+\cdots$
38720.2.a.bn	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$0$	$-1$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}-3q^{9}+6q^{13}+6q^{17}+\cdots$
38720.2.a.bo	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$0$	$-1$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}-2q^{13}+2q^{17}-4q^{19}+\cdots$
38720.2.a.bp	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$0$	$-1$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}-2q^{13}+2q^{17}+4q^{19}+\cdots$
38720.2.a.bq	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$0$	$-1$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}+2q^{13}-6q^{17}-4q^{19}+\cdots$
38720.2.a.br	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$0$	$-1$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}+2q^{13}-6q^{17}+4q^{19}+\cdots$
38720.2.a.bs	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$0$	$-1$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}-3q^{9}-2q^{13}-2q^{17}+\cdots$
38720.2.a.bt	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$0$	$-1$	$4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}-3q^{9}+6q^{13}+6q^{17}+\cdots$
38720.2.a.bu	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$0$	$1$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{7}-3q^{9}-4q^{13}-4q^{17}+\cdots$
38720.2.a.bv	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$0$	$1$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{7}-3q^{9}+4q^{13}+4q^{17}+\cdots$
38720.2.a.bw	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$0$	$1$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-3q^{9}-4q^{13}+4q^{17}+\cdots$
38720.2.a.bx	$38720$	$2$	38720.a	1.a	$1$	$1$	$1$	$309.181$	$\Q$	None	✓	?				$-1$		$0$	$0$	$1$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-3q^{9}+8q^{19}+8q^{23}+\cdots$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.