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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 79 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	29	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4176.2.a.a	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-4$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-3q^{7}+q^{11}+q^{13}+q^{17}+\cdots$
4176.2.a.b	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-4$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-q^{7}-3q^{11}+5q^{13}-5q^{17}+\cdots$
4176.2.a.c	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-3$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-4q^{7}-q^{11}-3q^{13}-2q^{17}+\cdots$
4176.2.a.d	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-3$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+q^{7}+2q^{13}+3q^{17}-5q^{19}+\cdots$
4176.2.a.e	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-3$	$3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+3q^{7}+6q^{11}-7q^{17}-5q^{19}+\cdots$
4176.2.a.f	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-3$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+4q^{7}+3q^{11}+5q^{13}+6q^{17}+\cdots$
4176.2.a.g	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-3$	$5$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+5q^{7}-4q^{11}-6q^{13}+q^{17}+\cdots$
4176.2.a.h	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-2$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{7}+2q^{13}+2q^{17}-4q^{23}+\cdots$
4176.2.a.i	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-2$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}+q^{11}-3q^{13}+3q^{17}+\cdots$
4176.2.a.j	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{11}+6q^{13}+2q^{17}-4q^{19}+\cdots$
4176.2.a.k	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-2$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+4q^{7}+2q^{13}-6q^{17}-4q^{23}+\cdots$
4176.2.a.l	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+3q^{11}-q^{13}+4q^{23}+\cdots$
4176.2.a.m	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-1$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}+6q^{11}-4q^{13}+7q^{17}+\cdots$
4176.2.a.n	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-3q^{11}-q^{13}-8q^{17}+\cdots$
4176.2.a.o	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+3q^{7}-2q^{11}+4q^{13}-5q^{17}+\cdots$
4176.2.a.p	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-5q^{11}-3q^{13}+5q^{17}+2q^{19}+\cdots$
4176.2.a.q	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+5q^{11}-3q^{13}-5q^{17}+2q^{19}+\cdots$
4176.2.a.r	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{11}+q^{13}-7q^{17}+6q^{19}+\cdots$
4176.2.a.s	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{11}+q^{13}+q^{17}-6q^{23}+\cdots$
4176.2.a.t	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+3q^{11}+q^{13}+7q^{17}+6q^{19}+\cdots$
4176.2.a.u	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{7}-3q^{11}-3q^{13}-q^{17}+4q^{19}+\cdots$
4176.2.a.v	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$0$	$5$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+5q^{7}-5q^{11}+q^{13}+3q^{17}+4q^{19}+\cdots$
4176.2.a.w	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}-2q^{11}+3q^{17}+q^{19}+\cdots$
4176.2.a.x	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$2$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}-6q^{11}+2q^{13}-2q^{17}+\cdots$
4176.2.a.y	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$2$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}+2q^{13}-2q^{17}+4q^{23}+\cdots$
4176.2.a.z	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$2$	$-3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-3q^{7}-5q^{11}+q^{13}+7q^{17}+\cdots$
4176.2.a.ba	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$2$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}+3q^{11}+5q^{13}+q^{17}+\cdots$
4176.2.a.bb	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$2$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-3q^{11}-7q^{13}-3q^{17}+\cdots$
4176.2.a.bc	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$2$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{7}+2q^{13}+6q^{17}+4q^{23}+\cdots$
4176.2.a.bd	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$3$	$-5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-5q^{7}+6q^{11}-4q^{13}-3q^{17}+\cdots$
4176.2.a.be	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$3$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-2q^{7}-3q^{11}-5q^{13}+4q^{17}+\cdots$
4176.2.a.bf	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$3$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-q^{7}-2q^{11}+4q^{13}-7q^{17}+\cdots$
4176.2.a.bg	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$3$	$1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+q^{7}+2q^{13}-3q^{17}-5q^{19}+\cdots$
4176.2.a.bh	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$3$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+2q^{7}-q^{11}+3q^{13}+4q^{17}+\cdots$
4176.2.a.bi	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$3$	$5$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+5q^{7}+4q^{11}-6q^{13}-q^{17}+\cdots$
4176.2.a.bj	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$4$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-q^{7}+3q^{11}+5q^{13}+5q^{17}+\cdots$
4176.2.a.bk	$4176$	$2$	4176.a	1.a	$1$	$1$	$1$	$33.346$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$4$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+3q^{7}-q^{11}-3q^{13}+5q^{17}+\cdots$
4176.2.a.bl	$4176$	$2$	4176.a	1.a	$1$	$2$	$2$	$33.346$	$\Q(\sqrt{41}) $	None	✓	$1$	$1$	$0$	$0$	$-4$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+(-1-\beta )q^{7}+(3-\beta )q^{11}+\cdots$
4176.2.a.bm	$4176$	$2$	4176.a	1.a	$1$	$2$	$2$	$33.346$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$0$	$-4$	$0$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-2q^{5}+\beta q^{7}+(4+\beta )q^{11}+(-1+2\beta )q^{13}+\cdots$
4176.2.a.bn	$4176$	$2$	4176.a	1.a	$1$	$2$	$2$	$33.346$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$0$	$-2$	$4$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+(2-\beta )q^{7}+(2-\beta )q^{11}+\cdots$
4176.2.a.bo	$4176$	$2$	4176.a	1.a	$1$	$2$	$2$	$33.346$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}+q^{7}+(1-\beta )q^{11}+(-3+\beta )q^{13}+\cdots$
4176.2.a.bp	$4176$	$2$	4176.a	1.a	$1$	$2$	$2$	$33.346$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$0$	$1$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+q^{7}+(-1+\beta )q^{11}+(-3+\cdots)q^{13}+\cdots$
4176.2.a.bq	$4176$	$2$	4176.a	1.a	$1$	$2$	$2$	$33.346$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2\beta q^{7}+(1+\beta )q^{11}+(-1+2\beta )q^{13}+\cdots$
4176.2.a.br	$4176$	$2$	4176.a	1.a	$1$	$2$	$2$	$33.346$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$0$	$2$	$8$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+2\beta )q^{5}+4q^{7}+(-1-\beta )q^{11}+\cdots$
4176.2.a.bs	$4176$	$2$	4176.a	1.a	$1$	$2$	$2$	$33.346$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$0$	$3$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+(-1+2\beta )q^{7}+(2+\beta )q^{11}+\cdots$
4176.2.a.bt	$4176$	$2$	4176.a	1.a	$1$	$2$	$2$	$33.346$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$0$	$4$	$0$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+2q^{5}-\beta q^{7}+(-4+\beta )q^{11}+(-1+\cdots)q^{13}+\cdots$
4176.2.a.bu	$4176$	$2$	4176.a	1.a	$1$	$3$	$3$	$33.346$	3.3.568.1	None	✓	$1$	$0$	$0$	$0$	$-4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{5}+(1+\beta _{1}+2\beta _{2})q^{11}+\cdots$
4176.2.a.bv	$4176$	$2$	4176.a	1.a	$1$	$3$	$3$	$33.346$	3.3.892.1	None	✓	$1$	$1$	$0$	$0$	$-1$	$-9$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}-3q^{7}+(1-\beta _{2})q^{11}+(1+\beta _{2})q^{13}+\cdots$
4176.2.a.bw	$4176$	$2$	4176.a	1.a	$1$	$3$	$3$	$33.346$	3.3.961.1	None	✓	$1$	$0$	$0$	$0$	$-1$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+(1-\beta _{1}+\beta _{2})q^{11}+\cdots$
4176.2.a.bx	$4176$	$2$	4176.a	1.a	$1$	$3$	$3$	$33.346$	3.3.229.1	None	✓	$1$	$1$	$0$	$0$	$0$	$-4$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{2})q^{5}+(-1+\beta _{2})q^{7}+(-3+\cdots)q^{11}+\cdots$

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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.