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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 82 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	5	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4050.2.a.a	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$-5$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-5q^{7}-q^{8}+q^{13}+5q^{14}+\cdots$
4050.2.a.b	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{7}-q^{8}+3q^{11}-4q^{13}+\cdots$
4050.2.a.c	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}-3q^{11}-2q^{13}+\cdots$
4050.2.a.d	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}+4q^{13}+2q^{14}+\cdots$
4050.2.a.e	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{7}-q^{8}-4q^{11}-3q^{13}+\cdots$
4050.2.a.f	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{7}-q^{8}-4q^{13}+q^{14}+\cdots$
4050.2.a.g	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{11}-6q^{13}+\cdots$
4050.2.a.h	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{7}-q^{8}+6q^{11}+2q^{13}+\cdots$
4050.2.a.i	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}-6q^{11}-2q^{13}+\cdots$
4050.2.a.j	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}+6q^{13}+\cdots$
4050.2.a.k	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}-5q^{13}-q^{14}+\cdots$
4050.2.a.l	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}+4q^{13}-q^{14}+\cdots$
4050.2.a.m	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}+4q^{11}+3q^{13}+\cdots$
4050.2.a.n	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}+6q^{11}-2q^{13}+\cdots$
4050.2.a.o	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{7}-q^{8}-4q^{13}-2q^{14}+\cdots$
4050.2.a.p	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{7}-q^{8}-3q^{11}+4q^{13}+\cdots$
4050.2.a.q	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{7}-q^{8}-3q^{11}+4q^{13}+\cdots$
4050.2.a.r	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{7}-q^{8}+q^{13}-4q^{14}+\cdots$
4050.2.a.s	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$-5$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-5q^{7}+q^{8}+q^{13}-5q^{14}+\cdots$
4050.2.a.t	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{7}+q^{8}-3q^{11}-4q^{13}+\cdots$
4050.2.a.u	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}+4q^{13}-2q^{14}+\cdots$
4050.2.a.v	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}+3q^{11}-2q^{13}+\cdots$
4050.2.a.w	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}-6q^{11}+2q^{13}+\cdots$
4050.2.a.x	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}-6q^{13}+\cdots$
4050.2.a.y	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}-4q^{13}-q^{14}+\cdots$
4050.2.a.z	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}+4q^{11}-3q^{13}+\cdots$
4050.2.a.ba	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}-6q^{11}-2q^{13}+\cdots$
4050.2.a.bb	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}-4q^{11}+3q^{13}+\cdots$
4050.2.a.bc	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}-5q^{13}+q^{14}+\cdots$
4050.2.a.bd	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{13}+q^{14}+\cdots$
4050.2.a.be	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+6q^{13}+\cdots$
4050.2.a.bf	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}+6q^{11}-2q^{13}+\cdots$
4050.2.a.bg	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-4q^{13}+2q^{14}+\cdots$
4050.2.a.bh	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{7}+q^{8}+q^{13}+4q^{14}+\cdots$
4050.2.a.bi	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{7}+q^{8}+3q^{11}+4q^{13}+\cdots$
4050.2.a.bj	$4050$	$2$	4050.a	1.a	$1$	$1$	$1$	$32.339$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{7}+q^{8}+3q^{11}+4q^{13}+\cdots$
4050.2.a.bk	$4050$	$2$	4050.a	1.a	$1$	$2$	$2$	$32.339$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$-2$	$0$	$0$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-2+\beta )q^{7}-q^{8}+2\beta q^{11}+\cdots$
4050.2.a.bl	$4050$	$2$	4050.a	1.a	$1$	$2$	$2$	$32.339$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$-2$	$0$	$0$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-2+\beta )q^{7}-q^{8}+2\beta q^{11}+\cdots$
4050.2.a.bm	$4050$	$2$	4050.a	1.a	$1$	$2$	$2$	$32.339$	$\Q(\sqrt{6}) $	None	✓	$1$	$1$	$-2$	$0$	$0$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-2+\beta )q^{7}-q^{8}+(1+\cdots)q^{11}+\cdots$
4050.2.a.bn	$4050$	$2$	4050.a	1.a	$1$	$2$	$2$	$32.339$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$-2$	$0$	$0$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+2\beta )q^{7}-q^{8}+(-3+\cdots)q^{11}+\cdots$
4050.2.a.bo	$4050$	$2$	4050.a	1.a	$1$	$2$	$2$	$32.339$	$\Q(\sqrt{33}) $	None	✓	$1$	$0$	$-2$	$0$	$0$	$-1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta q^{7}-q^{8}+(1+\beta )q^{11}+\cdots$
4050.2.a.bp	$4050$	$2$	4050.a	1.a	$1$	$2$	$2$	$32.339$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$-2$	$0$	$0$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+2\beta )q^{7}-q^{8}+(3+\beta )q^{11}+\cdots$
4050.2.a.bq	$4050$	$2$	4050.a	1.a	$1$	$2$	$2$	$32.339$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$-2$	$0$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2+\beta )q^{7}-q^{8}+(-1+\cdots)q^{11}+\cdots$
4050.2.a.br	$4050$	$2$	4050.a	1.a	$1$	$2$	$2$	$32.339$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$-2$	$0$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2+\beta )q^{7}-q^{8}+2\beta q^{11}+\cdots$
4050.2.a.bs	$4050$	$2$	4050.a	1.a	$1$	$2$	$2$	$32.339$	$\Q(\sqrt{6}) $	None	✓	$1$	$1$	$2$	$0$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-2+\beta )q^{7}+q^{8}+(-1+\cdots)q^{11}+\cdots$
4050.2.a.bt	$4050$	$2$	4050.a	1.a	$1$	$2$	$2$	$32.339$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$2$	$0$	$0$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-2+\beta )q^{7}+q^{8}-2\beta q^{11}+\cdots$
4050.2.a.bu	$4050$	$2$	4050.a	1.a	$1$	$2$	$2$	$32.339$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$2$	$0$	$0$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-2+\beta )q^{7}+q^{8}-2\beta q^{11}+\cdots$
4050.2.a.bv	$4050$	$2$	4050.a	1.a	$1$	$2$	$2$	$32.339$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$0$	$0$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+2\beta )q^{7}+q^{8}+(3+\cdots)q^{11}+\cdots$
4050.2.a.bw	$4050$	$2$	4050.a	1.a	$1$	$2$	$2$	$32.339$	$\Q(\sqrt{33}) $	None	✓	$1$	$0$	$2$	$0$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta q^{7}+q^{8}+(-1-\beta )q^{11}+\cdots$
4050.2.a.bx	$4050$	$2$	4050.a	1.a	$1$	$2$	$2$	$32.339$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$2$	$0$	$0$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1+2\beta )q^{7}+q^{8}+(-3+\cdots)q^{11}+\cdots$

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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.