LMFDB - Newform search results

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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 64 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	7	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8512.2.a.a	$8512$	$2$	8512.a	1.a	$1$	$1$	$1$	$67.969$	$\Q$	None	✓				4256.2.a.a	$1$	$0$	$0$	$0$	$-2$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}-3q^{9}+4q^{13}+6q^{17}+\cdots$
8512.2.a.b	$8512$	$2$	8512.a	1.a	$1$	$1$	$1$	$67.969$	$\Q$	None	✓				4256.2.a.a	$1$	$0$	$0$	$0$	$-2$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}-3q^{9}+4q^{13}+6q^{17}+\cdots$
8512.2.a.c	$8512$	$2$	8512.a	1.a	$1$	$1$	$1$	$67.969$	$\Q$	None	✓				532.2.a.a	$1$	$1$	$0$	$0$	$2$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}-3q^{9}+4q^{11}-4q^{13}+\cdots$
8512.2.a.d	$8512$	$2$	8512.a	1.a	$1$	$1$	$1$	$67.969$	$\Q$	None	✓				532.2.a.a	$1$	$0$	$0$	$0$	$2$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-3q^{9}-4q^{11}-4q^{13}+\cdots$
8512.2.a.e	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				1064.2.a.e	$1$	$1$	$0$	$-3$	$-5$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(-2-\beta )q^{5}+q^{7}+\cdots$
8512.2.a.f	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				133.2.a.c	$1$	$1$	$0$	$-3$	$-2$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}-q^{5}+q^{7}+(-1+3\beta )q^{9}+\cdots$
8512.2.a.g	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				4256.2.a.c	$1$	$1$	$0$	$-3$	$-1$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}-\beta q^{5}-q^{7}+(-1+3\beta )q^{9}+\cdots$
8512.2.a.h	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				266.2.a.b	$1$	$1$	$0$	$-3$	$-1$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(-2+3\beta )q^{5}+q^{7}+\cdots$
8512.2.a.i	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				1064.2.a.a	$1$	$1$	$0$	$-3$	$0$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(-1+2\beta )q^{5}-q^{7}+\cdots$
8512.2.a.j	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				133.2.a.a	$1$	$1$	$0$	$-3$	$0$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(1-2\beta )q^{5}+q^{7}+(-1+\cdots)q^{9}+\cdots$
8512.2.a.k	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				532.2.a.b	$1$	$0$	$0$	$-3$	$2$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+q^{5}-q^{7}+(-1+3\beta )q^{9}+\cdots$
8512.2.a.l	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{13}) $	None	✓				133.2.a.b	$1$	$1$	$0$	$-3$	$6$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+3q^{5}-q^{7}+(1+3\beta )q^{9}+\cdots$
8512.2.a.m	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{21}) $	None	✓				532.2.a.c	$1$	$1$	$0$	$-1$	$-6$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-3q^{5}-q^{7}+(2+\beta )q^{9}+(-1+\cdots)q^{11}+\cdots$
8512.2.a.n	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{13}) $	None	✓				266.2.a.c	$1$	$0$	$0$	$-1$	$-1$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-1+\beta )q^{5}+q^{7}+\beta q^{9}+\cdots$
8512.2.a.o	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				1064.2.a.c	$1$	$0$	$0$	$-1$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1-2\beta )q^{5}-q^{7}+(-2+\beta )q^{9}+\cdots$
8512.2.a.p	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{29}) $	None	✓				266.2.a.a	$1$	$1$	$0$	$-1$	$1$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1-\beta )q^{5}-q^{7}+(4+\beta )q^{9}+\cdots$
8512.2.a.q	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				1064.2.a.d	$1$	$0$	$0$	$-1$	$2$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+q^{5}-q^{7}+(-2+\beta )q^{9}+(-1+\cdots)q^{11}+\cdots$
8512.2.a.r	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{13}) $	None	✓				1064.2.a.b	$1$	$0$	$0$	$-1$	$2$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+q^{5}+q^{7}+\beta q^{9}+(-1+\beta )q^{11}+\cdots$
8512.2.a.s	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				532.2.a.d	$1$	$1$	$0$	$-1$	$4$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1+2\beta )q^{5}-q^{7}+(-2+\beta )q^{9}+\cdots$
8512.2.a.t	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{21}) $	None	✓				532.2.a.c	$1$	$0$	$0$	$1$	$-6$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-3q^{5}+q^{7}+(2+\beta )q^{9}+(1+\cdots)q^{11}+\cdots$
8512.2.a.u	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{13}) $	None	✓				266.2.a.c	$1$	$1$	$0$	$1$	$-1$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1+\beta )q^{5}-q^{7}+\beta q^{9}+\cdots$
8512.2.a.v	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				1064.2.a.c	$1$	$1$	$0$	$1$	$0$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1-2\beta )q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots$
8512.2.a.w	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{29}) $	None	✓				266.2.a.a	$1$	$0$	$0$	$1$	$1$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1-\beta )q^{5}+q^{7}+(4+\beta )q^{9}+\cdots$
8512.2.a.x	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{13}) $	None	✓				1064.2.a.b	$1$	$1$	$0$	$1$	$2$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}-q^{7}+\beta q^{9}+(1-\beta )q^{11}+\cdots$
8512.2.a.y	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				1064.2.a.d	$1$	$1$	$0$	$1$	$2$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}+q^{7}+(-2+\beta )q^{9}+(1+\cdots)q^{11}+\cdots$
8512.2.a.z	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				532.2.a.d	$1$	$0$	$0$	$1$	$4$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1+2\beta )q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots$
8512.2.a.ba	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				1064.2.a.e	$1$	$0$	$0$	$3$	$-5$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-2-\beta )q^{5}-q^{7}+(-1+\cdots)q^{9}+\cdots$
8512.2.a.bb	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				133.2.a.c	$1$	$0$	$0$	$3$	$-2$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{5}-q^{7}+(-1+3\beta )q^{9}+\cdots$
8512.2.a.bc	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				266.2.a.b	$1$	$0$	$0$	$3$	$-1$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-2+3\beta )q^{5}-q^{7}+(-1+\cdots)q^{9}+\cdots$
8512.2.a.bd	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				4256.2.a.c	$1$	$1$	$0$	$3$	$-1$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-\beta q^{5}+q^{7}+(-1+3\beta )q^{9}+\cdots$
8512.2.a.be	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				133.2.a.a	$1$	$0$	$0$	$3$	$0$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(1-2\beta )q^{5}-q^{7}+(-1+\cdots)q^{9}+\cdots$
8512.2.a.bf	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				1064.2.a.a	$1$	$0$	$0$	$3$	$0$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-1+2\beta )q^{5}+q^{7}+(-1+\cdots)q^{9}+\cdots$
8512.2.a.bg	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{5}) $	None	✓				532.2.a.b	$1$	$1$	$0$	$3$	$2$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+q^{7}+(-1+3\beta )q^{9}+\cdots$
8512.2.a.bh	$8512$	$2$	8512.a	1.a	$1$	$2$	$2$	$67.969$	$\Q(\sqrt{13}) $	None	✓				133.2.a.b	$1$	$0$	$0$	$3$	$6$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+3q^{5}+q^{7}+(1+3\beta )q^{9}+\cdots$
8512.2.a.bi	$8512$	$2$	8512.a	1.a	$1$	$3$	$3$	$67.969$	3.3.229.1	None	✓				133.2.a.d	$1$	$1$	$0$	$-3$	$2$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots$
8512.2.a.bj	$8512$	$2$	8512.a	1.a	$1$	$3$	$3$	$67.969$	3.3.469.1	None	✓				266.2.a.d	$1$	$1$	$0$	$-1$	$-5$	$3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(-2+\beta _{1})q^{5}+q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
8512.2.a.bk	$8512$	$2$	8512.a	1.a	$1$	$3$	$3$	$67.969$	3.3.1101.1	None	✓				1064.2.a.f	$1$	$0$	$0$	$-1$	$-2$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{2})q^{5}-q^{7}+(4-\beta _{1}+\cdots)q^{9}+\cdots$
8512.2.a.bl	$8512$	$2$	8512.a	1.a	$1$	$3$	$3$	$67.969$	3.3.733.1	None	✓				532.2.a.e	$1$	$1$	$0$	$-1$	$-2$	$3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+q^{7}+\cdots$
8512.2.a.bm	$8512$	$2$	8512.a	1.a	$1$	$3$	$3$	$67.969$	3.3.469.1	None	✓				266.2.a.d	$1$	$0$	$0$	$1$	$-5$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(-2+\beta _{1})q^{5}-q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
8512.2.a.bn	$8512$	$2$	8512.a	1.a	$1$	$3$	$3$	$67.969$	3.3.733.1	None	✓				532.2.a.e	$1$	$0$	$0$	$1$	$-2$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}-q^{7}+\cdots$
8512.2.a.bo	$8512$	$2$	8512.a	1.a	$1$	$3$	$3$	$67.969$	3.3.1101.1	None	✓				1064.2.a.f	$1$	$1$	$0$	$1$	$-2$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+q^{7}+(4-\beta _{1}+\cdots)q^{9}+\cdots$
8512.2.a.bp	$8512$	$2$	8512.a	1.a	$1$	$3$	$3$	$67.969$	3.3.229.1	None	✓				133.2.a.d	$1$	$0$	$0$	$3$	$2$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+q^{7}+\cdots$
8512.2.a.bq	$8512$	$2$	8512.a	1.a	$1$	$4$	$4$	$67.969$	4.4.25857.1	None	✓				1064.2.a.h	$1$	$0$	$0$	$-2$	$-1$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots$
8512.2.a.br	$8512$	$2$	8512.a	1.a	$1$	$4$	$4$	$67.969$	4.4.2624.1	None	✓				4256.2.a.e	$1$	$1$	$0$	$-2$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots$
8512.2.a.bs	$8512$	$2$	8512.a	1.a	$1$	$4$	$4$	$67.969$	4.4.18097.1	None	✓				1064.2.a.g	$1$	$0$	$0$	$0$	$3$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+(1+\beta _{2}-\beta _{3})q^{5}-q^{7}+(2+\cdots)q^{9}+\cdots$
8512.2.a.bt	$8512$	$2$	8512.a	1.a	$1$	$4$	$4$	$67.969$	4.4.18097.1	None	✓				1064.2.a.g	$1$	$1$	$0$	$0$	$3$	$4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+(1+\beta _{2}-\beta _{3})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots$
8512.2.a.bu	$8512$	$2$	8512.a	1.a	$1$	$4$	$4$	$67.969$	4.4.25857.1	None	✓				1064.2.a.h	$1$	$1$	$0$	$2$	$-1$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots$
8512.2.a.bv	$8512$	$2$	8512.a	1.a	$1$	$4$	$4$	$67.969$	4.4.2624.1	None	✓				4256.2.a.e	$1$	$1$	$0$	$2$	$0$	$4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-1+\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots$
8512.2.a.bw	$8512$	$2$	8512.a	1.a	$1$	$5$	$5$	$67.969$	5.5.1730752.1	None	✓				4256.2.a.g	$1$	$0$	$0$	$-2$	$6$	$-5$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1+\beta _{3})q^{5}-q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
8512.2.a.bx	$8512$	$2$	8512.a	1.a	$1$	$5$	$5$	$67.969$	5.5.10463409.1	None	✓				1064.2.a.i	$1$	$1$	$0$	$0$	$-3$	$-5$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{4})q^{5}-q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots$

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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.