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 (45 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	3	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8664.2.a.a	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	$\Q$	None	✓				456.2.a.c	$1$	$1$	$0$	$-1$	$-3$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-3q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$
8664.2.a.b	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	$\Q$	None	✓				456.2.q.c	$1$	$1$	$0$	$-1$	$-2$	$-5$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-5q^{7}+q^{9}-4q^{11}+\cdots$
8664.2.a.c	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	$\Q$	None	✓	✓			8664.2.a.c	$1$	$1$	$0$	$-1$	$-2$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots$
8664.2.a.d	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	$\Q$	None	✓				456.2.q.b	$1$	$1$	$0$	$-1$	$0$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{7}+q^{9}+2q^{11}-q^{13}+\cdots$
8664.2.a.e	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	$\Q$	None	✓				456.2.q.a	$1$	$1$	$0$	$-1$	$2$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-3q^{7}+q^{9}-5q^{13}+\cdots$
8664.2.a.f	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	$\Q$	None	✓				456.2.a.d	$1$	$1$	$0$	$-1$	$2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots$
8664.2.a.g	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	$\Q$	None	✓	✓			8664.2.a.g	$1$	$1$	$0$	$-1$	$3$	$1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}+q^{7}+q^{9}-3q^{11}-3q^{15}+\cdots$
8664.2.a.h	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	$\Q$	None	✓				456.2.q.c	$1$	$2$	$0$	$1$	$-2$	$-5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-5q^{7}+q^{9}-4q^{11}+\cdots$
8664.2.a.i	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	$\Q$	None	✓	✓			8664.2.a.c	$1$	$1$	$0$	$1$	$-2$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots$
8664.2.a.j	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	$\Q$	None	✓				24.2.a.a	$1$	$1$	$0$	$1$	$-2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
8664.2.a.k	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	$\Q$	None	✓				456.2.q.b	$1$	$0$	$0$	$1$	$0$	$3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{7}+q^{9}+2q^{11}+q^{13}+\cdots$
8664.2.a.l	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	$\Q$	None	✓				456.2.a.a	$1$	$1$	$0$	$1$	$1$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-3q^{7}+q^{9}-5q^{11}+2q^{13}+\cdots$
8664.2.a.m	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	$\Q$	None	✓				456.2.q.a	$1$	$0$	$0$	$1$	$2$	$-3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-3q^{7}+q^{9}+5q^{13}+\cdots$
8664.2.a.n	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	$\Q$	None	✓	✓			8664.2.a.g	$1$	$1$	$0$	$1$	$3$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}+q^{7}+q^{9}-3q^{11}+3q^{15}+\cdots$
8664.2.a.o	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	$\Q$	None	✓				456.2.a.b	$1$	$0$	$0$	$1$	$4$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots$
8664.2.a.p	$8664$	$2$	8664.a	1.a	$1$	$2$	$2$	$69.182$	$\Q(\sqrt{5}) $	None	✓	✓			8664.2.a.p	$1$	$1$	$0$	$-2$	$-3$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots$
8664.2.a.q	$8664$	$2$	8664.a	1.a	$1$	$2$	$2$	$69.182$	$\Q(\sqrt{5}) $	None	✓				456.2.q.d	$1$	$0$	$0$	$-2$	$-2$	$4$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta )q^{5}+(2-\beta )q^{7}+q^{9}+\cdots$
8664.2.a.r	$8664$	$2$	8664.a	1.a	$1$	$2$	$2$	$69.182$	$\Q(\sqrt{17}) $	None	✓				456.2.a.f	$1$	$0$	$0$	$-2$	$1$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots$
8664.2.a.s	$8664$	$2$	8664.a	1.a	$1$	$2$	$2$	$69.182$	$\Q(\sqrt{5}) $	None	✓				456.2.q.e	$1$	$1$	$0$	$-2$	$2$	$0$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta )q^{5}-\beta q^{7}+q^{9}+(3+\beta )q^{11}+\cdots$
8664.2.a.t	$8664$	$2$	8664.a	1.a	$1$	$2$	$2$	$69.182$	$\Q(\sqrt{5}) $	None	✓	✓			8664.2.a.p	$1$	$1$	$0$	$2$	$-3$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots$
8664.2.a.u	$8664$	$2$	8664.a	1.a	$1$	$2$	$2$	$69.182$	$\Q(\sqrt{5}) $	None	✓				456.2.q.d	$1$	$1$	$0$	$2$	$-2$	$4$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{5}+(2-\beta )q^{7}+q^{9}+\cdots$
8664.2.a.v	$8664$	$2$	8664.a	1.a	$1$	$2$	$2$	$69.182$	$\Q(\sqrt{41}) $	None	✓				456.2.a.e	$1$	$0$	$0$	$2$	$-1$	$-3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta q^{5}+(-2+\beta )q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots$
8664.2.a.w	$8664$	$2$	8664.a	1.a	$1$	$2$	$2$	$69.182$	$\Q(\sqrt{5}) $	None	✓				456.2.q.e	$1$	$0$	$0$	$2$	$2$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{5}-\beta q^{7}+q^{9}+(3+\beta )q^{11}+\cdots$
8664.2.a.x	$8664$	$2$	8664.a	1.a	$1$	$3$	$3$	$69.182$	$\Q(\zeta_{18})^+$	None	✓				456.2.q.f	$1$	$0$	$0$	$-3$	$0$	$3$	$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{1}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
8664.2.a.y	$8664$	$2$	8664.a	1.a	$1$	$3$	$3$	$69.182$	3.3.316.1	None	✓	✓			8664.2.a.y	$1$	$0$	$0$	$-3$	$3$	$1$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{1})q^{5}-\beta _{2}q^{7}+q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots$
8664.2.a.z	$8664$	$2$	8664.a	1.a	$1$	$3$	$3$	$69.182$	$\Q(\zeta_{18})^+$	None	✓				456.2.q.f	$1$	$1$	$0$	$3$	$0$	$3$	$+$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{1}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
8664.2.a.ba	$8664$	$2$	8664.a	1.a	$1$	$3$	$3$	$69.182$	3.3.316.1	None	✓	✓			8664.2.a.y	$1$	$0$	$0$	$3$	$3$	$1$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{1})q^{5}-\beta _{2}q^{7}+q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots$
8664.2.a.bb	$8664$	$2$	8664.a	1.a	$1$	$4$	$4$	$69.182$	4.4.34025.1	None	✓	✓			8664.2.a.bb	$1$	$1$	$0$	$-4$	$-2$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{2}q^{5}+(\beta _{2}-\beta _{3})q^{7}+q^{9}+\cdots$
8664.2.a.bc	$8664$	$2$	8664.a	1.a	$1$	$4$	$4$	$69.182$	4.4.5225.1	None	✓	✓			8664.2.a.bc	$1$	$0$	$0$	$-4$	$2$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{3}q^{5}+\beta _{3}q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
8664.2.a.bd	$8664$	$2$	8664.a	1.a	$1$	$4$	$4$	$69.182$	4.4.34025.1	None	✓	✓			8664.2.a.bb	$1$	$1$	$0$	$4$	$-2$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{2}q^{5}+(\beta _{2}-\beta _{3})q^{7}+q^{9}+\cdots$
8664.2.a.be	$8664$	$2$	8664.a	1.a	$1$	$4$	$4$	$69.182$	4.4.5225.1	None	✓	✓			8664.2.a.bc	$1$	$0$	$0$	$4$	$2$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{3}q^{5}+\beta _{3}q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
8664.2.a.bf	$8664$	$2$	8664.a	1.a	$1$	$6$	$6$	$69.182$	6.6.1528713.1	None	✓				456.2.bg.a	$1$	$0$	$0$	$-6$	$-3$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{1}q^{5}+(-1+2\beta _{1}+\beta _{2})q^{7}+\cdots$
8664.2.a.bg	$8664$	$2$	8664.a	1.a	$1$	$6$	$6$	$69.182$	6.6.142368125.1	None	✓	✓			8664.2.a.bg	$1$	$0$	$0$	$-6$	$1$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{5}q^{5}+\beta _{2}q^{7}+q^{9}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$
8664.2.a.bh	$8664$	$2$	8664.a	1.a	$1$	$6$	$6$	$69.182$	6.6.65669049.1	None	✓		✓		456.2.bg.b	$1$	$1$	$0$	$-6$	$3$	$6$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{4})q^{7}+q^{9}+\cdots$
8664.2.a.bi	$8664$	$2$	8664.a	1.a	$1$	$6$	$6$	$69.182$	6.6.1528713.1	None	✓				456.2.bg.a	$1$	$1$	$0$	$6$	$-3$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{1}q^{5}+(-1+2\beta _{1}+\beta _{2})q^{7}+\cdots$
8664.2.a.bj	$8664$	$2$	8664.a	1.a	$1$	$6$	$6$	$69.182$	6.6.142368125.1	None	✓	✓			8664.2.a.bg	$1$	$0$	$0$	$6$	$1$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{5}q^{5}+\beta _{2}q^{7}+q^{9}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$
8664.2.a.bk	$8664$	$2$	8664.a	1.a	$1$	$6$	$6$	$69.182$	6.6.65669049.1	None	✓				456.2.bg.b	$1$	$0$	$0$	$6$	$3$	$6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{4})q^{7}+q^{9}+\cdots$
8664.2.a.bl	$8664$	$2$	8664.a	1.a	$1$	$8$	$8$	$69.182$	8.8.$\cdots$.1	None	✓	✓			8664.2.a.bl	$1$	$1$	$0$	$-8$	$-6$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{2})q^{5}-\beta _{1}q^{7}+q^{9}+\cdots$
8664.2.a.bm	$8664$	$2$	8664.a	1.a	$1$	$8$	$8$	$69.182$	8.8.$\cdots$.1	None	✓	✓	✓		8664.2.a.bl	$1$	$1$	$0$	$8$	$-6$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta _{2})q^{5}-\beta _{1}q^{7}+q^{9}+\cdots$
8664.2.a.bn	$8664$	$2$	8664.a	1.a	$1$	$9$	$9$	$69.182$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓				456.2.bg.d	$1$	$0$	$0$	$-9$	$-3$	$-6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots$
8664.2.a.bo	$8664$	$2$	8664.a	1.a	$1$	$9$	$9$	$69.182$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓		✓		456.2.bg.c	$1$	$1$	$0$	$-9$	$3$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{5}+\beta _{7}q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots$
8664.2.a.bp	$8664$	$2$	8664.a	1.a	$1$	$9$	$9$	$69.182$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓		✓		456.2.bg.d	$1$	$1$	$0$	$9$	$-3$	$-6$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots$
8664.2.a.bq	$8664$	$2$	8664.a	1.a	$1$	$9$	$9$	$69.182$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓		✓		456.2.bg.c	$1$	$0$	$0$	$9$	$3$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{5}+\beta _{7}q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots$
8664.2.a.br	$8664$	$2$	8664.a	1.a	$1$	$12$	$12$	$69.182$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		8664.2.a.br	$1$	$0$	$0$	$-12$	$2$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{5}+\beta _{10}q^{7}+q^{9}+(1+\beta _{4}+\cdots)q^{11}+\cdots$
8664.2.a.bs	$8664$	$2$	8664.a	1.a	$1$	$12$	$12$	$69.182$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		8664.2.a.br	$1$	$0$	$0$	$12$	$2$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{5}+\beta _{10}q^{7}+q^{9}+(1+\beta _{4}+\cdots)q^{11}+\cdots$

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Elliptic curves over $\Q$
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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.