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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	5	7	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4655.2.a.a	$4655$	$2$	4655.a	1.a	$1$	$1$	$1$	$37.170$	$\Q$	None	✓				665.2.a.b	$1$	$2$	$-2$	$-3$	$-1$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+2q^{4}-q^{5}+6q^{6}+\cdots$
4655.2.a.b	$4655$	$2$	4655.a	1.a	$1$	$1$	$1$	$37.170$	$\Q$	None	✓				665.2.j.f	$1$	$2$	$-2$	$0$	$-1$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}-3q^{9}+2q^{10}+\cdots$
4655.2.a.c	$4655$	$2$	4655.a	1.a	$1$	$1$	$1$	$37.170$	$\Q$	None	✓				665.2.j.e	$1$	$0$	$-2$	$0$	$-1$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}-3q^{9}+2q^{10}+\cdots$
4655.2.a.d	$4655$	$2$	4655.a	1.a	$1$	$1$	$1$	$37.170$	$\Q$	None	✓				665.2.j.f	$1$	$1$	$-2$	$0$	$1$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+q^{5}-3q^{9}-2q^{10}+\cdots$
4655.2.a.e	$4655$	$2$	4655.a	1.a	$1$	$1$	$1$	$37.170$	$\Q$	None	✓				665.2.j.e	$1$	$1$	$-2$	$0$	$1$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+q^{5}-3q^{9}-2q^{10}+\cdots$
4655.2.a.f	$4655$	$2$	4655.a	1.a	$1$	$1$	$1$	$37.170$	$\Q$	None	✓				665.2.a.a	$1$	$1$	$-2$	$1$	$-1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}-2q^{9}+\cdots$
4655.2.a.g	$4655$	$2$	4655.a	1.a	$1$	$1$	$1$	$37.170$	$\Q$	None	✓				665.2.j.d	$1$	$1$	$-1$	$-1$	$1$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots$
4655.2.a.h	$4655$	$2$	4655.a	1.a	$1$	$1$	$1$	$37.170$	$\Q$	None	✓				665.2.j.d	$1$	$0$	$-1$	$1$	$-1$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+3q^{8}+\cdots$
4655.2.a.i	$4655$	$2$	4655.a	1.a	$1$	$1$	$1$	$37.170$	$\Q$	None	✓				665.2.a.c	$1$	$1$	$-1$	$1$	$1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots$
4655.2.a.j	$4655$	$2$	4655.a	1.a	$1$	$1$	$1$	$37.170$	$\Q$	None	✓				665.2.j.c	$1$	$2$	$0$	$-2$	$-1$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{4}-q^{5}+q^{9}-3q^{11}+\cdots$
4655.2.a.k	$4655$	$2$	4655.a	1.a	$1$	$1$	$1$	$37.170$	$\Q$	None	✓	✓			4655.2.a.k	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{5}-2q^{9}-3q^{11}+\cdots$
4655.2.a.l	$4655$	$2$	4655.a	1.a	$1$	$1$	$1$	$37.170$	$\Q$	None	✓				665.2.j.b	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{5}-3q^{9}+q^{11}+2q^{13}+\cdots$
4655.2.a.m	$4655$	$2$	4655.a	1.a	$1$	$1$	$1$	$37.170$	$\Q$	None	✓				665.2.j.b	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{5}-3q^{9}+q^{11}-2q^{13}+\cdots$
4655.2.a.n	$4655$	$2$	4655.a	1.a	$1$	$1$	$1$	$37.170$	$\Q$	None	✓	✓			4655.2.a.k	$1$	$1$	$0$	$1$	$1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{5}-2q^{9}-3q^{11}+\cdots$
4655.2.a.o	$4655$	$2$	4655.a	1.a	$1$	$1$	$1$	$37.170$	$\Q$	None	✓				665.2.j.c	$1$	$1$	$0$	$2$	$1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{4}+q^{5}+q^{9}-3q^{11}+\cdots$
4655.2.a.p	$4655$	$2$	4655.a	1.a	$1$	$1$	$1$	$37.170$	$\Q$	None	✓				665.2.a.e	$1$	$0$	$1$	$0$	$-1$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}-3q^{8}-3q^{9}-q^{10}+\cdots$
4655.2.a.q	$4655$	$2$	4655.a	1.a	$1$	$1$	$1$	$37.170$	$\Q$	None	✓				665.2.a.d	$1$	$1$	$1$	$1$	$-1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots$
4655.2.a.r	$4655$	$2$	4655.a	1.a	$1$	$1$	$1$	$37.170$	$\Q$	None	✓				665.2.j.a	$1$	$0$	$2$	$-2$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots$
4655.2.a.s	$4655$	$2$	4655.a	1.a	$1$	$1$	$1$	$37.170$	$\Q$	None	✓				665.2.j.a	$1$	$1$	$2$	$2$	$-1$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots$
4655.2.a.t	$4655$	$2$	4655.a	1.a	$1$	$2$	$2$	$37.170$	$\Q(\sqrt{17}) $	None	✓				665.2.a.f	$1$	$0$	$-2$	$1$	$-2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta )q^{3}-q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots$
4655.2.a.u	$4655$	$2$	4655.a	1.a	$1$	$3$	$3$	$37.170$	3.3.148.1	None	✓				95.2.a.a	$1$	$1$	$1$	$-2$	$-3$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
4655.2.a.v	$4655$	$2$	4655.a	1.a	$1$	$3$	$3$	$37.170$	3.3.148.1	None	✓				665.2.a.g	$1$	$1$	$1$	$-1$	$-3$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots$
4655.2.a.w	$4655$	$2$	4655.a	1.a	$1$	$3$	$3$	$37.170$	3.3.229.1	None	✓				665.2.j.g	$1$	$1$	$1$	$-1$	$-3$	$0$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+\beta _{2}q^{3}+(2-\beta _{1})q^{4}-q^{5}+\cdots$
4655.2.a.x	$4655$	$2$	4655.a	1.a	$1$	$3$	$3$	$37.170$	3.3.229.1	None	✓				665.2.j.g	$1$	$0$	$1$	$1$	$3$	$0$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-\beta _{2}q^{3}+(2-\beta _{1})q^{4}+q^{5}+\cdots$
4655.2.a.y	$4655$	$2$	4655.a	1.a	$1$	$4$	$4$	$37.170$	4.4.11344.1	None	✓				95.2.a.b	$1$	$1$	$-2$	$-2$	$4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots$
4655.2.a.z	$4655$	$2$	4655.a	1.a	$1$	$4$	$4$	$37.170$	4.4.6224.1	None	✓	✓			4655.2.a.z	$1$	$1$	$0$	$-2$	$4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
4655.2.a.ba	$4655$	$2$	4655.a	1.a	$1$	$4$	$4$	$37.170$	4.4.6224.1	None	✓	✓			4655.2.a.z	$1$	$1$	$0$	$2$	$-4$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
4655.2.a.bb	$4655$	$2$	4655.a	1.a	$1$	$4$	$4$	$37.170$	4.4.11348.1	None	✓				665.2.a.h	$1$	$1$	$1$	$-2$	$4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
4655.2.a.bc	$4655$	$2$	4655.a	1.a	$1$	$6$	$6$	$37.170$	6.6.79799552.1	None	✓				665.2.a.i	$1$	$0$	$-1$	$4$	$6$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
4655.2.a.bd	$4655$	$2$	4655.a	1.a	$1$	$7$	$7$	$37.170$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓				665.2.a.j	$1$	$0$	$3$	$-1$	$7$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(2+\beta _{2})q^{4}+q^{5}+\cdots$
4655.2.a.be	$4655$	$2$	4655.a	1.a	$1$	$8$	$8$	$37.170$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓				665.2.j.i	$1$	$1$	$1$	$-4$	$8$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}-\beta _{5}-\beta _{7})q^{3}+\cdots$
4655.2.a.bf	$4655$	$2$	4655.a	1.a	$1$	$8$	$8$	$37.170$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓		✓		665.2.j.h	$1$	$1$	$1$	$-2$	$-8$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2}+\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots$
4655.2.a.bg	$4655$	$2$	4655.a	1.a	$1$	$8$	$8$	$37.170$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓				665.2.j.h	$1$	$0$	$1$	$2$	$8$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots$
4655.2.a.bh	$4655$	$2$	4655.a	1.a	$1$	$8$	$8$	$37.170$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓				665.2.j.i	$1$	$0$	$1$	$4$	$-8$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{7})q^{3}+\cdots$
4655.2.a.bi	$4655$	$2$	4655.a	1.a	$1$	$8$	$8$	$37.170$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓				665.2.a.k	$1$	$0$	$2$	$3$	$-8$	$0$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots$
4655.2.a.bj	$4655$	$2$	4655.a	1.a	$1$	$10$	$10$	$37.170$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓		4655.2.a.bj	$1$	$1$	$0$	$-2$	$10$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots$
4655.2.a.bk	$4655$	$2$	4655.a	1.a	$1$	$10$	$10$	$37.170$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓			4655.2.a.bj	$1$	$1$	$0$	$2$	$-10$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{7}q^{3}+\beta _{2}q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots$
4655.2.a.bl	$4655$	$2$	4655.a	1.a	$1$	$11$	$11$	$37.170$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓		✓		665.2.j.j	$1$	$1$	$0$	$-5$	$-11$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
4655.2.a.bm	$4655$	$2$	4655.a	1.a	$1$	$11$	$11$	$37.170$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓				665.2.j.j	$1$	$0$	$0$	$5$	$11$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
4655.2.a.bn	$4655$	$2$	4655.a	1.a	$1$	$12$	$12$	$37.170$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓		✓		665.2.j.k	$1$	$1$	$-4$	$-7$	$12$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{9})q^{3}+(1+\beta _{2})q^{4}+\cdots$
4655.2.a.bo	$4655$	$2$	4655.a	1.a	$1$	$12$	$12$	$37.170$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓				665.2.j.k	$1$	$0$	$-4$	$7$	$-12$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{9})q^{3}+(1+\beta _{2})q^{4}+\cdots$
4655.2.a.bp	$4655$	$2$	4655.a	1.a	$1$	$13$	$13$	$37.170$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	✓	✓		4655.2.a.bp	$1$	$0$	$2$	$-3$	$-13$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{10}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
4655.2.a.bq	$4655$	$2$	4655.a	1.a	$1$	$13$	$13$	$37.170$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	✓	✓		4655.2.a.bp	$1$	$0$	$2$	$3$	$13$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{10}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
4655.2.a.br	$4655$	$2$	4655.a	1.a	$1$	$26$	$26$	$37.170$		None	✓	✓	✓		4655.2.a.br	$1$	$0$	$4$	$-6$	$-26$	$0$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
4655.2.a.bs	$4655$	$2$	4655.a	1.a	$1$	$26$	$26$	$37.170$		None	✓	✓	✓		4655.2.a.br	$1$	$0$	$4$	$6$	$26$	$0$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$

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Elliptic curves over $\Q$
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Genus 2 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.