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 76 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	5	37	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8325.2.a.a	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				1665.2.a.a	$1$	$2$	$-2$	$0$	$0$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-4q^{7}-q^{13}+8q^{14}+\cdots$
8325.2.a.b	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓	✓			8325.2.a.b	$1$	$2$	$-2$	$0$	$0$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{7}-6q^{11}-7q^{13}+\cdots$
8325.2.a.c	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				2775.2.a.b	$1$	$1$	$-2$	$0$	$0$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{7}+5q^{13}+2q^{14}+\cdots$
8325.2.a.d	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				555.2.c.a	$1$	$0$	$-2$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+2q^{11}+q^{13}-4q^{16}+\cdots$
8325.2.a.e	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				37.2.a.a	$1$	$1$	$-2$	$0$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+q^{7}+5q^{11}+2q^{13}+\cdots$
8325.2.a.f	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓	✓			8325.2.a.b	$1$	$0$	$-2$	$0$	$0$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+q^{7}+6q^{11}+7q^{13}+\cdots$
8325.2.a.g	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				185.2.a.a	$1$	$1$	$-2$	$0$	$0$	$5$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+5q^{7}-3q^{11}+2q^{13}+\cdots$
8325.2.a.h	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				333.2.a.a	$1$	$0$	$-1$	$0$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+4q^{7}+3q^{8}+4q^{11}+\cdots$
8325.2.a.i	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				2775.2.a.c	$1$	$2$	$0$	$0$	$0$	$-3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-3q^{7}-4q^{11}-5q^{13}+4q^{16}+\cdots$
8325.2.a.j	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓	✓			8325.2.a.j	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-3q^{7}-4q^{11}+q^{13}+4q^{16}+\cdots$
8325.2.a.k	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓	✓			8325.2.a.j	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-3q^{7}+4q^{11}+q^{13}+4q^{16}+\cdots$
8325.2.a.l	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				1665.2.c.b	$1$	$2$	$0$	$0$	$0$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-2q^{7}-6q^{11}-q^{13}+4q^{16}+\cdots$
8325.2.a.m	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				555.2.a.b	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-2q^{7}+q^{13}+4q^{16}+6q^{17}+\cdots$
8325.2.a.n	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				1665.2.c.b	$1$	$0$	$0$	$0$	$0$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-2q^{7}+6q^{11}-q^{13}+4q^{16}+\cdots$
8325.2.a.o	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				2775.2.a.e	$1$	$1$	$0$	$0$	$0$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{7}+2q^{11}+q^{13}+4q^{16}+\cdots$
8325.2.a.p	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				37.2.a.b	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{7}-3q^{11}+4q^{13}+4q^{16}+\cdots$
8325.2.a.q	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				2775.2.a.e	$1$	$1$	$0$	$0$	$0$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{7}+2q^{11}-q^{13}+4q^{16}+\cdots$
8325.2.a.r	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				1665.2.c.b	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+2q^{7}-6q^{11}+q^{13}+4q^{16}+\cdots$
8325.2.a.s	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				555.2.a.a	$1$	$1$	$0$	$0$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+2q^{7}-4q^{11}-5q^{13}+4q^{16}+\cdots$
8325.2.a.t	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				1665.2.c.b	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+2q^{7}+6q^{11}+q^{13}+4q^{16}+\cdots$
8325.2.a.u	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓	✓			8325.2.a.j	$1$	$1$	$0$	$0$	$0$	$3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+3q^{7}-4q^{11}-q^{13}+4q^{16}+\cdots$
8325.2.a.v	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				2775.2.a.c	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+3q^{7}-4q^{11}+5q^{13}+4q^{16}+\cdots$
8325.2.a.w	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓	✓			8325.2.a.j	$1$	$1$	$0$	$0$	$0$	$3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+3q^{7}+4q^{11}-q^{13}+4q^{16}+\cdots$
8325.2.a.x	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				185.2.a.b	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+3q^{7}+5q^{11}-4q^{13}+4q^{16}+\cdots$
8325.2.a.y	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				185.2.a.c	$1$	$1$	$1$	$0$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{7}-3q^{8}+2q^{13}+\cdots$
8325.2.a.z	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				333.2.a.a	$1$	$0$	$1$	$0$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+4q^{7}-3q^{8}-4q^{11}+\cdots$
8325.2.a.ba	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				1665.2.a.a	$1$	$0$	$2$	$0$	$0$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-4q^{7}-q^{13}-8q^{14}+\cdots$
8325.2.a.bb	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓	✓			8325.2.a.b	$1$	$0$	$2$	$0$	$0$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-q^{7}+6q^{11}-7q^{13}+\cdots$
8325.2.a.bc	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				555.2.c.a	$1$	$1$	$2$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+2q^{11}-q^{13}-4q^{16}+\cdots$
8325.2.a.bd	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓	✓			8325.2.a.b	$1$	$0$	$2$	$0$	$0$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{7}-6q^{11}+7q^{13}+\cdots$
8325.2.a.be	$8325$	$2$	8325.a	1.a	$1$	$1$	$1$	$66.475$	$\Q$	None	✓				2775.2.a.b	$1$	$1$	$2$	$0$	$0$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{7}-5q^{13}+2q^{14}+\cdots$
8325.2.a.bf	$8325$	$2$	8325.a	1.a	$1$	$2$	$2$	$66.475$	$\Q(\sqrt{5}) $	None	✓				555.2.a.c	$1$	$1$	$-3$	$0$	$0$	$4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+3\beta q^{4}+(3-2\beta )q^{7}+\cdots$
8325.2.a.bg	$8325$	$2$	8325.a	1.a	$1$	$2$	$2$	$66.475$	$\Q(\sqrt{2}) $	None	✓				2775.2.a.k	$1$	$0$	$-2$	$0$	$0$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+2q^{7}+\cdots$
8325.2.a.bh	$8325$	$2$	8325.a	1.a	$1$	$2$	$2$	$66.475$	$\Q(\sqrt{5}) $	None	✓				555.2.a.e	$1$	$0$	$-1$	$0$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(-1+2\beta )q^{8}+\cdots$
8325.2.a.bi	$8325$	$2$	8325.a	1.a	$1$	$2$	$2$	$66.475$	$\Q(\sqrt{13}) $	None	✓				555.2.a.d	$1$	$0$	$-1$	$0$	$0$	$6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1+\beta )q^{4}+3q^{7}-3q^{8}+(-1+\cdots)q^{11}+\cdots$
8325.2.a.bj	$8325$	$2$	8325.a	1.a	$1$	$2$	$2$	$66.475$	$\Q(\sqrt{7}) $	None	✓	✓			8325.2.a.bj	$2$	$0$	$0$	$0$	$0$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+5q^{4}-2q^{7}+3\beta q^{8}-2q^{13}+\cdots$
8325.2.a.bk	$8325$	$2$	8325.a	1.a	$1$	$2$	$2$	$66.475$	$\Q(\sqrt{7}) $	None	✓	✓			8325.2.a.bj	$2$	$0$	$0$	$0$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+5q^{4}+2q^{7}+3\beta q^{8}+2q^{13}+\cdots$
8325.2.a.bl	$8325$	$2$	8325.a	1.a	$1$	$2$	$2$	$66.475$	$\Q(\sqrt{5}) $	None	✓				555.2.a.f	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots$
8325.2.a.bm	$8325$	$2$	8325.a	1.a	$1$	$2$	$2$	$66.475$	$\Q(\sqrt{13}) $	None	✓				555.2.a.g	$1$	$1$	$1$	$0$	$0$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}-q^{7}+3q^{8}+(-1+\cdots)q^{11}+\cdots$
8325.2.a.bn	$8325$	$2$	8325.a	1.a	$1$	$2$	$2$	$66.475$	$\Q(\sqrt{2}) $	None	✓				2775.2.a.k	$1$	$0$	$2$	$0$	$0$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2q^{7}+(3+\cdots)q^{8}+\cdots$
8325.2.a.bo	$8325$	$2$	8325.a	1.a	$1$	$3$	$3$	$66.475$	3.3.257.1	None	✓				2775.2.a.u	$1$	$1$	$0$	$0$	$0$	$-6$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-2+\beta _{2})q^{7}+\cdots$
8325.2.a.bp	$8325$	$2$	8325.a	1.a	$1$	$3$	$3$	$66.475$	3.3.257.1	None	✓				2775.2.a.u	$1$	$1$	$0$	$0$	$0$	$6$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(2-\beta _{2})q^{7}+\cdots$
8325.2.a.bq	$8325$	$2$	8325.a	1.a	$1$	$3$	$3$	$66.475$	3.3.469.1	None	✓				555.2.a.h	$1$	$1$	$1$	$0$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots$
8325.2.a.br	$8325$	$2$	8325.a	1.a	$1$	$3$	$3$	$66.475$	3.3.229.1	None	✓				555.2.a.i	$1$	$0$	$2$	$0$	$0$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+(2+\beta _{1})q^{4}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
8325.2.a.bs	$8325$	$2$	8325.a	1.a	$1$	$3$	$3$	$66.475$	3.3.148.1	None	✓				111.2.a.a	$1$	$0$	$3$	$0$	$0$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{7}+\cdots$
8325.2.a.bt	$8325$	$2$	8325.a	1.a	$1$	$4$	$4$	$66.475$	4.4.4400.1	None	✓				555.2.c.b	$1$	$1$	$-2$	$0$	$0$	$-8$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(-2-\beta _{3})q^{7}+\cdots$
8325.2.a.bu	$8325$	$2$	8325.a	1.a	$1$	$4$	$4$	$66.475$	4.4.27648.1	None	✓				333.2.a.f	$2$	$1$	$0$	$0$	$0$	$-8$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-2q^{7}+(\beta _{1}+\beta _{3})q^{8}+\cdots$
8325.2.a.bv	$8325$	$2$	8325.a	1.a	$1$	$4$	$4$	$66.475$	4.4.6224.1	None	✓				111.2.a.b	$1$	$1$	$0$	$0$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-2+2\beta _{3})q^{7}+\cdots$
8325.2.a.bw	$8325$	$2$	8325.a	1.a	$1$	$4$	$4$	$66.475$	4.4.4400.1	None	✓				555.2.c.b	$1$	$0$	$2$	$0$	$0$	$8$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+(2-\beta _{3})q^{7}+\cdots$
8325.2.a.bx	$8325$	$2$	8325.a	1.a	$1$	$5$	$5$	$66.475$	5.5.600268.1	None	✓				555.2.a.j	$1$	$0$	$-3$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{2}+(2-\beta _{3}+\beta _{4})q^{4}+\cdots$

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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.