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 51 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8820.2.a.a	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				140.2.i.a	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-6q^{11}-2q^{13}-6q^{17}-8q^{19}+\cdots$
8820.2.a.b	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				420.2.a.c	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-6q^{11}+4q^{13}+6q^{17}-2q^{19}+\cdots$
8820.2.a.c	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				1260.2.a.b	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{11}+2q^{17}+6q^{19}-6q^{23}+\cdots$
8820.2.a.d	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓	✓			8820.2.a.d	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{11}+4q^{13}-2q^{17}-4q^{23}+\cdots$
8820.2.a.e	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				2940.2.a.e	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{11}-4q^{13}-2q^{17}-2q^{23}+\cdots$
8820.2.a.f	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				420.2.a.a	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{11}-4q^{13}+6q^{17}-6q^{19}+\cdots$
8820.2.a.g	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				20.2.a.a	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{13}-6q^{17}+4q^{19}-6q^{23}+\cdots$
8820.2.a.h	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				1260.2.a.d	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{13}-6q^{17}-2q^{19}+6q^{23}+\cdots$
8820.2.a.i	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				980.2.a.d	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{11}+5q^{13}+q^{17}+6q^{19}+\cdots$
8820.2.a.j	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				420.2.q.a	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{11}+q^{13}+4q^{17}-q^{19}+\cdots$
8820.2.a.k	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				140.2.i.b	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{11}+6q^{13}+2q^{17}+9q^{23}+\cdots$
8820.2.a.l	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				420.2.q.b	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{11}-7q^{13}-6q^{17}-3q^{19}+\cdots$
8820.2.a.m	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓	✓			8820.2.a.d	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{11}-4q^{13}-2q^{17}+4q^{23}+\cdots$
8820.2.a.n	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				140.2.a.b	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+5q^{11}+3q^{13}-q^{17}-6q^{19}+\cdots$
8820.2.a.o	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				2940.2.a.a	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+6q^{11}+6q^{17}-4q^{19}-6q^{23}+\cdots$
8820.2.a.p	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				140.2.i.a	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-6q^{11}+2q^{13}+6q^{17}+8q^{19}+\cdots$
8820.2.a.q	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓	✓			8820.2.a.d	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{11}-4q^{13}+2q^{17}-4q^{23}+\cdots$
8820.2.a.r	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				140.2.a.a	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{11}+q^{13}-3q^{17}-2q^{19}+\cdots$
8820.2.a.s	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				420.2.a.d	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{11}-4q^{13}+2q^{17}+2q^{19}+\cdots$
8820.2.a.t	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				2940.2.a.e	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{11}+4q^{13}+2q^{17}-2q^{23}+\cdots$
8820.2.a.u	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				1260.2.a.d	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{13}+6q^{17}-2q^{19}-6q^{23}+\cdots$
8820.2.a.v	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				980.2.a.d	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{11}-5q^{13}-q^{17}-6q^{19}+\cdots$
8820.2.a.w	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				140.2.i.b	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{11}-6q^{13}-2q^{17}+9q^{23}+\cdots$
8820.2.a.x	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				420.2.a.b	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{11}-4q^{13}+2q^{17}-2q^{19}+\cdots$
8820.2.a.y	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				420.2.q.a	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{11}-q^{13}-4q^{17}+q^{19}+\cdots$
8820.2.a.z	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				1260.2.a.b	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{11}-2q^{17}+6q^{19}+6q^{23}+\cdots$
8820.2.a.ba	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓	✓			8820.2.a.d	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{11}+4q^{13}+2q^{17}+4q^{23}+\cdots$
8820.2.a.bb	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				420.2.q.b	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{11}+7q^{13}+6q^{17}+3q^{19}+\cdots$
8820.2.a.bc	$8820$	$2$	8820.a	1.a	$1$	$1$	$1$	$70.428$	$\Q$	None	✓				2940.2.a.a	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+6q^{11}-6q^{17}+4q^{19}-6q^{23}+\cdots$
8820.2.a.bd	$8820$	$2$	8820.a	1.a	$1$	$2$	$2$	$70.428$	$\Q(\sqrt{2}) $	None	✓				2940.2.a.n	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(-2+2\beta )q^{11}-2\beta q^{17}-\beta q^{19}+\cdots$
8820.2.a.be	$8820$	$2$	8820.a	1.a	$1$	$2$	$2$	$70.428$	$\Q(\sqrt{7}) $	None	✓				420.2.q.c	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(-1+\beta )q^{11}-\beta q^{13}+(-1+\cdots)q^{17}+\cdots$
8820.2.a.bf	$8820$	$2$	8820.a	1.a	$1$	$2$	$2$	$70.428$	$\Q(\sqrt{2}) $	None	✓		✓		420.2.q.d	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$3$	$\mathrm{SU}(2)$	$q-q^{5}+\beta q^{11}+(1-\beta )q^{13}+\beta q^{17}+\cdots$
8820.2.a.bg	$8820$	$2$	8820.a	1.a	$1$	$2$	$2$	$70.428$	$\Q(\sqrt{2}) $	None	✓				980.2.a.j	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(1+2\beta )q^{11}+(-5+\beta )q^{13}+\cdots$
8820.2.a.bh	$8820$	$2$	8820.a	1.a	$1$	$2$	$2$	$70.428$	$\Q(\sqrt{2}) $	None	✓				2940.2.a.o	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{11}+2\beta q^{13}+(-4+2\beta )q^{17}+\cdots$
8820.2.a.bi	$8820$	$2$	8820.a	1.a	$1$	$2$	$2$	$70.428$	$\Q(\sqrt{2}) $	None	✓				2940.2.a.n	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(-2+2\beta )q^{11}+2\beta q^{17}+\beta q^{19}+\cdots$
8820.2.a.bj	$8820$	$2$	8820.a	1.a	$1$	$2$	$2$	$70.428$	$\Q(\sqrt{7}) $	None	✓		✓		420.2.q.c	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(-1+\beta )q^{11}+\beta q^{13}+(1-\beta )q^{17}+\cdots$
8820.2.a.bk	$8820$	$2$	8820.a	1.a	$1$	$2$	$2$	$70.428$	$\Q(\sqrt{2}) $	None	✓				420.2.q.d	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$3$	$\mathrm{SU}(2)$	$q+q^{5}+\beta q^{11}+(-1+\beta )q^{13}-\beta q^{17}+\cdots$
8820.2.a.bl	$8820$	$2$	8820.a	1.a	$1$	$2$	$2$	$70.428$	$\Q(\sqrt{2}) $	None	✓				980.2.a.j	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(1+2\beta )q^{11}+(5-\beta )q^{13}+(-5+\cdots)q^{17}+\cdots$
8820.2.a.bm	$8820$	$2$	8820.a	1.a	$1$	$2$	$2$	$70.428$	$\Q(\sqrt{2}) $	None	✓				2940.2.a.o	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{11}-2\beta q^{13}+(4-2\beta )q^{17}+\cdots$
8820.2.a.bn	$8820$	$2$	8820.a	1.a	$1$	$3$	$3$	$70.428$	3.3.404.1	None	✓				1260.2.s.g	$1$	$0$	$0$	$0$	$-3$	$0$	$-$	$3$	$\mathrm{SU}(2)$	$q-q^{5}+(-1+\beta _{2})q^{11}+(-2+\beta _{2})q^{13}+\cdots$
8820.2.a.bo	$8820$	$2$	8820.a	1.a	$1$	$3$	$3$	$70.428$	3.3.404.1	None	✓		✓		1260.2.s.g	$1$	$1$	$0$	$0$	$-3$	$0$	$+$	$3$	$\mathrm{SU}(2)$	$q-q^{5}+(1-\beta _{2})q^{11}+(2-\beta _{2})q^{13}+\cdots$
8820.2.a.bp	$8820$	$2$	8820.a	1.a	$1$	$3$	$3$	$70.428$	3.3.404.1	None	✓		✓		1260.2.s.g	$1$	$0$	$0$	$0$	$3$	$0$	$-$	$3$	$\mathrm{SU}(2)$	$q+q^{5}+(-1+\beta _{2})q^{11}+(2-\beta _{2})q^{13}+\cdots$
8820.2.a.bq	$8820$	$2$	8820.a	1.a	$1$	$3$	$3$	$70.428$	3.3.404.1	None	✓				1260.2.s.g	$1$	$1$	$0$	$0$	$3$	$0$	$+$	$3$	$\mathrm{SU}(2)$	$q+q^{5}+(1-\beta _{2})q^{11}+(-2+\beta _{2})q^{13}+\cdots$
8820.2.a.br	$8820$	$2$	8820.a	1.a	$1$	$4$	$4$	$70.428$	$\Q(\sqrt{2}, \sqrt{5})$	None	✓	✓	✓		8820.2.a.br	$2$	$0$	$0$	$0$	$-4$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{5}+(\beta _{1}+\beta _{2})q^{11}+(-\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots$
8820.2.a.bs	$8820$	$2$	8820.a	1.a	$1$	$4$	$4$	$70.428$	$\Q(\sqrt{2}, \sqrt{5})$	None	✓	✓	✓		8820.2.a.br	$2$	$1$	$0$	$0$	$4$	$0$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+q^{5}+(\beta _{1}+\beta _{2})q^{11}+(\beta _{1}-\beta _{2})q^{13}+\cdots$
8820.2.d.a	$8820$	$2$	8820.d	21.c	$2$	$12$	$12$	$70.428$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					1260.2.cg.a	$2$	$0$	$0$	$0$	$-12$	$0$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{5}+(\beta _{1}-\beta _{7})q^{11}-\beta _{8}q^{13}+\beta _{5}q^{17}+\cdots$
8820.2.d.b	$8820$	$2$	8820.d	21.c	$2$	$12$	$12$	$70.428$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					1260.2.cg.a	$2$	$0$	$0$	$0$	$12$	$0$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{5}+(\beta _{1}-\beta _{7})q^{11}+\beta _{8}q^{13}-\beta _{5}q^{17}+\cdots$
8820.2.d.c	$8820$	$2$	8820.d	21.c	$2$	$16$	$16$	$70.428$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			8820.2.d.c	$2$	$0$	$0$	$0$	$-16$	$0$		$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{5}+(-\beta _{10}+\beta _{11}-\beta _{12})q^{11}+\cdots$
8820.2.d.d	$8820$	$2$	8820.d	21.c	$2$	$16$	$16$	$70.428$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			8820.2.d.c	$2$	$0$	$0$	$0$	$16$	$0$		$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{5}+(-\beta _{10}+\beta _{11}-\beta _{12})q^{11}+\cdots$
8820.2.f.a	$8820$	$2$	8820.f	105.g	$2$	$32$	$32$	$70.428$		None					1260.2.dc.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.