LMFDB - Newform search results

The results below are complete, since the LMFDB contains all newforms with trivial character and $Nk^2$ at most 40000

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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 (40 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	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8624.2.a.a	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓				77.2.a.a	$1$	$0$	$0$	$-3$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}+6q^{9}+q^{11}+4q^{13}+\cdots$
8624.2.a.d	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓				154.2.e.d	$1$	$0$	$0$	$-3$	$4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+4q^{5}+6q^{9}+q^{11}+q^{13}+\cdots$
8624.2.a.h	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓				4312.2.a.a	$1$	$0$	$0$	$-2$	$4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+4q^{5}+q^{9}-q^{11}+2q^{13}+\cdots$
8624.2.a.m	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓				616.2.a.b	$1$	$0$	$0$	$-1$	$1$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{9}-q^{11}-q^{15}+2q^{17}+\cdots$
8624.2.a.o	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓				154.2.a.c	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-3q^{9}+q^{11}-2q^{13}-2q^{17}+\cdots$
8624.2.a.r	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓				154.2.a.a	$1$	$0$	$0$	$0$	$4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-3q^{9}+q^{11}-2q^{13}+4q^{17}+\cdots$
8624.2.a.s	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓				77.2.a.b	$1$	$0$	$0$	$1$	$-3$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}-2q^{9}+q^{11}+4q^{13}+\cdots$
8624.2.a.t	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓				154.2.e.b	$1$	$0$	$0$	$1$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{9}+q^{11}-5q^{13}-6q^{17}+\cdots$
8624.2.a.u	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓				154.2.e.c	$1$	$0$	$0$	$1$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{9}+q^{11}+q^{13}+6q^{17}+\cdots$
8624.2.a.v	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓				616.2.q.a	$1$	$0$	$0$	$1$	$2$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-2q^{9}+q^{11}+3q^{13}+\cdots$
8624.2.a.w	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓				44.2.a.a	$1$	$0$	$0$	$1$	$3$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}-2q^{9}+q^{11}+4q^{13}+\cdots$
8624.2.a.x	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓				4312.2.a.a	$1$	$0$	$0$	$2$	$-4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-4q^{5}+q^{9}-q^{11}-2q^{13}+\cdots$
8624.2.a.be	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓				154.2.e.a	$1$	$0$	$0$	$3$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-2q^{5}+6q^{9}+q^{11}+7q^{13}+\cdots$
8624.2.a.bi	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{17}) $	None	✓				616.2.a.f	$1$	$0$	$0$	$-1$	$3$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(2-\beta )q^{5}+(1+\beta )q^{9}-q^{11}+\cdots$
8624.2.a.bj	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{6}) $	None	✓				308.2.a.b	$1$	$0$	$0$	$0$	$-4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2q^{5}+3q^{9}+q^{11}+(-2+\cdots)q^{13}+\cdots$
8624.2.a.bl	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓				1078.2.a.p	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{5}-3q^{9}-q^{11}+3\beta q^{13}-2\beta q^{17}+\cdots$
8624.2.a.bm	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓				2156.2.a.d	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-3q^{9}-q^{11}-3\beta q^{13}-\beta q^{17}+\cdots$
8624.2.a.bt	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓				4312.2.a.q	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{5}-q^{9}+q^{11}-2q^{15}+\cdots$
8624.2.a.bu	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓				2156.2.a.e	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{9}+q^{11}+\beta q^{13}+5\beta q^{17}+\cdots$
8624.2.a.by	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓				1078.2.a.r	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{3}+5q^{9}+q^{11}+\beta q^{13}-\beta q^{17}+\cdots$
8624.2.a.ca	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{7}) $	None	✓				154.2.e.f	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1+\beta )q^{5}+4q^{9}-q^{11}+5q^{13}+\cdots$
8624.2.a.cc	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓				154.2.e.e	$1$	$0$	$0$	$2$	$-4$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-2+\beta )q^{5}+2\beta q^{9}+\cdots$
8624.2.a.cd	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓				616.2.q.b	$1$	$0$	$0$	$2$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+\beta q^{5}+2\beta q^{9}-q^{11}+\cdots$
8624.2.a.ce	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{5}) $	None	✓				77.2.a.d	$1$	$0$	$0$	$2$	$4$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+2q^{5}+(3+2\beta )q^{9}+q^{11}+\cdots$
8624.2.a.cf	$8624$	$2$	8624.a	1.a	$1$	$3$	$3$	$68.863$	$\Q(\zeta_{14})^+$	None	✓				616.2.q.c	$1$	$0$	$0$	$-5$	$2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta _{2})q^{3}+(-1+3\beta _{1}-2\beta _{2})q^{5}+\cdots$
8624.2.a.ch	$8624$	$2$	8624.a	1.a	$1$	$3$	$3$	$68.863$	$\Q(\zeta_{18})^+$	None	✓				77.2.e.a	$1$	$0$	$0$	$-3$	$6$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}+(2+\beta _{1}-\beta _{2})q^{5}+\cdots$
8624.2.a.ck	$8624$	$2$	8624.a	1.a	$1$	$3$	$3$	$68.863$	3.3.257.1	None	✓				77.2.e.b	$1$	$0$	$0$	$-1$	$2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{9}+\cdots$
8624.2.a.cm	$8624$	$2$	8624.a	1.a	$1$	$3$	$3$	$68.863$	3.3.229.1	None	✓				616.2.a.g	$1$	$0$	$0$	$1$	$-1$	$0$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+\beta _{2}q^{5}+(1-\beta _{1})q^{9}-q^{11}+\cdots$
8624.2.a.cn	$8624$	$2$	8624.a	1.a	$1$	$3$	$3$	$68.863$	3.3.321.1	None	✓				308.2.i.a	$1$	$0$	$0$	$1$	$2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(1-\beta _{1}-2\beta _{2})q^{9}+\cdots$
8624.2.a.cp	$8624$	$2$	8624.a	1.a	$1$	$3$	$3$	$68.863$	3.3.257.1	None	✓				308.2.i.b	$1$	$0$	$0$	$3$	$-2$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
8624.2.a.ct	$8624$	$2$	8624.a	1.a	$1$	$4$	$4$	$68.863$	4.4.9248.1	None	✓				4312.2.a.ba	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}-\beta _{2}q^{5}-\beta _{3}q^{9}-q^{11}+(\beta _{1}+\cdots)q^{13}+\cdots$
8624.2.a.cu	$8624$	$2$	8624.a	1.a	$1$	$4$	$4$	$68.863$	4.4.9248.1	None	✓		✓		539.2.a.k	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}-\beta _{3}q^{9}+q^{11}+\cdots$
8624.2.a.cv	$8624$	$2$	8624.a	1.a	$1$	$4$	$4$	$68.863$	$\Q(\sqrt{7}, \sqrt{15})$	None	✓				4312.2.a.bb	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+\beta _{2}q^{5}+(2-\beta _{3})q^{9}-q^{11}+\cdots$
8624.2.a.cy	$8624$	$2$	8624.a	1.a	$1$	$4$	$4$	$68.863$	4.4.11348.1	None	✓				616.2.a.h	$1$	$0$	$0$	$1$	$-5$	$0$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+(2+\beta _{2}-\beta _{3})q^{9}+\cdots$
8624.2.a.cz	$8624$	$2$	8624.a	1.a	$1$	$4$	$4$	$68.863$	4.4.89289.1	None	✓				616.2.q.d	$1$	$0$	$0$	$2$	$-4$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+(3+\beta _{1}+\cdots)q^{9}+\cdots$
8624.2.a.dc	$8624$	$2$	8624.a	1.a	$1$	$5$	$5$	$68.863$	5.5.559701.1	None	✓				616.2.q.f	$1$	$0$	$0$	$1$	$4$	$0$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{9}+\cdots$
8624.2.a.dd	$8624$	$2$	8624.a	1.a	$1$	$5$	$5$	$68.863$	5.5.352076.1	None	✓		✓		616.2.q.e	$1$	$0$	$0$	$3$	$-4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{4})q^{5}+\cdots$
8624.2.a.de	$8624$	$2$	8624.a	1.a	$1$	$8$	$8$	$68.863$	8.8.$\cdots$.1	None	✓				4312.2.a.bi	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+(-\beta _{3}-\beta _{4}+\beta _{5})q^{5}+(1+\cdots)q^{9}+\cdots$
8624.2.a.df	$8624$	$2$	8624.a	1.a	$1$	$10$	$10$	$68.863$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓		✓		539.2.a.l	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{6}q^{5}+(2+\beta _{2})q^{9}-q^{11}+\cdots$
8624.2.a.dg	$8624$	$2$	8624.a	1.a	$1$	$12$	$12$	$68.863$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓		✓		4312.2.a.bj	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$2^{7}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{9}q^{5}+(3+\beta _{2})q^{9}+q^{11}+\cdots$

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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.