LMFDB - Newform search results

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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (50 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	13	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8619.2.a.a	$8619$	$2$	8619.a	1.a	$1$	$1$	$1$	$68.823$	$\Q$	None	✓	$1$	$0$	$-2$	$-1$	$-4$	$3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}-4q^{5}+2q^{6}+\cdots$
8619.2.a.b	$8619$	$2$	8619.a	1.a	$1$	$1$	$1$	$68.823$	$\Q$	None	✓	$1$	$0$	$-2$	$-1$	$2$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+2q^{5}+2q^{6}+\cdots$
8619.2.a.c	$8619$	$2$	8619.a	1.a	$1$	$1$	$1$	$68.823$	$\Q$	None	✓	$1$	$1$	$-2$	$1$	$3$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}+3q^{5}-2q^{6}+\cdots$
8619.2.a.d	$8619$	$2$	8619.a	1.a	$1$	$1$	$1$	$68.823$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$1$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
8619.2.a.e	$8619$	$2$	8619.a	1.a	$1$	$1$	$1$	$68.823$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$4$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+4q^{5}+q^{6}-2q^{7}+\cdots$
8619.2.a.f	$8619$	$2$	8619.a	1.a	$1$	$1$	$1$	$68.823$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$0$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}-4q^{7}+3q^{8}+\cdots$
8619.2.a.g	$8619$	$2$	8619.a	1.a	$1$	$1$	$1$	$68.823$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-3$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-3q^{5}+4q^{7}+q^{9}+3q^{11}+\cdots$
8619.2.a.h	$8619$	$2$	8619.a	1.a	$1$	$1$	$1$	$68.823$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$-1$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+2q^{7}+\cdots$
8619.2.a.i	$8619$	$2$	8619.a	1.a	$1$	$1$	$1$	$68.823$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$2$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+2q^{5}-q^{6}-3q^{8}+\cdots$
8619.2.a.j	$8619$	$2$	8619.a	1.a	$1$	$1$	$1$	$68.823$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}+2q^{7}-3q^{8}+\cdots$
8619.2.a.k	$8619$	$2$	8619.a	1.a	$1$	$1$	$1$	$68.823$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}+4q^{7}-3q^{8}+\cdots$
8619.2.a.l	$8619$	$2$	8619.a	1.a	$1$	$1$	$1$	$68.823$	$\Q$	None	✓	$1$	$0$	$2$	$-1$	$-2$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-2q^{5}-2q^{6}+\cdots$
8619.2.a.m	$8619$	$2$	8619.a	1.a	$1$	$1$	$1$	$68.823$	$\Q$	None	✓	$1$	$0$	$2$	$-1$	$4$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}+4q^{5}-2q^{6}+\cdots$
8619.2.a.n	$8619$	$2$	8619.a	1.a	$1$	$1$	$1$	$68.823$	$\Q$	None	✓	$1$	$1$	$2$	$1$	$-3$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots$
8619.2.a.o	$8619$	$2$	8619.a	1.a	$1$	$2$	$2$	$68.823$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$-2$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-\beta q^{5}+q^{9}-3\beta q^{11}+\cdots$
8619.2.a.p	$8619$	$2$	8619.a	1.a	$1$	$2$	$2$	$68.823$	$\Q(\sqrt{3}) $	None	✓	$2$	$1$	$0$	$-2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-\beta q^{5}-2\beta q^{7}+q^{9}+\cdots$
8619.2.a.q	$8619$	$2$	8619.a	1.a	$1$	$2$	$2$	$68.823$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$1$	$-2$	$-3$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(2+\beta )q^{4}+(-1-\beta )q^{5}+\cdots$
8619.2.a.r	$8619$	$2$	8619.a	1.a	$1$	$3$	$3$	$68.823$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$-2$	$3$	$-1$	$5$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$
8619.2.a.s	$8619$	$2$	8619.a	1.a	$1$	$3$	$3$	$68.823$	3.3.148.1	None	✓	$1$	$1$	$1$	$-3$	$0$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
8619.2.a.t	$8619$	$2$	8619.a	1.a	$1$	$3$	$3$	$68.823$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$2$	$3$	$1$	$-5$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+q^{3}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots$
8619.2.a.u	$8619$	$2$	8619.a	1.a	$1$	$3$	$3$	$68.823$	3.3.148.1	None	✓	$1$	$0$	$3$	$3$	$6$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
8619.2.a.v	$8619$	$2$	8619.a	1.a	$1$	$4$	$4$	$68.823$	$\Q(\zeta_{24})^+$	None	✓	$2$	$0$	$0$	$4$	$0$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+q^{3}+(-\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{6}+\cdots$
8619.2.a.w	$8619$	$2$	8619.a	1.a	$1$	$5$	$5$	$68.823$	5.5.153424.1	None	✓	$1$	$0$	$-3$	$5$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3})q^{2}+q^{3}+(2+\beta _{3}-\beta _{4})q^{4}+\cdots$
8619.2.a.x	$8619$	$2$	8619.a	1.a	$1$	$5$	$5$	$68.823$	5.5.1004368.1	None	✓	$1$	$1$	$-1$	$-5$	$-2$	$-8$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots$
8619.2.a.y	$8619$	$2$	8619.a	1.a	$1$	$6$	$6$	$68.823$	6.6.15187408.1	None	✓	$1$	$1$	$-4$	$6$	$-4$	$-2$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
8619.2.a.z	$8619$	$2$	8619.a	1.a	$1$	$6$	$6$	$68.823$	6.6.83831632.1	None	✓	$1$	$0$	$-2$	$-6$	$0$	$-2$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$
8619.2.a.ba	$8619$	$2$	8619.a	1.a	$1$	$6$	$6$	$68.823$	6.6.485125.1	None	✓	$1$	$1$	$-2$	$6$	$4$	$5$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{3}+\beta _{4})q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots$
8619.2.a.bb	$8619$	$2$	8619.a	1.a	$1$	$6$	$6$	$68.823$	6.6.31337472.1	None	✓	$2$	$1$	$0$	$-6$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(\beta _{1}-\beta _{5})q^{5}+\cdots$
8619.2.a.bc	$8619$	$2$	8619.a	1.a	$1$	$6$	$6$	$68.823$	6.6.485125.1	None	✓	$1$	$1$	$2$	$6$	$-4$	$-5$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(\beta _{3}+\beta _{4})q^{4}+(-2+\cdots)q^{5}+\cdots$
8619.2.a.bd	$8619$	$2$	8619.a	1.a	$1$	$8$	$8$	$68.823$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$-8$	$-1$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{7})q^{5}+\cdots$
8619.2.a.be	$8619$	$2$	8619.a	1.a	$1$	$8$	$8$	$68.823$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$-8$	$1$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
8619.2.a.bf	$8619$	$2$	8619.a	1.a	$1$	$8$	$8$	$68.823$	8.8.$\cdots$.1	None	✓	$2$	$0$	$0$	$-8$	$0$	$0$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{7})q^{2}-q^{3}+(2+\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
8619.2.a.bg	$8619$	$2$	8619.a	1.a	$1$	$8$	$8$	$68.823$	8.8.$\cdots$.1	None	✓	$2$	$1$	$0$	$8$	$0$	$0$	$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
8619.2.a.bh	$8619$	$2$	8619.a	1.a	$1$	$9$	$9$	$68.823$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$-1$	$-9$	$-5$	$3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2}+\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$
8619.2.a.bi	$8619$	$2$	8619.a	1.a	$1$	$9$	$9$	$68.823$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$1$	$-9$	$5$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2}+\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots$
8619.2.a.bj	$8619$	$2$	8619.a	1.a	$1$	$10$	$10$	$68.823$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$2$	$0$	$0$	$10$	$0$	$0$	$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{8}q^{5}+\cdots$
8619.2.a.bk	$8619$	$2$	8619.a	1.a	$1$	$11$	$11$	$68.823$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$0$	$11$	$0$	$-3$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots$
8619.2.a.bl	$8619$	$2$	8619.a	1.a	$1$	$11$	$11$	$68.823$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$0$	$11$	$0$	$3$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots$
8619.2.a.bm	$8619$	$2$	8619.a	1.a	$1$	$12$	$12$	$68.823$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$1$	$0$	$-12$	$0$	$0$	$+$	$-$	$-$	$+$	$3$	$\mathrm{SU}(2)$	$q+\beta _{7}q^{2}-q^{3}+(1-\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
8619.2.a.bn	$8619$	$2$	8619.a	1.a	$1$	$16$	$16$	$68.823$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$2$	$1$	$0$	$16$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{14}q^{5}+\cdots$
8619.2.a.bo	$8619$	$2$	8619.a	1.a	$1$	$20$	$20$	$68.823$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$2$	$0$	$0$	$20$	$0$	$0$	$-$	$-$	$-$	$-$	$2^{2}\cdot 5^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{15}q^{5}+\cdots$
8619.2.a.bp	$8619$	$2$	8619.a	1.a	$1$	$21$	$21$	$68.823$		None	✓	$1$	$1$	$-9$	$21$	$-26$	$5$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
8619.2.a.bq	$8619$	$2$	8619.a	1.a	$1$	$21$	$21$	$68.823$		None	✓	$1$	$0$	$9$	$21$	$26$	$-5$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
8619.2.a.br	$8619$	$2$	8619.a	1.a	$1$	$22$	$22$	$68.823$		None	✓	$2$	$0$	$0$	$-22$	$0$	$0$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
8619.2.a.bs	$8619$	$2$	8619.a	1.a	$1$	$24$	$24$	$68.823$		None	✓	$1$	$1$	$-11$	$24$	$-23$	$-10$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
8619.2.a.bt	$8619$	$2$	8619.a	1.a	$1$	$24$	$24$	$68.823$		None	✓	$1$	$0$	$-7$	$-24$	$13$	$12$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
8619.2.a.bu	$8619$	$2$	8619.a	1.a	$1$	$24$	$24$	$68.823$		None	✓	$1$	$1$	$-1$	$-24$	$-11$	$-2$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
8619.2.a.bv	$8619$	$2$	8619.a	1.a	$1$	$24$	$24$	$68.823$		None	✓	$1$	$0$	$1$	$-24$	$11$	$2$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
8619.2.a.bw	$8619$	$2$	8619.a	1.a	$1$	$24$	$24$	$68.823$		None	✓	$1$	$1$	$7$	$-24$	$-13$	$-12$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
8619.2.a.bx	$8619$	$2$	8619.a	1.a	$1$	$24$	$24$	$68.823$		None	✓	$1$	$0$	$11$	$24$	$23$	$10$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

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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.