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 (46 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	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4864.2.a.a	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	$\Q$	None	✓				1216.2.c.b	$1$	$2$	$0$	$-3$	$-4$	$1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-4q^{5}+q^{7}+6q^{9}-5q^{13}+\cdots$
4864.2.a.b	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	$\Q$	None	✓				1216.2.c.b	$1$	$0$	$0$	$-3$	$4$	$-1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+4q^{5}-q^{7}+6q^{9}+5q^{13}+\cdots$
4864.2.a.c	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	$\Q$	None	✓				2432.2.c.a	$1$	$2$	$0$	$-1$	$-2$	$-1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-q^{7}-2q^{9}-4q^{11}+\cdots$
4864.2.a.d	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	$\Q$	None	✓				1216.2.c.a	$1$	$1$	$0$	$-1$	$0$	$-3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{7}-2q^{9}-3q^{13}+3q^{17}+\cdots$
4864.2.a.e	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	$\Q$	None	✓				1216.2.c.a	$1$	$1$	$0$	$-1$	$0$	$3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{7}-2q^{9}+3q^{13}+3q^{17}+\cdots$
4864.2.a.f	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	$\Q$	None	✓				2432.2.c.a	$1$	$1$	$0$	$-1$	$2$	$1$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{7}-2q^{9}-4q^{11}+\cdots$
4864.2.a.g	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	$\Q$	None	✓				152.2.c.a	$1$	$0$	$0$	$0$	$0$	$-2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-3q^{9}-4q^{11}-2q^{13}+2q^{17}+\cdots$
4864.2.a.h	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	$\Q$	None	✓				152.2.c.a	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-3q^{9}+4q^{11}+2q^{13}+2q^{17}+\cdots$
4864.2.a.i	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	$\Q$	None	✓				152.2.c.a	$1$	$1$	$0$	$0$	$0$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-3q^{9}-4q^{11}+2q^{13}+2q^{17}+\cdots$
4864.2.a.j	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	$\Q$	None	✓				152.2.c.a	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-3q^{9}+4q^{11}-2q^{13}+2q^{17}+\cdots$
4864.2.a.k	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	$\Q$	None	✓				2432.2.c.a	$1$	$1$	$0$	$1$	$-2$	$1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{7}-2q^{9}+4q^{11}+\cdots$
4864.2.a.l	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	$\Q$	None	✓				1216.2.c.a	$1$	$1$	$0$	$1$	$0$	$-3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{7}-2q^{9}+3q^{13}+3q^{17}+\cdots$
4864.2.a.m	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	$\Q$	None	✓				1216.2.c.a	$1$	$1$	$0$	$1$	$0$	$3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{7}-2q^{9}-3q^{13}+3q^{17}+\cdots$
4864.2.a.n	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	$\Q$	None	✓				2432.2.c.a	$1$	$0$	$0$	$1$	$2$	$-1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-q^{7}-2q^{9}+4q^{11}+\cdots$
4864.2.a.o	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	$\Q$	None	✓				1216.2.c.b	$1$	$0$	$0$	$3$	$-4$	$-1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-4q^{5}-q^{7}+6q^{9}-5q^{13}+\cdots$
4864.2.a.p	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	$\Q$	None	✓				1216.2.c.b	$1$	$0$	$0$	$3$	$4$	$1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+4q^{5}+q^{7}+6q^{9}+5q^{13}+\cdots$
4864.2.a.q	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	$\Q(\sqrt{3}) $	None	✓				1216.2.c.e	$2$	$1$	$0$	$-4$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-\beta q^{5}-\beta q^{7}+q^{9}+3q^{11}+\cdots$
4864.2.a.r	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	$\Q(\sqrt{11}) $	None	✓				1216.2.c.f	$2$	$0$	$0$	$-4$	$0$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+\beta q^{5}-\beta q^{7}+q^{9}+5q^{11}+\cdots$
4864.2.a.s	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	$\Q(\sqrt{3}) $	None	✓				2432.2.c.c	$1$	$1$	$0$	$-2$	$-4$	$2$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+(1+\beta )q^{7}-2q^{9}+4q^{11}+\cdots$
4864.2.a.t	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	$\Q(\sqrt{3}) $	None	✓				1216.2.c.g	$2$	$1$	$0$	$-2$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2\beta q^{5}-\beta q^{7}-2q^{9}+3\beta q^{13}+\cdots$
4864.2.a.u	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	$\Q(\sqrt{3}) $	None	✓				2432.2.c.c	$1$	$0$	$0$	$-2$	$4$	$-2$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+(-1+\beta )q^{7}-2q^{9}+\cdots$
4864.2.a.v	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	$\Q(\sqrt{3}) $	None	✓				2432.2.c.c	$1$	$0$	$0$	$2$	$-4$	$-2$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+(-1+\beta )q^{7}-2q^{9}+\cdots$
4864.2.a.w	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	$\Q(\sqrt{3}) $	None	✓				1216.2.c.g	$2$	$1$	$0$	$2$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2\beta q^{5}+\beta q^{7}-2q^{9}+3\beta q^{13}+\cdots$
4864.2.a.x	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	$\Q(\sqrt{3}) $	None	✓				2432.2.c.c	$1$	$1$	$0$	$2$	$4$	$2$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+(1-\beta )q^{7}-2q^{9}-4q^{11}+\cdots$
4864.2.a.y	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	$\Q(\sqrt{11}) $	None	✓				1216.2.c.f	$2$	$0$	$0$	$4$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+\beta q^{5}+\beta q^{7}+q^{9}-5q^{11}+\cdots$
4864.2.a.z	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	$\Q(\sqrt{3}) $	None	✓				1216.2.c.e	$2$	$1$	$0$	$4$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-\beta q^{5}+\beta q^{7}+q^{9}-3q^{11}+\cdots$
4864.2.a.ba	$4864$	$2$	4864.a	1.a	$1$	$3$	$3$	$38.839$	3.3.316.1	None	✓				2432.2.c.e	$1$	$1$	$0$	$-2$	$-4$	$-4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}-\beta _{2})q^{3}+(-1-\beta _{1})q^{5}+\cdots$
4864.2.a.bb	$4864$	$2$	4864.a	1.a	$1$	$3$	$3$	$38.839$	3.3.316.1	None	✓				2432.2.c.e	$1$	$0$	$0$	$-2$	$4$	$4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1})q^{5}+\cdots$
4864.2.a.bc	$4864$	$2$	4864.a	1.a	$1$	$3$	$3$	$38.839$	3.3.892.1	None	✓				2432.2.c.f	$1$	$1$	$0$	$-1$	$-2$	$-3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1+\beta _{1})q^{5}+(-1-\beta _{2})q^{7}+\cdots$
4864.2.a.bd	$4864$	$2$	4864.a	1.a	$1$	$3$	$3$	$38.839$	3.3.892.1	None	✓				2432.2.c.f	$1$	$0$	$0$	$-1$	$2$	$3$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{2})q^{7}+\cdots$
4864.2.a.be	$4864$	$2$	4864.a	1.a	$1$	$3$	$3$	$38.839$	3.3.892.1	None	✓				2432.2.c.f	$1$	$0$	$0$	$1$	$-2$	$3$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{1})q^{5}+(1+\beta _{2})q^{7}+\cdots$
4864.2.a.bf	$4864$	$2$	4864.a	1.a	$1$	$3$	$3$	$38.839$	3.3.892.1	None	✓				2432.2.c.f	$1$	$1$	$0$	$1$	$2$	$-3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1-\beta _{1})q^{5}+(-1-\beta _{2})q^{7}+\cdots$
4864.2.a.bg	$4864$	$2$	4864.a	1.a	$1$	$3$	$3$	$38.839$	3.3.316.1	None	✓				2432.2.c.e	$1$	$0$	$0$	$2$	$-4$	$4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{1})q^{5}+\cdots$
4864.2.a.bh	$4864$	$2$	4864.a	1.a	$1$	$3$	$3$	$38.839$	3.3.316.1	None	✓				2432.2.c.e	$1$	$1$	$0$	$2$	$4$	$-4$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots$
4864.2.a.bi	$4864$	$2$	4864.a	1.a	$1$	$4$	$4$	$38.839$	$\Q(\sqrt{3}, \sqrt{11})$	None	✓				1216.2.c.h	$2$	$0$	$0$	$-2$	$0$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots$
4864.2.a.bj	$4864$	$2$	4864.a	1.a	$1$	$4$	$4$	$38.839$	$\Q(\sqrt{3}, \sqrt{19})$	None	✓				1216.2.c.i	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}-\beta _{2}q^{7}-3q^{9}+(-2-\beta _{3})q^{11}+\cdots$
4864.2.a.bk	$4864$	$2$	4864.a	1.a	$1$	$4$	$4$	$38.839$	$\Q(\sqrt{3}, \sqrt{19})$	None	✓				1216.2.c.i	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+\beta _{2}q^{7}-3q^{9}+(2+\beta _{3})q^{11}+\cdots$
4864.2.a.bl	$4864$	$2$	4864.a	1.a	$1$	$4$	$4$	$38.839$	$\Q(\sqrt{3}, \sqrt{11})$	None	✓				1216.2.c.h	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{3})q^{3}-\beta _{1}q^{5}+(2\beta _{1}-\beta _{2})q^{7}+\cdots$
4864.2.a.bm	$4864$	$2$	4864.a	1.a	$1$	$8$	$8$	$38.839$	8.8.$\cdots$.1	None	✓				2432.2.c.i	$2$	$1$	$0$	$-4$	$0$	$0$	$-$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{6}q^{5}+\beta _{4}q^{7}+(-\beta _{1}+\beta _{7})q^{9}+\cdots$
4864.2.a.bn	$4864$	$2$	4864.a	1.a	$1$	$8$	$8$	$38.839$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓				152.2.c.b	$1$	$1$	$0$	$0$	$-8$	$-4$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{3}+(-1+\beta _{2})q^{5}-\beta _{4}q^{7}+(1+\cdots)q^{9}+\cdots$
4864.2.a.bo	$4864$	$2$	4864.a	1.a	$1$	$8$	$8$	$38.839$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓				152.2.c.b	$1$	$1$	$0$	$0$	$-8$	$4$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{5}q^{3}+(-1+\beta _{2})q^{5}+\beta _{4}q^{7}+(1+\cdots)q^{9}+\cdots$
4864.2.a.bp	$4864$	$2$	4864.a	1.a	$1$	$8$	$8$	$38.839$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓				152.2.c.b	$1$	$0$	$0$	$0$	$8$	$-4$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{5}q^{3}+(1-\beta _{2})q^{5}-\beta _{4}q^{7}+(1-\beta _{7})q^{9}+\cdots$
4864.2.a.bq	$4864$	$2$	4864.a	1.a	$1$	$8$	$8$	$38.839$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓				152.2.c.b	$1$	$0$	$0$	$0$	$8$	$4$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{3}+(1-\beta _{2})q^{5}+\beta _{4}q^{7}+(1-\beta _{7})q^{9}+\cdots$
4864.2.a.br	$4864$	$2$	4864.a	1.a	$1$	$8$	$8$	$38.839$	8.8.$\cdots$.1	None	✓				2432.2.c.i	$2$	$0$	$0$	$4$	$0$	$0$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{6}q^{5}+\beta _{4}q^{7}+(-\beta _{1}+\beta _{7})q^{9}+\cdots$
4864.2.a.bs	$4864$	$2$	4864.a	1.a	$1$	$10$	$10$	$38.839$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓		✓		2432.2.c.j	$2$	$1$	$0$	$-4$	$0$	$0$	$+$	$+$	$+$	$2^{6}$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{3}-\beta _{1}q^{5}+(\beta _{1}-\beta _{6})q^{7}+(1+\cdots)q^{9}+\cdots$
4864.2.a.bt	$4864$	$2$	4864.a	1.a	$1$	$10$	$10$	$38.839$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓		✓		2432.2.c.j	$2$	$0$	$0$	$4$	$0$	$0$	$+$	$-$	$-$	$2^{6}$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{3}-\beta _{1}q^{5}+(-\beta _{1}+\beta _{6})q^{7}+\cdots$

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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.