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 (48 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	7	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
7581.2.a.a	$7581$	$2$	7581.a	1.a	$1$	$1$	$1$	$60.535$	$\Q$	None	✓	✓			7581.2.a.a	$1$	$2$	$-1$	$1$	$-4$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-4q^{5}-q^{6}-q^{7}+\cdots$
7581.2.a.b	$7581$	$2$	7581.a	1.a	$1$	$1$	$1$	$60.535$	$\Q$	None	✓				399.2.a.c	$1$	$1$	$-1$	$1$	$0$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}-q^{7}+3q^{8}+\cdots$
7581.2.a.c	$7581$	$2$	7581.a	1.a	$1$	$1$	$1$	$60.535$	$\Q$	None	✓	✓			7581.2.a.a	$1$	$1$	$1$	$-1$	$-4$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-4q^{5}-q^{6}-q^{7}+\cdots$
7581.2.a.d	$7581$	$2$	7581.a	1.a	$1$	$1$	$1$	$60.535$	$\Q$	None	✓				21.2.a.a	$1$	$0$	$1$	$-1$	$-2$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
7581.2.a.e	$7581$	$2$	7581.a	1.a	$1$	$1$	$1$	$60.535$	$\Q$	None	✓				399.2.a.b	$1$	$0$	$1$	$-1$	$4$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+4q^{5}-q^{6}-q^{7}+\cdots$
7581.2.a.f	$7581$	$2$	7581.a	1.a	$1$	$1$	$1$	$60.535$	$\Q$	None	✓				399.2.a.a	$1$	$0$	$1$	$1$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}+q^{7}-3q^{8}+\cdots$
7581.2.a.g	$7581$	$2$	7581.a	1.a	$1$	$2$	$2$	$60.535$	$\Q(\sqrt{5}) $	None	✓	✓			7581.2.a.g	$1$	$1$	$-2$	$2$	$3$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+(1+\beta )q^{5}-q^{6}+\cdots$
7581.2.a.h	$7581$	$2$	7581.a	1.a	$1$	$2$	$2$	$60.535$	$\Q(\sqrt{5}) $	None	✓	✓			7581.2.a.h	$1$	$1$	$-1$	$2$	$-4$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-3+2\beta )q^{5}+\cdots$
7581.2.a.i	$7581$	$2$	7581.a	1.a	$1$	$2$	$2$	$60.535$	$\Q(\sqrt{5}) $	None	✓	✓			7581.2.a.h	$1$	$0$	$1$	$-2$	$-4$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-3+2\beta )q^{5}+\cdots$
7581.2.a.j	$7581$	$2$	7581.a	1.a	$1$	$2$	$2$	$60.535$	$\Q(\sqrt{5}) $	None	✓	✓			7581.2.a.g	$1$	$0$	$2$	$-2$	$3$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+(2-\beta )q^{5}-q^{6}+\cdots$
7581.2.a.k	$7581$	$2$	7581.a	1.a	$1$	$3$	$3$	$60.535$	$\Q(\zeta_{18})^+$	None	✓				399.2.bo.a	$1$	$1$	$-3$	$3$	$0$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots$
7581.2.a.l	$7581$	$2$	7581.a	1.a	$1$	$3$	$3$	$60.535$	3.3.404.1	None	✓				399.2.a.e	$1$	$0$	$-1$	$-3$	$0$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
7581.2.a.m	$7581$	$2$	7581.a	1.a	$1$	$3$	$3$	$60.535$	3.3.148.1	None	✓	✓			7581.2.a.m	$1$	$1$	$-1$	$3$	$2$	$3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
7581.2.a.n	$7581$	$2$	7581.a	1.a	$1$	$3$	$3$	$60.535$	3.3.148.1	None	✓				399.2.a.d	$1$	$1$	$-1$	$3$	$4$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
7581.2.a.o	$7581$	$2$	7581.a	1.a	$1$	$3$	$3$	$60.535$	3.3.148.1	None	✓	✓			7581.2.a.m	$1$	$0$	$1$	$-3$	$2$	$3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
7581.2.a.p	$7581$	$2$	7581.a	1.a	$1$	$3$	$3$	$60.535$	$\Q(\zeta_{18})^+$	None	✓				399.2.bo.a	$1$	$1$	$3$	$-3$	$0$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+(2\beta _{1}-\beta _{2})q^{5}-q^{6}+\cdots$
7581.2.a.q	$7581$	$2$	7581.a	1.a	$1$	$4$	$4$	$60.535$	4.4.6224.1	None	✓	✓			7581.2.a.q	$1$	$1$	$-2$	$-4$	$6$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{2}-q^{3}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
7581.2.a.r	$7581$	$2$	7581.a	1.a	$1$	$4$	$4$	$60.535$	4.4.1957.1	None	✓				399.2.k.b	$1$	$1$	$-1$	$-4$	$-2$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}-q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
7581.2.a.s	$7581$	$2$	7581.a	1.a	$1$	$4$	$4$	$60.535$	4.4.12197.1	None	✓				399.2.k.a	$1$	$1$	$-1$	$-4$	$-2$	$4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$
7581.2.a.t	$7581$	$2$	7581.a	1.a	$1$	$4$	$4$	$60.535$	4.4.1957.1	None	✓				399.2.k.b	$1$	$1$	$1$	$4$	$-2$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
7581.2.a.u	$7581$	$2$	7581.a	1.a	$1$	$4$	$4$	$60.535$	4.4.12197.1	None	✓				399.2.k.a	$1$	$1$	$1$	$4$	$-2$	$4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$
7581.2.a.v	$7581$	$2$	7581.a	1.a	$1$	$4$	$4$	$60.535$	4.4.6224.1	None	✓	✓			7581.2.a.q	$1$	$0$	$2$	$4$	$6$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{3})q^{2}+q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\cdots$
7581.2.a.w	$7581$	$2$	7581.a	1.a	$1$	$5$	$5$	$60.535$	5.5.368464.1	None	✓				399.2.a.g	$1$	$0$	$-3$	$5$	$4$	$5$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
7581.2.a.x	$7581$	$2$	7581.a	1.a	$1$	$5$	$5$	$60.535$	5.5.1240016.1	None	✓				399.2.a.f	$1$	$1$	$-1$	$-5$	$-2$	$5$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}-q^{3}+(1+\beta _{4})q^{4}+\beta _{2}q^{5}+\cdots$
7581.2.a.y	$7581$	$2$	7581.a	1.a	$1$	$6$	$6$	$60.535$	6.6.5953625.1	None	✓	✓			7581.2.a.y	$1$	$1$	$-3$	$6$	$2$	$-6$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3})q^{2}+q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
7581.2.a.z	$7581$	$2$	7581.a	1.a	$1$	$6$	$6$	$60.535$	6.6.8512625.1	None	✓	✓			7581.2.a.z	$1$	$0$	$-2$	$-6$	$-5$	$-6$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{3}+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots$
7581.2.a.ba	$7581$	$2$	7581.a	1.a	$1$	$6$	$6$	$60.535$	6.6.343395288.1	None	✓				399.2.k.c	$1$	$0$	$-1$	$-6$	$0$	$-6$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
7581.2.a.bb	$7581$	$2$	7581.a	1.a	$1$	$6$	$6$	$60.535$	6.6.130040728.1	None	✓				399.2.k.d	$1$	$0$	$-1$	$-6$	$4$	$6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{5})q^{5}+\cdots$
7581.2.a.bc	$7581$	$2$	7581.a	1.a	$1$	$6$	$6$	$60.535$	6.6.343395288.1	None	✓				399.2.k.c	$1$	$0$	$1$	$6$	$0$	$-6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
7581.2.a.bd	$7581$	$2$	7581.a	1.a	$1$	$6$	$6$	$60.535$	6.6.130040728.1	None	✓				399.2.k.d	$1$	$0$	$1$	$6$	$4$	$6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{5})q^{5}+\cdots$
7581.2.a.be	$7581$	$2$	7581.a	1.a	$1$	$6$	$6$	$60.535$	6.6.8512625.1	None	✓	✓			7581.2.a.z	$1$	$1$	$2$	$6$	$-5$	$-6$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{3}+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots$
7581.2.a.bf	$7581$	$2$	7581.a	1.a	$1$	$6$	$6$	$60.535$	6.6.5953625.1	None	✓	✓			7581.2.a.y	$1$	$0$	$3$	$-6$	$2$	$-6$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{3})q^{2}-q^{3}+(2-\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
7581.2.a.bg	$7581$	$2$	7581.a	1.a	$1$	$9$	$9$	$60.535$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓				399.2.bo.b	$1$	$1$	$-3$	$-9$	$0$	$-9$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1-\beta _{5}-\beta _{7}+\beta _{8})q^{4}+\cdots$
7581.2.a.bh	$7581$	$2$	7581.a	1.a	$1$	$9$	$9$	$60.535$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓		✓		399.2.bo.b	$1$	$1$	$3$	$9$	$0$	$-9$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1-\beta _{5}-\beta _{7}+\beta _{8})q^{4}+\cdots$
7581.2.a.bi	$7581$	$2$	7581.a	1.a	$1$	$12$	$12$	$60.535$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓			7581.2.a.bi	$1$	$1$	$-4$	$12$	$-2$	$12$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{4}-\beta _{5})q^{4}+\cdots$
7581.2.a.bj	$7581$	$2$	7581.a	1.a	$1$	$12$	$12$	$60.535$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓			7581.2.a.bj	$1$	$1$	$-3$	$-12$	$-2$	$12$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots$
7581.2.a.bk	$7581$	$2$	7581.a	1.a	$1$	$12$	$12$	$60.535$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓			7581.2.a.bk	$1$	$1$	$-1$	$-12$	$-2$	$12$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots$
7581.2.a.bl	$7581$	$2$	7581.a	1.a	$1$	$12$	$12$	$60.535$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓				399.2.bo.c	$1$	$1$	$0$	$-12$	$-12$	$12$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{4}+\cdots)q^{5}+\cdots$
7581.2.a.bm	$7581$	$2$	7581.a	1.a	$1$	$12$	$12$	$60.535$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓				399.2.bo.c	$1$	$1$	$0$	$12$	$-12$	$12$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{4}+\cdots)q^{5}+\cdots$
7581.2.a.bn	$7581$	$2$	7581.a	1.a	$1$	$12$	$12$	$60.535$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓			7581.2.a.bk	$1$	$0$	$1$	$12$	$-2$	$12$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots$
7581.2.a.bo	$7581$	$2$	7581.a	1.a	$1$	$12$	$12$	$60.535$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓			7581.2.a.bj	$1$	$0$	$3$	$12$	$-2$	$12$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots$
7581.2.a.bp	$7581$	$2$	7581.a	1.a	$1$	$12$	$12$	$60.535$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓			7581.2.a.bi	$1$	$0$	$4$	$-12$	$-2$	$12$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{4}-\beta _{5})q^{4}+\cdots$
7581.2.a.bq	$7581$	$2$	7581.a	1.a	$1$	$18$	$18$	$60.535$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓		✓		399.2.bo.e	$1$	$0$	$0$	$-18$	$0$	$-18$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{12}q^{5}+\cdots$
7581.2.a.br	$7581$	$2$	7581.a	1.a	$1$	$18$	$18$	$60.535$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓		✓		399.2.bo.d	$1$	$0$	$0$	$-18$	$12$	$18$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{9}+\cdots)q^{5}+\cdots$
7581.2.a.bs	$7581$	$2$	7581.a	1.a	$1$	$18$	$18$	$60.535$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓				399.2.bo.e	$1$	$0$	$0$	$18$	$0$	$-18$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{12}q^{5}+\cdots$
7581.2.a.bt	$7581$	$2$	7581.a	1.a	$1$	$18$	$18$	$60.535$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓		✓		399.2.bo.d	$1$	$0$	$0$	$18$	$12$	$18$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{9}+\cdots)q^{5}+\cdots$
7581.2.a.bu	$7581$	$2$	7581.a	1.a	$1$	$20$	$20$	$60.535$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	✓	✓		7581.2.a.bu	$1$	$1$	$-4$	$-20$	$-2$	$-20$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots$
7581.2.a.bv	$7581$	$2$	7581.a	1.a	$1$	$20$	$20$	$60.535$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	✓	✓		7581.2.a.bu	$1$	$0$	$4$	$20$	$-2$	$-20$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots$

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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.