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 56 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	13	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9386.2.a.a	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	$\Q$	None	✓				494.2.f.d	$1$	$1$	$-1$	$-3$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}+q^{4}+3q^{6}-q^{8}+6q^{9}+\cdots$
9386.2.a.b	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	$\Q$	None	✓				494.2.f.c	$1$	$1$	$-1$	$-1$	$4$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+4q^{5}+q^{6}+2q^{7}+\cdots$
9386.2.a.c	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	$\Q$	None	✓				494.2.a.d	$1$	$0$	$-1$	$1$	$-1$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-3q^{7}+\cdots$
9386.2.a.d	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	$\Q$	None	✓				494.2.f.b	$1$	$1$	$-1$	$2$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots$
9386.2.a.e	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	$\Q$	None	✓				494.2.f.a	$1$	$1$	$-1$	$3$	$-4$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-4q^{5}-3q^{6}-2q^{7}+\cdots$
9386.2.a.f	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	$\Q$	None	✓				26.2.a.b	$1$	$1$	$-1$	$3$	$-1$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots$
9386.2.a.g	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	$\Q$	None	✓				494.2.f.a	$1$	$2$	$1$	$-3$	$-4$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}-4q^{5}-3q^{6}-2q^{7}+\cdots$
9386.2.a.h	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	$\Q$	None	✓				494.2.a.c	$1$	$0$	$1$	$-3$	$-3$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}-3q^{5}-3q^{6}+3q^{7}+\cdots$
9386.2.a.i	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	$\Q$	None	✓				494.2.f.b	$1$	$0$	$1$	$-2$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots$
9386.2.a.j	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	$\Q$	None	✓				26.2.a.a	$1$	$1$	$1$	$-1$	$-3$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots$
9386.2.a.k	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	$\Q$	None	✓				494.2.a.b	$1$	$0$	$1$	$0$	$2$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+4q^{7}+q^{8}-3q^{9}+\cdots$
9386.2.a.l	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	$\Q$	None	✓				494.2.a.a	$1$	$0$	$1$	$1$	$1$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
9386.2.a.m	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	$\Q$	None	✓				494.2.f.c	$1$	$0$	$1$	$1$	$4$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+2q^{7}+\cdots$
9386.2.a.n	$9386$	$2$	9386.a	1.a	$1$	$1$	$1$	$74.948$	$\Q$	None	✓				494.2.f.d	$1$	$0$	$1$	$3$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+3q^{6}+q^{8}+6q^{9}+\cdots$
9386.2.a.o	$9386$	$2$	9386.a	1.a	$1$	$2$	$2$	$74.948$	$\Q(\sqrt{6}) $	None	✓				494.2.f.g	$1$	$1$	$-2$	$-2$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta q^{5}+q^{6}+2\beta q^{7}+\cdots$
9386.2.a.p	$9386$	$2$	9386.a	1.a	$1$	$2$	$2$	$74.948$	$\Q(\sqrt{3}) $	None	✓				494.2.f.e	$1$	$1$	$-2$	$0$	$-2$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}+(-1-\beta )q^{5}-\beta q^{6}+\cdots$
9386.2.a.q	$9386$	$2$	9386.a	1.a	$1$	$2$	$2$	$74.948$	$\Q(\sqrt{6}) $	None	✓				494.2.f.f	$1$	$0$	$-2$	$2$	$0$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}+2q^{7}+\cdots$
9386.2.a.r	$9386$	$2$	9386.a	1.a	$1$	$2$	$2$	$74.948$	$\Q(\sqrt{6}) $	None	✓				494.2.f.f	$1$	$1$	$2$	$-2$	$0$	$4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}+2q^{7}+\cdots$
9386.2.a.s	$9386$	$2$	9386.a	1.a	$1$	$2$	$2$	$74.948$	$\Q(\sqrt{3}) $	None	✓				494.2.f.e	$1$	$0$	$2$	$0$	$-2$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+(-1+\beta )q^{5}+\beta q^{6}+\cdots$
9386.2.a.t	$9386$	$2$	9386.a	1.a	$1$	$2$	$2$	$74.948$	$\Q(\sqrt{6}) $	None	✓				494.2.f.g	$1$	$0$	$2$	$2$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-\beta q^{5}+q^{6}+2\beta q^{7}+\cdots$
9386.2.a.u	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	$\Q(\zeta_{14})^+$	None	✓				494.2.a.g	$1$	$1$	$-3$	$-5$	$5$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-2-\beta _{2})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
9386.2.a.v	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	3.3.316.1	None	✓				494.2.f.h	$1$	$1$	$-3$	$-2$	$2$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
9386.2.a.w	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	3.3.148.1	None	✓				494.2.f.i	$1$	$0$	$-3$	$-1$	$-2$	$-4$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{2}q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots$
9386.2.a.x	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	$\Q(\zeta_{18})^+$	None	✓				494.2.x.a	$1$	$0$	$-3$	$0$	$-6$	$3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(-2-\beta _{2})q^{5}+\cdots$
9386.2.a.y	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	$\Q(\zeta_{18})^+$	None	✓	✓			9386.2.a.y	$1$	$1$	$-3$	$3$	$-3$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1-\beta _{2})q^{5}+\cdots$
9386.2.a.z	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	$\Q(\zeta_{18})^+$	None	✓	✓			9386.2.a.y	$1$	$1$	$3$	$-3$	$-3$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{2})q^{5}+\cdots$
9386.2.a.ba	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	$\Q(\zeta_{18})^+$	None	✓				494.2.x.a	$1$	$1$	$3$	$0$	$-6$	$3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+(-2-\beta _{2})q^{5}+\cdots$
9386.2.a.bb	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	3.3.148.1	None	✓				494.2.f.i	$1$	$1$	$3$	$1$	$-2$	$-4$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{2}q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots$
9386.2.a.bc	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	3.3.361.1	None	✓				494.2.a.f	$1$	$1$	$3$	$1$	$1$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+\beta _{1}q^{5}+\cdots$
9386.2.a.bd	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	3.3.316.1	None	✓				494.2.f.h	$1$	$0$	$3$	$2$	$2$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots$
9386.2.a.be	$9386$	$2$	9386.a	1.a	$1$	$3$	$3$	$74.948$	$\Q(\zeta_{18})^+$	None	✓				494.2.a.e	$1$	$0$	$3$	$3$	$3$	$-6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+2\beta _{1}-\beta _{2})q^{3}+q^{4}+(1+\cdots)q^{5}+\cdots$
9386.2.a.bf	$9386$	$2$	9386.a	1.a	$1$	$4$	$4$	$74.948$	4.4.16609.1	None	✓				494.2.a.h	$1$	$0$	$-4$	$-2$	$2$	$7$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{2}q^{3}+q^{4}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
9386.2.a.bg	$9386$	$2$	9386.a	1.a	$1$	$4$	$4$	$74.948$	4.4.11344.1	None	✓				494.2.f.j	$1$	$0$	$-4$	$0$	$-2$	$-4$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{2}q^{6}+\cdots$
9386.2.a.bh	$9386$	$2$	9386.a	1.a	$1$	$4$	$4$	$74.948$	4.4.11344.1	None	✓				494.2.f.j	$1$	$1$	$4$	$0$	$-2$	$-4$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{2}q^{6}+\cdots$
9386.2.a.bi	$9386$	$2$	9386.a	1.a	$1$	$6$	$6$	$74.948$	6.6.980125.1	None	✓	✓			9386.2.a.bi	$1$	$1$	$-6$	$-2$	$2$	$-6$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1}-\beta _{4})q^{3}+q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
9386.2.a.bj	$9386$	$2$	9386.a	1.a	$1$	$6$	$6$	$74.948$	6.6.2235125.1	None	✓	✓			9386.2.a.bj	$1$	$1$	$-6$	$0$	$0$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{3}q^{3}+q^{4}+(\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots$
9386.2.a.bk	$9386$	$2$	9386.a	1.a	$1$	$6$	$6$	$74.948$	6.6.784399964.1	None	✓	✓			9386.2.a.bk	$1$	$0$	$-6$	$3$	$-1$	$6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{5}q^{5}-\beta _{1}q^{6}+\cdots$
9386.2.a.bl	$9386$	$2$	9386.a	1.a	$1$	$6$	$6$	$74.948$	6.6.784399964.1	None	✓	✓			9386.2.a.bk	$1$	$0$	$6$	$-3$	$-1$	$6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{5}q^{5}-\beta _{1}q^{6}+\cdots$
9386.2.a.bm	$9386$	$2$	9386.a	1.a	$1$	$6$	$6$	$74.948$	6.6.2235125.1	None	✓	✓			9386.2.a.bj	$1$	$1$	$6$	$0$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{3}q^{3}+q^{4}+(\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots$
9386.2.a.bn	$9386$	$2$	9386.a	1.a	$1$	$6$	$6$	$74.948$	6.6.980125.1	None	✓	✓			9386.2.a.bi	$1$	$1$	$6$	$2$	$2$	$-6$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1}+\beta _{4})q^{3}+q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
9386.2.a.bo	$9386$	$2$	9386.a	1.a	$1$	$9$	$9$	$74.948$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓				494.2.x.b	$1$	$0$	$-9$	$3$	$-3$	$-6$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{8}q^{5}-\beta _{1}q^{6}+\cdots$
9386.2.a.bp	$9386$	$2$	9386.a	1.a	$1$	$9$	$9$	$74.948$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓				494.2.x.b	$1$	$1$	$9$	$-3$	$-3$	$-6$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{8}q^{5}-\beta _{1}q^{6}+\cdots$
9386.2.a.bq	$9386$	$2$	9386.a	1.a	$1$	$12$	$12$	$74.948$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓			9386.2.a.bq	$1$	$0$	$-12$	$-2$	$6$	$10$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(1+\beta _{7})q^{5}+\beta _{1}q^{6}+\cdots$
9386.2.a.br	$9386$	$2$	9386.a	1.a	$1$	$12$	$12$	$74.948$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓			9386.2.a.br	$1$	$0$	$-12$	$0$	$4$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{8}q^{5}+\beta _{1}q^{6}+\cdots$
9386.2.a.bs	$9386$	$2$	9386.a	1.a	$1$	$12$	$12$	$74.948$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓			9386.2.a.bs	$1$	$1$	$-12$	$2$	$-2$	$-10$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{1}q^{6}+\cdots$
9386.2.a.bt	$9386$	$2$	9386.a	1.a	$1$	$12$	$12$	$74.948$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		9386.2.a.bs	$1$	$1$	$12$	$-2$	$-2$	$-10$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{1}q^{6}+\cdots$
9386.2.a.bu	$9386$	$2$	9386.a	1.a	$1$	$12$	$12$	$74.948$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓			9386.2.a.br	$1$	$0$	$12$	$0$	$4$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{8}q^{5}+\beta _{1}q^{6}+\cdots$
9386.2.a.bv	$9386$	$2$	9386.a	1.a	$1$	$12$	$12$	$74.948$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓			9386.2.a.bq	$1$	$0$	$12$	$2$	$6$	$10$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{7})q^{5}+\beta _{1}q^{6}+\cdots$
9386.2.a.bw	$9386$	$2$	9386.a	1.a	$1$	$15$	$15$	$74.948$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓		✓		494.2.x.d	$1$	$1$	$-15$	$-3$	$3$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots$
9386.2.a.bx	$9386$	$2$	9386.a	1.a	$1$	$15$	$15$	$74.948$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓				494.2.x.c	$1$	$0$	$-15$	$3$	$-9$	$-9$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{6})q^{5}+\cdots$

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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.