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 63 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	3	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8712.2.a.a	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				264.2.a.d	$1$	$1$	$0$	$0$	$-4$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+2q^{7}-6q^{17}-4q^{19}+6q^{23}+\cdots$
8712.2.a.b	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				968.2.a.b	$1$	$1$	$0$	$0$	$-3$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-4q^{7}-3q^{13}+3q^{17}-4q^{19}+\cdots$
8712.2.a.c	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				968.2.a.b	$1$	$0$	$0$	$0$	$-3$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+4q^{7}+3q^{13}-3q^{17}+4q^{19}+\cdots$
8712.2.a.d	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓	✓			8712.2.a.d	$1$	$0$	$0$	$0$	$-2$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{7}-2q^{13}-2q^{17}-4q^{19}+\cdots$
8712.2.a.e	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				2904.2.a.f	$1$	$0$	$0$	$0$	$-2$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{7}-6q^{17}+6q^{19}+4q^{23}+\cdots$
8712.2.a.f	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				264.2.a.a	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{13}+6q^{17}-4q^{23}-q^{25}+\cdots$
8712.2.a.g	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				2904.2.a.f	$1$	$1$	$0$	$0$	$-2$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{7}+6q^{17}-6q^{19}+4q^{23}+\cdots$
8712.2.a.h	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓	✓			8712.2.a.d	$1$	$1$	$0$	$0$	$-2$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{7}+2q^{13}+2q^{17}+4q^{19}+\cdots$
8712.2.a.i	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				968.2.a.d	$1$	$1$	$0$	$0$	$-1$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}-4q^{13}+4q^{17}+4q^{19}+\cdots$
8712.2.a.j	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				968.2.a.d	$1$	$0$	$0$	$0$	$-1$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}+4q^{13}-4q^{17}-4q^{19}+\cdots$
8712.2.a.k	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				264.2.a.c	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-2q^{17}-8q^{19}+2q^{23}-5q^{25}+\cdots$
8712.2.a.l	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				2904.2.a.m	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+6q^{13}-4q^{17}-q^{19}+2q^{23}+\cdots$
8712.2.a.m	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				2904.2.a.m	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-6q^{13}+4q^{17}+q^{19}+2q^{23}+\cdots$
8712.2.a.n	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				792.2.a.c	$1$	$1$	$0$	$0$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+6q^{13}-6q^{17}+2q^{19}-8q^{23}+\cdots$
8712.2.a.o	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				792.2.a.c	$1$	$0$	$0$	$0$	$0$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+6q^{13}+6q^{17}+2q^{19}+8q^{23}+\cdots$
8712.2.a.p	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				2904.2.a.d	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{13}-3q^{17}-4q^{23}-4q^{25}+\cdots$
8712.2.a.q	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				2904.2.a.d	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{13}+3q^{17}-4q^{23}-4q^{25}+\cdots$
8712.2.a.r	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				264.2.a.b	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}-6q^{13}+6q^{17}+8q^{19}+\cdots$
8712.2.a.s	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓	✓			8712.2.a.d	$1$	$1$	$0$	$0$	$2$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-2q^{7}-2q^{13}+2q^{17}-4q^{19}+\cdots$
8712.2.a.t	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				2904.2.a.j	$1$	$0$	$0$	$0$	$2$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-2q^{7}+4q^{13}+2q^{17}+2q^{19}+\cdots$
8712.2.a.u	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				24.2.a.a	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2q^{13}+2q^{17}+4q^{19}+8q^{23}+\cdots$
8712.2.a.v	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				2904.2.a.j	$1$	$1$	$0$	$0$	$2$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2q^{7}-4q^{13}-2q^{17}-2q^{19}+\cdots$
8712.2.a.w	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓	✓			8712.2.a.d	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2q^{7}+2q^{13}-2q^{17}+4q^{19}+\cdots$
8712.2.a.x	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				88.2.a.a	$1$	$1$	$0$	$0$	$3$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+2q^{7}-6q^{17}-4q^{19}-q^{23}+\cdots$
8712.2.a.y	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				2904.2.a.a	$1$	$1$	$0$	$0$	$4$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-4q^{7}+6q^{13}-6q^{17}-6q^{19}+\cdots$
8712.2.a.z	$8712$	$2$	8712.a	1.a	$1$	$1$	$1$	$69.566$	$\Q$	None	✓				2904.2.a.a	$1$	$0$	$0$	$0$	$4$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+4q^{7}-6q^{13}+6q^{17}+6q^{19}+\cdots$
8712.2.a.ba	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{5}) $	None	✓				264.2.q.b	$1$	$1$	$0$	$0$	$-3$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+(-3+2\beta )q^{7}+(1-2\beta )q^{13}+\cdots$
8712.2.a.bb	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{17}) $	None	✓				88.2.a.b	$1$	$0$	$0$	$0$	$-3$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+(2-2\beta )q^{7}+2\beta q^{13}+\cdots$
8712.2.a.bc	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{5}) $	None	✓				264.2.q.b	$1$	$1$	$0$	$0$	$-3$	$4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+(3-2\beta )q^{7}+(-1+2\beta )q^{13}+\cdots$
8712.2.a.bd	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{3}) $	None	✓				2904.2.a.x	$1$	$0$	$0$	$0$	$-2$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+(-2-\beta )q^{13}+(2-\beta )q^{17}+\cdots$
8712.2.a.be	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{3}) $	None	✓				2904.2.a.x	$1$	$1$	$0$	$0$	$-2$	$4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}+(2+\beta )q^{13}+(-2+\beta )q^{17}+\cdots$
8712.2.a.bf	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{5}) $	None	✓				264.2.q.a	$1$	$1$	$0$	$0$	$-1$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-3\beta )q^{5}-3\beta q^{7}+(-2+2\beta )q^{13}+\cdots$
8712.2.a.bg	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{5}) $	None	✓				264.2.q.a	$1$	$1$	$0$	$0$	$-1$	$3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-3\beta )q^{5}+3\beta q^{7}+(2-2\beta )q^{13}+\cdots$
8712.2.a.bh	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{2}) $	None	✓				792.2.a.i	$1$	$0$	$0$	$0$	$0$	$-4$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-2+\beta )q^{7}+(-2-\beta )q^{13}+\cdots$
8712.2.a.bi	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{2}) $	None	✓				792.2.a.i	$1$	$1$	$0$	$0$	$0$	$-4$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-2-\beta )q^{7}+(-2+\beta )q^{13}+\cdots$
8712.2.a.bj	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{5}) $	None	✓				968.2.a.f	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{5}+(-1-\beta )q^{7}+(-4+\beta )q^{13}+\cdots$
8712.2.a.bk	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{5}) $	None	✓				968.2.a.f	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{5}+(1+\beta )q^{7}+(4-\beta )q^{13}-q^{17}+\cdots$
8712.2.a.bl	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{33}) $	None	✓				2904.2.a.t	$1$	$0$	$0$	$0$	$1$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-1+\beta )q^{7}+(-2+\beta )q^{13}+\cdots$
8712.2.a.bm	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{5}) $	None	✓				88.2.i.a	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-1+\beta )q^{7}+(4-3\beta )q^{13}+\cdots$
8712.2.a.bn	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{5}) $	None	✓				264.2.q.d	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(1-2\beta )q^{7}+(-3+2\beta )q^{13}+\cdots$
8712.2.a.bo	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{5}) $	None	✓				264.2.q.d	$1$	$1$	$0$	$0$	$1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-1+2\beta )q^{7}+(3-2\beta )q^{13}+\cdots$
8712.2.a.bp	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{5}) $	None	✓				88.2.i.a	$1$	$1$	$0$	$0$	$1$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(1-\beta )q^{7}+(-4+3\beta )q^{13}+\cdots$
8712.2.a.bq	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{33}) $	None	✓				2904.2.a.t	$1$	$1$	$0$	$0$	$1$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(1-\beta )q^{7}+(2-\beta )q^{13}+(-4+\cdots)q^{17}+\cdots$
8712.2.a.br	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{3}) $	None	✓				968.2.a.k	$1$	$1$	$0$	$0$	$4$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}+(-1-\beta )q^{7}+(-1-2\beta )q^{13}+\cdots$
8712.2.a.bs	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{3}) $	None	✓				968.2.a.k	$1$	$0$	$0$	$0$	$4$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}+(1+\beta )q^{7}+(1+2\beta )q^{13}+\cdots$
8712.2.a.bt	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{5}) $	None	✓				264.2.q.c	$1$	$0$	$0$	$0$	$5$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(3-\beta )q^{5}+(-1-2\beta )q^{7}+(-1+2\beta )q^{13}+\cdots$
8712.2.a.bu	$8712$	$2$	8712.a	1.a	$1$	$2$	$2$	$69.566$	$\Q(\sqrt{5}) $	None	✓				264.2.q.c	$1$	$0$	$0$	$0$	$5$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(3-\beta )q^{5}+(1+2\beta )q^{7}+(1-2\beta )q^{13}+\cdots$
8712.2.a.bv	$8712$	$2$	8712.a	1.a	$1$	$3$	$3$	$69.566$	3.3.1436.1	None	✓	✓			8712.2.a.bv	$1$	$1$	$0$	$0$	$0$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}-\beta _{2}q^{7}+(1+\beta _{2})q^{13}+(-2+\cdots)q^{17}+\cdots$
8712.2.a.bw	$8712$	$2$	8712.a	1.a	$1$	$3$	$3$	$69.566$	3.3.1436.1	None	✓	✓			8712.2.a.bv	$1$	$0$	$0$	$0$	$0$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}-\beta _{2}q^{7}+(1+\beta _{2})q^{13}+(2+\cdots)q^{17}+\cdots$
8712.2.a.bx	$8712$	$2$	8712.a	1.a	$1$	$3$	$3$	$69.566$	3.3.1436.1	None	✓	✓			8712.2.a.bv	$1$	$1$	$0$	$0$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+\beta _{2}q^{7}+(-1-\beta _{2})q^{13}+\cdots$

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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.