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 66 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	5	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5200.2.a.a	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				2600.2.a.a	$1$	$0$	$0$	$-3$	$0$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-2q^{7}+6q^{9}+2q^{11}-q^{13}+\cdots$
5200.2.a.b	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				650.2.a.a	$1$	$0$	$0$	$-3$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+6q^{9}+3q^{11}+q^{13}-7q^{17}+\cdots$
5200.2.a.c	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				26.2.a.b	$1$	$1$	$0$	$-3$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{7}+6q^{9}+2q^{11}+q^{13}+\cdots$
5200.2.a.d	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				65.2.a.a	$1$	$1$	$0$	$-2$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{7}+q^{9}-2q^{11}+q^{13}+\cdots$
5200.2.a.e	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				130.2.a.a	$1$	$0$	$0$	$-2$	$0$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{7}+q^{9}+6q^{11}-q^{13}+\cdots$
5200.2.a.f	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				2600.2.a.b	$1$	$1$	$0$	$-2$	$0$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-3q^{7}+q^{9}-3q^{11}+q^{13}+\cdots$
5200.2.a.g	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				650.2.a.b	$1$	$0$	$0$	$-2$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{7}+q^{9}-3q^{11}-q^{13}+\cdots$
5200.2.a.h	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				2600.2.a.d	$1$	$1$	$0$	$-2$	$0$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+3q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
5200.2.a.i	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				650.2.a.f	$1$	$0$	$0$	$-2$	$0$	$5$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+5q^{7}+q^{9}+3q^{11}-q^{13}+\cdots$
5200.2.a.j	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				650.2.a.e	$1$	$1$	$0$	$-1$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{7}-2q^{9}-q^{11}+q^{13}+\cdots$
5200.2.a.k	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				325.2.a.a	$1$	$1$	$0$	$-1$	$0$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}-2q^{9}-2q^{11}-q^{13}+\cdots$
5200.2.a.l	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				2600.2.a.f	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}+2q^{11}-q^{13}+2q^{17}+\cdots$
5200.2.a.m	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				1300.2.a.b	$1$	$1$	$0$	$-1$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}-2q^{9}+2q^{11}+q^{13}+\cdots$
5200.2.a.n	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				325.2.a.b	$1$	$0$	$0$	$-1$	$0$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}-2q^{9}+6q^{11}+q^{13}+\cdots$
5200.2.a.o	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				520.2.d.a	$1$	$1$	$0$	$0$	$0$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}-3q^{9}+2q^{11}+q^{13}+4q^{17}+\cdots$
5200.2.a.p	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				1300.2.a.c	$1$	$0$	$0$	$0$	$0$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{7}-3q^{9}-3q^{11}-q^{13}+q^{17}+\cdots$
5200.2.a.q	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				52.2.a.a	$1$	$1$	$0$	$0$	$0$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-3q^{9}+2q^{11}+q^{13}-6q^{17}+\cdots$
5200.2.a.r	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				130.2.a.b	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{9}-q^{13}-2q^{17}+8q^{19}-4q^{23}+\cdots$
5200.2.a.s	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				520.2.a.a	$1$	$0$	$0$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{9}+4q^{11}+q^{13}+6q^{17}-4q^{19}+\cdots$
5200.2.a.t	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				1300.2.a.c	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{7}-3q^{9}-3q^{11}+q^{13}-q^{17}+\cdots$
5200.2.a.u	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				520.2.d.a	$1$	$0$	$0$	$0$	$0$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}-3q^{9}+2q^{11}-q^{13}-4q^{17}+\cdots$
5200.2.a.v	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				325.2.a.b	$1$	$0$	$0$	$1$	$0$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}-2q^{9}+6q^{11}-q^{13}+\cdots$
5200.2.a.w	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				1300.2.a.b	$1$	$1$	$0$	$1$	$0$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}-2q^{9}+2q^{11}-q^{13}+\cdots$
5200.2.a.x	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				26.2.a.a	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}-6q^{11}-q^{13}+\cdots$
5200.2.a.y	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				2600.2.a.f	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{9}+2q^{11}+q^{13}-2q^{17}+\cdots$
5200.2.a.z	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				325.2.a.a	$1$	$1$	$0$	$1$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}-2q^{9}-2q^{11}+q^{13}+\cdots$
5200.2.a.ba	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				650.2.a.e	$1$	$1$	$0$	$1$	$0$	$4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{7}-2q^{9}-q^{11}-q^{13}+\cdots$
5200.2.a.bb	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				104.2.a.a	$1$	$0$	$0$	$1$	$0$	$5$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+5q^{7}-2q^{9}+2q^{11}+q^{13}+\cdots$
5200.2.a.bc	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				650.2.a.f	$1$	$0$	$0$	$2$	$0$	$-5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-5q^{7}+q^{9}+3q^{11}+q^{13}+\cdots$
5200.2.a.bd	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				130.2.a.c	$1$	$1$	$0$	$2$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-4q^{7}+q^{9}+2q^{11}+q^{13}+\cdots$
5200.2.a.be	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				2600.2.a.d	$1$	$1$	$0$	$2$	$0$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-3q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
5200.2.a.bf	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				520.2.a.b	$1$	$1$	$0$	$2$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}-2q^{11}-q^{13}-2q^{17}+\cdots$
5200.2.a.bg	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				650.2.a.b	$1$	$0$	$0$	$2$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{7}+q^{9}-3q^{11}+q^{13}+\cdots$
5200.2.a.bh	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				260.2.a.a	$1$	$1$	$0$	$2$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{7}+q^{9}-4q^{11}+q^{13}+\cdots$
5200.2.a.bi	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				2600.2.a.b	$1$	$1$	$0$	$2$	$0$	$3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+3q^{7}+q^{9}-3q^{11}-q^{13}+\cdots$
5200.2.a.bj	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				650.2.a.a	$1$	$0$	$0$	$3$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+6q^{9}+3q^{11}-q^{13}+7q^{17}+\cdots$
5200.2.a.bk	$5200$	$2$	5200.a	1.a	$1$	$1$	$1$	$41.522$	$\Q$	None	✓				2600.2.a.a	$1$	$0$	$0$	$3$	$0$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+2q^{7}+6q^{9}+2q^{11}+q^{13}+\cdots$
5200.2.a.bl	$5200$	$2$	5200.a	1.a	$1$	$2$	$2$	$41.522$	$\Q(\sqrt{2}) $	None	✓				520.2.a.c	$1$	$0$	$0$	$-4$	$0$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{3}-2q^{7}+(3-4\beta )q^{9}+\cdots$
5200.2.a.bm	$5200$	$2$	5200.a	1.a	$1$	$2$	$2$	$41.522$	$\Q(\sqrt{73}) $	None	✓				2600.2.a.n	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}+\beta q^{11}-q^{13}+\beta q^{17}+\cdots$
5200.2.a.bn	$5200$	$2$	5200.a	1.a	$1$	$2$	$2$	$41.522$	$\Q(\sqrt{3}) $	None	✓				520.2.a.e	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+2\beta q^{7}+(1-2\beta )q^{9}+\cdots$
5200.2.a.bo	$5200$	$2$	5200.a	1.a	$1$	$2$	$2$	$41.522$	$\Q(\sqrt{3}) $	None	✓				520.2.a.d	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-2\beta q^{7}+(1-2\beta )q^{9}+\cdots$
5200.2.a.bp	$5200$	$2$	5200.a	1.a	$1$	$2$	$2$	$41.522$	$\Q(\sqrt{33}) $	None	✓				1300.2.a.g	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1-\beta )q^{7}+(5+\beta )q^{9}+(1+\beta )q^{11}+\cdots$
5200.2.a.bq	$5200$	$2$	5200.a	1.a	$1$	$2$	$2$	$41.522$	$\Q(\sqrt{10}) $	None	✓				2600.2.a.r	$1$	$0$	$0$	$0$	$0$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{7}-3q^{9}+(-3-\beta )q^{11}+\cdots$
5200.2.a.br	$5200$	$2$	5200.a	1.a	$1$	$2$	$2$	$41.522$	$\Q(\sqrt{2}) $	None	✓				325.2.a.f	$1$	$1$	$0$	$0$	$0$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{3}+(-1-\beta )q^{7}+5q^{9}+(-5+\cdots)q^{11}+\cdots$
5200.2.a.bs	$5200$	$2$	5200.a	1.a	$1$	$2$	$2$	$41.522$	$\Q(\sqrt{10}) $	None	✓				2600.2.a.r	$1$	$0$	$0$	$0$	$0$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta )q^{7}-3q^{9}+(-3+\beta )q^{11}+\cdots$
5200.2.a.bt	$5200$	$2$	5200.a	1.a	$1$	$2$	$2$	$41.522$	$\Q(\sqrt{2}) $	None	✓				325.2.a.f	$1$	$1$	$0$	$0$	$0$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{3}+(1-\beta )q^{7}+5q^{9}+(-5+\beta )q^{11}+\cdots$
5200.2.a.bu	$5200$	$2$	5200.a	1.a	$1$	$2$	$2$	$41.522$	$\Q(\sqrt{2}) $	None	✓				65.2.a.b	$1$	$1$	$0$	$0$	$0$	$4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2-2\beta )q^{7}-q^{9}+(-2+\beta )q^{11}+\cdots$
5200.2.a.bv	$5200$	$2$	5200.a	1.a	$1$	$2$	$2$	$41.522$	$\Q(\sqrt{6}) $	None	✓				520.2.a.f	$1$	$0$	$0$	$0$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+2q^{7}+3q^{9}+(2-\beta )q^{11}+\cdots$
5200.2.a.bw	$5200$	$2$	5200.a	1.a	$1$	$2$	$2$	$41.522$	$\Q(\sqrt{17}) $	None	✓				104.2.a.b	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{7}+(1+\beta )q^{9}+2\beta q^{11}+\cdots$
5200.2.a.bx	$5200$	$2$	5200.a	1.a	$1$	$2$	$2$	$41.522$	$\Q(\sqrt{33}) $	None	✓				1300.2.a.g	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1+\beta )q^{7}+(5+\beta )q^{9}+(1+\cdots)q^{11}+\cdots$

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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.