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 60 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	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4851.2.a.a	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				77.2.a.c	$1$	$1$	$-1$	$0$	$-2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{5}+3q^{8}+2q^{10}+\cdots$
4851.2.a.b	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				33.2.a.a	$1$	$1$	$-1$	$0$	$-2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{5}+3q^{8}+2q^{10}+\cdots$
4851.2.a.c	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				1617.2.a.f	$1$	$0$	$-1$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}+q^{11}-4q^{13}+\cdots$
4851.2.a.d	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				231.2.i.a	$1$	$0$	$-1$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}+q^{11}-4q^{13}+\cdots$
4851.2.a.e	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				231.2.i.a	$1$	$1$	$-1$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}+q^{11}+4q^{13}+\cdots$
4851.2.a.f	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				1617.2.a.f	$1$	$0$	$-1$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}+q^{11}+4q^{13}+\cdots$
4851.2.a.g	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				99.2.a.a	$1$	$0$	$-1$	$0$	$4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+4q^{5}+3q^{8}-4q^{10}+\cdots$
4851.2.a.h	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				693.2.i.c	$1$	$1$	$0$	$0$	$-4$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-4q^{5}-q^{11}+5q^{13}+4q^{16}+\cdots$
4851.2.a.i	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				693.2.i.c	$1$	$1$	$0$	$0$	$-4$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-4q^{5}+q^{11}-5q^{13}+4q^{16}+\cdots$
4851.2.a.j	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				77.2.a.a	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{5}+q^{11}+4q^{13}+4q^{16}+\cdots$
4851.2.a.k	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				77.2.a.b	$1$	$0$	$0$	$0$	$3$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+3q^{5}+q^{11}+4q^{13}+4q^{16}+\cdots$
4851.2.a.l	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				693.2.i.c	$1$	$0$	$0$	$0$	$4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+4q^{5}-q^{11}-5q^{13}+4q^{16}+\cdots$
4851.2.a.m	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				693.2.i.c	$1$	$0$	$0$	$0$	$4$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+4q^{5}+q^{11}+5q^{13}+4q^{16}+\cdots$
4851.2.a.n	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				231.2.i.b	$1$	$1$	$1$	$0$	$-4$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-4q^{5}-3q^{8}-4q^{10}+\cdots$
4851.2.a.o	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				99.2.a.a	$1$	$1$	$1$	$0$	$-4$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-4q^{5}-3q^{8}-4q^{10}+\cdots$
4851.2.a.p	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				231.2.a.a	$1$	$0$	$1$	$0$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-2q^{5}-3q^{8}-2q^{10}+\cdots$
4851.2.a.q	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				231.2.i.b	$1$	$0$	$1$	$0$	$4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+4q^{5}-3q^{8}+4q^{10}+\cdots$
4851.2.a.r	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				231.2.i.c	$1$	$1$	$2$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{11}-5q^{13}-4q^{16}+\cdots$
4851.2.a.s	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				231.2.i.c	$1$	$0$	$2$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{11}+5q^{13}-4q^{16}+\cdots$
4851.2.a.t	$4851$	$2$	4851.a	1.a	$1$	$1$	$1$	$38.735$	$\Q$	None	✓				11.2.a.a	$1$	$1$	$2$	$0$	$1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{5}+2q^{10}-q^{11}+\cdots$
4851.2.a.u	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	$\Q(\sqrt{5}) $	None	✓				693.2.a.e	$1$	$1$	$-3$	$0$	$2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+3\beta q^{4}+q^{5}+(-1+\cdots)q^{8}+\cdots$
4851.2.a.v	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	$\Q(\sqrt{2}) $	None	✓	✓			4851.2.a.v	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+\beta q^{5}+3q^{8}-\beta q^{10}+\cdots$
4851.2.a.w	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	$\Q(\sqrt{5}) $	None	✓				231.2.a.c	$1$	$1$	$-1$	$0$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-1+2\beta )q^{8}+\cdots$
4851.2.a.x	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	$\Q(\sqrt{13}) $	None	✓				693.2.a.g	$1$	$0$	$-1$	$0$	$2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1+\beta )q^{4}+q^{5}-3q^{8}-\beta q^{10}+\cdots$
4851.2.a.y	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	$\Q(\sqrt{5}) $	None	✓				77.2.a.d	$1$	$0$	$0$	$0$	$-4$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+3q^{4}-2q^{5}-\beta q^{8}+2\beta q^{10}+\cdots$
4851.2.a.z	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	$\Q(\sqrt{13}) $	None	✓				693.2.a.g	$1$	$1$	$1$	$0$	$-2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}-q^{5}+3q^{8}-\beta q^{10}+\cdots$
4851.2.a.ba	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	$\Q(\sqrt{21}) $	None	✓				231.2.a.b	$1$	$0$	$1$	$0$	$6$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(3+\beta )q^{4}+3q^{5}+(5+2\beta )q^{8}+\cdots$
4851.2.a.bb	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	$\Q(\sqrt{2}) $	None	✓	✓			4851.2.a.v	$2$	$0$	$2$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-\beta q^{5}-3q^{8}-\beta q^{10}+\cdots$
4851.2.a.bc	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	$\Q(\sqrt{2}) $	None	✓				539.2.a.e	$2$	$1$	$2$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-\beta q^{5}-3q^{8}-\beta q^{10}+\cdots$
4851.2.a.bd	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	$\Q(\sqrt{2}) $	None	✓				231.2.i.d	$1$	$1$	$2$	$0$	$-4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2q^{5}+(3+\cdots)q^{8}+\cdots$
4851.2.a.be	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	$\Q(\sqrt{2}) $	None	✓				231.2.i.d	$1$	$0$	$2$	$0$	$4$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2q^{5}+(3+\cdots)q^{8}+\cdots$
4851.2.a.bf	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	$\Q(\sqrt{5}) $	None	✓				693.2.a.e	$1$	$0$	$3$	$0$	$-2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}-q^{5}+(1+4\beta )q^{8}+\cdots$
4851.2.a.bg	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	$\Q(\sqrt{5}) $	None	✓				1617.2.a.k	$1$	$0$	$3$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}+(1-2\beta )q^{5}+(1+\cdots)q^{8}+\cdots$
4851.2.a.bh	$4851$	$2$	4851.a	1.a	$1$	$2$	$2$	$38.735$	$\Q(\sqrt{5}) $	None	✓				1617.2.a.k	$1$	$0$	$3$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}+(-1+2\beta )q^{5}+\cdots$
4851.2.a.bi	$4851$	$2$	4851.a	1.a	$1$	$3$	$3$	$38.735$	3.3.229.1	None	✓				231.2.a.e	$1$	$0$	$-2$	$0$	$4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(2+\beta _{1})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
4851.2.a.bj	$4851$	$2$	4851.a	1.a	$1$	$3$	$3$	$38.735$	$\Q(\zeta_{18})^+$	None	✓				77.2.e.a	$1$	$0$	$0$	$0$	$-6$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-2-\beta _{2})q^{5}+(-1+\cdots)q^{8}+\cdots$
4851.2.a.bk	$4851$	$2$	4851.a	1.a	$1$	$3$	$3$	$38.735$	$\Q(\zeta_{18})^+$	None	✓				77.2.e.a	$1$	$1$	$0$	$0$	$6$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(2+\beta _{2})q^{5}+(-1+\cdots)q^{8}+\cdots$
4851.2.a.bl	$4851$	$2$	4851.a	1.a	$1$	$3$	$3$	$38.735$	3.3.229.1	None	✓				1617.2.a.q	$1$	$1$	$0$	$0$	$-4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots$
4851.2.a.bm	$4851$	$2$	4851.a	1.a	$1$	$3$	$3$	$38.735$	3.3.229.1	None	✓				1617.2.a.q	$1$	$1$	$0$	$0$	$4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{1}-\beta _{2})q^{5}+\cdots$
4851.2.a.bn	$4851$	$2$	4851.a	1.a	$1$	$3$	$3$	$38.735$	3.3.257.1	None	✓				77.2.e.b	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
4851.2.a.bo	$4851$	$2$	4851.a	1.a	$1$	$3$	$3$	$38.735$	3.3.257.1	None	✓				77.2.e.b	$1$	$1$	$0$	$0$	$2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
4851.2.a.bp	$4851$	$2$	4851.a	1.a	$1$	$3$	$3$	$38.735$	3.3.837.1	None	✓				231.2.a.d	$1$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
4851.2.a.bq	$4851$	$2$	4851.a	1.a	$1$	$4$	$4$	$38.735$	4.4.725.1	None	✓	✓			4851.2.a.bq	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{1})q^{4}+\beta _{2}q^{5}+(-1+\cdots)q^{8}+\cdots$
4851.2.a.br	$4851$	$2$	4851.a	1.a	$1$	$4$	$4$	$38.735$	4.4.2624.1	None	✓				1617.2.a.w	$1$	$1$	$-2$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+\beta _{2}q^{4}+(1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
4851.2.a.bs	$4851$	$2$	4851.a	1.a	$1$	$4$	$4$	$38.735$	4.4.2624.1	None	✓				1617.2.a.w	$1$	$1$	$-2$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
4851.2.a.bt	$4851$	$2$	4851.a	1.a	$1$	$4$	$4$	$38.735$	4.4.11344.1	None	✓				231.2.i.e	$1$	$1$	$-2$	$0$	$-4$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
4851.2.a.bu	$4851$	$2$	4851.a	1.a	$1$	$4$	$4$	$38.735$	4.4.11344.1	None	✓				231.2.i.e	$1$	$0$	$-2$	$0$	$4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
4851.2.a.bv	$4851$	$2$	4851.a	1.a	$1$	$4$	$4$	$38.735$	4.4.9248.1	None	✓				539.2.a.k	$2$	$0$	$-2$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(2-\beta _{3})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
4851.2.a.bw	$4851$	$2$	4851.a	1.a	$1$	$4$	$4$	$38.735$	4.4.725.1	None	✓	✓			4851.2.a.bq	$2$	$0$	$2$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{1})q^{4}-\beta _{2}q^{5}+(1+\cdots)q^{8}+\cdots$
4851.2.a.bx	$4851$	$2$	4851.a	1.a	$1$	$4$	$4$	$38.735$	4.4.2624.1	None	✓				1617.2.a.u	$1$	$0$	$2$	$0$	$-8$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+\beta _{2}q^{4}+(-1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$

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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.