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 53 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	5	7	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5355.2.a.a	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓				595.2.a.c	$1$	$1$	$-2$	$0$	$-1$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}+q^{7}+2q^{10}+\cdots$
5355.2.a.b	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓				595.2.a.b	$1$	$1$	$-2$	$0$	$1$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+q^{5}+q^{7}-2q^{10}+\cdots$
5355.2.a.c	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓				1785.2.a.k	$1$	$1$	$-1$	$0$	$-1$	$-1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}+q^{10}+\cdots$
5355.2.a.d	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓				1785.2.a.l	$1$	$1$	$-1$	$0$	$-1$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}+q^{7}+3q^{8}+q^{10}+\cdots$
5355.2.a.e	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓				1785.2.a.o	$1$	$0$	$-1$	$0$	$-1$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}+q^{7}+3q^{8}+q^{10}+\cdots$
5355.2.a.f	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓	✓			5355.2.a.f	$1$	$1$	$-1$	$0$	$1$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}-q^{7}+3q^{8}-q^{10}+\cdots$
5355.2.a.g	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓				1785.2.a.m	$1$	$0$	$-1$	$0$	$1$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}-q^{7}+3q^{8}-q^{10}+\cdots$
5355.2.a.h	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓				1785.2.a.i	$1$	$1$	$-1$	$0$	$1$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}-q^{7}+3q^{8}-q^{10}+\cdots$
5355.2.a.i	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓				1785.2.a.n	$1$	$1$	$-1$	$0$	$1$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}+q^{7}+3q^{8}-q^{10}+\cdots$
5355.2.a.j	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓				1785.2.a.j	$1$	$1$	$-1$	$0$	$1$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}+q^{7}+3q^{8}-q^{10}+\cdots$
5355.2.a.k	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓				1785.2.a.g	$1$	$0$	$0$	$0$	$-1$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{5}-q^{7}+2q^{11}+3q^{13}+\cdots$
5355.2.a.l	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓				1785.2.a.f	$1$	$0$	$0$	$0$	$1$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{5}+q^{7}-2q^{11}-5q^{13}+\cdots$
5355.2.a.m	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓				1785.2.a.h	$1$	$0$	$0$	$0$	$1$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{5}+q^{7}+6q^{11}-q^{13}+\cdots$
5355.2.a.n	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓				1785.2.a.d	$1$	$0$	$1$	$0$	$-1$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}-q^{7}-3q^{8}-q^{10}+\cdots$
5355.2.a.o	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓	✓			5355.2.a.f	$1$	$1$	$1$	$0$	$-1$	$-1$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}-q^{7}-3q^{8}-q^{10}+\cdots$
5355.2.a.p	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓				1785.2.a.b	$1$	$1$	$1$	$0$	$-1$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}+q^{7}-3q^{8}-q^{10}+\cdots$
5355.2.a.q	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓				1785.2.a.e	$1$	$1$	$1$	$0$	$-1$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}+q^{7}-3q^{8}-q^{10}+\cdots$
5355.2.a.r	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓				1785.2.a.c	$1$	$1$	$1$	$0$	$1$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}+q^{7}-3q^{8}+q^{10}+\cdots$
5355.2.a.s	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓				1785.2.a.a	$1$	$1$	$1$	$0$	$1$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}+q^{7}-3q^{8}+q^{10}+\cdots$
5355.2.a.t	$5355$	$2$	5355.a	1.a	$1$	$1$	$1$	$42.760$	$\Q$	None	✓				595.2.a.a	$1$	$1$	$2$	$0$	$1$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{5}-q^{7}+2q^{10}+\cdots$
5355.2.a.u	$5355$	$2$	5355.a	1.a	$1$	$2$	$2$	$42.760$	$\Q(\sqrt{17}) $	None	✓				1785.2.a.t	$1$	$0$	$-1$	$0$	$-2$	$2$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+q^{7}+(-4+\cdots)q^{8}+\cdots$
5355.2.a.v	$5355$	$2$	5355.a	1.a	$1$	$2$	$2$	$42.760$	$\Q(\sqrt{17}) $	None	✓				1785.2.a.s	$1$	$0$	$-1$	$0$	$2$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2+\beta )q^{4}+q^{5}-q^{7}+(-4+\cdots)q^{8}+\cdots$
5355.2.a.w	$5355$	$2$	5355.a	1.a	$1$	$2$	$2$	$42.760$	$\Q(\sqrt{3}) $	None	✓				1785.2.a.q	$1$	$0$	$0$	$0$	$-2$	$-2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-q^{5}-q^{7}-\beta q^{8}-\beta q^{10}+\cdots$
5355.2.a.x	$5355$	$2$	5355.a	1.a	$1$	$2$	$2$	$42.760$	$\Q(\sqrt{5}) $	None	✓				1785.2.a.r	$1$	$1$	$0$	$0$	$-2$	$2$	$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+3q^{4}-q^{5}+q^{7}-\beta q^{8}+\beta q^{10}+\cdots$
5355.2.a.y	$5355$	$2$	5355.a	1.a	$1$	$2$	$2$	$42.760$	$\Q(\sqrt{2}) $	None	✓				1785.2.a.p	$1$	$0$	$2$	$0$	$2$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}-q^{7}+\cdots$
5355.2.a.z	$5355$	$2$	5355.a	1.a	$1$	$3$	$3$	$42.760$	$\Q(\zeta_{14})^+$	None	✓				595.2.a.h	$1$	$1$	$-2$	$0$	$3$	$-3$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
5355.2.a.ba	$5355$	$2$	5355.a	1.a	$1$	$3$	$3$	$42.760$	$\Q(\zeta_{18})^+$	None	✓				595.2.a.g	$1$	$0$	$0$	$0$	$3$	$-3$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}-q^{7}+(-1+\cdots)q^{8}+\cdots$
5355.2.a.bb	$5355$	$2$	5355.a	1.a	$1$	$3$	$3$	$42.760$	3.3.148.1	None	✓				1785.2.a.w	$1$	$1$	$1$	$0$	$-3$	$-3$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}-q^{7}+\cdots$
5355.2.a.bc	$5355$	$2$	5355.a	1.a	$1$	$3$	$3$	$42.760$	3.3.148.1	None	✓				1785.2.a.v	$1$	$1$	$1$	$0$	$3$	$-3$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+q^{5}-q^{7}+\cdots$
5355.2.a.bd	$5355$	$2$	5355.a	1.a	$1$	$3$	$3$	$42.760$	3.3.564.1	None	✓				1785.2.a.x	$1$	$0$	$1$	$0$	$-3$	$3$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+q^{7}+(1+\cdots)q^{8}+\cdots$
5355.2.a.be	$5355$	$2$	5355.a	1.a	$1$	$3$	$3$	$42.760$	$\Q(\zeta_{14})^+$	None	✓				595.2.a.e	$1$	$0$	$2$	$0$	$-3$	$-3$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots$
5355.2.a.bf	$5355$	$2$	5355.a	1.a	$1$	$3$	$3$	$42.760$	3.3.169.1	None	✓				595.2.a.f	$1$	$0$	$2$	$0$	$3$	$3$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
5355.2.a.bg	$5355$	$2$	5355.a	1.a	$1$	$3$	$3$	$42.760$	3.3.148.1	None	✓				1785.2.a.u	$1$	$0$	$3$	$0$	$3$	$3$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
5355.2.a.bh	$5355$	$2$	5355.a	1.a	$1$	$3$	$3$	$42.760$	$\Q(\zeta_{14})^+$	None	✓				595.2.a.d	$1$	$0$	$4$	$0$	$-3$	$3$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots$
5355.2.a.bi	$5355$	$2$	5355.a	1.a	$1$	$4$	$4$	$42.760$	4.4.2777.1	None	✓				595.2.a.j	$1$	$1$	$-2$	$0$	$-4$	$-4$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{2}+(1-\beta _{2}-\beta _{3})q^{4}+\cdots$
5355.2.a.bj	$5355$	$2$	5355.a	1.a	$1$	$4$	$4$	$42.760$	4.4.11348.1	None	✓		✓		1785.2.a.ba	$1$	$1$	$-2$	$0$	$4$	$-4$	$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(2+\beta _{2}-\beta _{3})q^{4}+\cdots$
5355.2.a.bk	$5355$	$2$	5355.a	1.a	$1$	$4$	$4$	$42.760$	4.4.10889.1	None	✓		✓		595.2.a.i	$1$	$1$	$-1$	$0$	$-4$	$4$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+q^{7}+\cdots$
5355.2.a.bl	$5355$	$2$	5355.a	1.a	$1$	$4$	$4$	$42.760$	4.4.8468.1	None	✓		✓		1785.2.a.z	$1$	$0$	$1$	$0$	$-4$	$4$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+q^{7}+(1+\cdots)q^{8}+\cdots$
5355.2.a.bm	$5355$	$2$	5355.a	1.a	$1$	$4$	$4$	$42.760$	4.4.8468.1	None	✓				1785.2.a.y	$1$	$1$	$2$	$0$	$-4$	$-4$	$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(2-\beta _{1})q^{4}-q^{5}-q^{7}+(-1+\cdots)q^{8}+\cdots$
5355.2.a.bn	$5355$	$2$	5355.a	1.a	$1$	$5$	$5$	$42.760$	5.5.1034856.1	None	✓		✓		595.2.a.k	$1$	$1$	$-2$	$0$	$5$	$5$	$-$	$-$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+q^{5}+q^{7}+\cdots$
5355.2.a.bo	$5355$	$2$	5355.a	1.a	$1$	$5$	$5$	$42.760$	5.5.609872.1	None	✓	✓			5355.2.a.bo	$1$	$0$	$-1$	$0$	$-5$	$5$	$+$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+q^{7}+(1+\cdots)q^{8}+\cdots$
5355.2.a.bp	$5355$	$2$	5355.a	1.a	$1$	$5$	$5$	$42.760$	5.5.223824.1	None	✓	✓	✓		5355.2.a.bp	$1$	$1$	$-1$	$0$	$5$	$-5$	$+$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}+(1-\beta _{1}+\beta _{4})q^{4}+q^{5}-q^{7}+\cdots$
5355.2.a.bq	$5355$	$2$	5355.a	1.a	$1$	$5$	$5$	$42.760$	5.5.223824.1	None	✓	✓	✓		5355.2.a.bp	$1$	$1$	$1$	$0$	$-5$	$-5$	$+$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+(1-\beta _{1}+\beta _{4})q^{4}-q^{5}-q^{7}+\cdots$
5355.2.a.br	$5355$	$2$	5355.a	1.a	$1$	$5$	$5$	$42.760$	5.5.609872.1	None	✓	✓			5355.2.a.bo	$1$	$0$	$1$	$0$	$5$	$5$	$+$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+q^{7}+(-1+\cdots)q^{8}+\cdots$
5355.2.a.bs	$5355$	$2$	5355.a	1.a	$1$	$5$	$5$	$42.760$	5.5.674848.1	None	✓		✓		1785.2.a.bc	$1$	$0$	$1$	$0$	$5$	$5$	$-$	$-$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+q^{7}+(2\beta _{1}+\cdots)q^{8}+\cdots$
5355.2.a.bt	$5355$	$2$	5355.a	1.a	$1$	$5$	$5$	$42.760$	5.5.246832.1	None	✓		✓		1785.2.a.bb	$1$	$0$	$2$	$0$	$5$	$-5$	$-$	$-$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{4})q^{4}+q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots$
5355.2.a.bu	$5355$	$2$	5355.a	1.a	$1$	$6$	$6$	$42.760$	6.6.17749184.1	None	✓		✓		1785.2.a.bd	$1$	$0$	$-3$	$0$	$-6$	$-6$	$-$	$+$	$+$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2+\beta _{4})q^{4}-q^{5}+\cdots$
5355.2.a.bv	$5355$	$2$	5355.a	1.a	$1$	$6$	$6$	$42.760$	6.6.810448.1	None	✓	✓	✓	✓	5355.2.a.bv	$1$	$1$	$-2$	$0$	$6$	$6$	$+$	$-$	$-$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(-\beta _{2}+\beta _{3})q^{4}+q^{5}+q^{7}+\cdots$
5355.2.a.bw	$5355$	$2$	5355.a	1.a	$1$	$6$	$6$	$42.760$	6.6.810448.1	None	✓	✓	✓	✓	5355.2.a.bv	$1$	$1$	$2$	$0$	$-6$	$6$	$+$	$+$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(-\beta _{2}-\beta _{4})q^{4}-q^{5}+q^{7}+\cdots$
5355.2.a.bx	$5355$	$2$	5355.a	1.a	$1$	$7$	$7$	$42.760$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓		5355.2.a.bx	$1$	$0$	$-1$	$0$	$-7$	$7$	$+$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+q^{7}+(-2+\cdots)q^{8}+\cdots$

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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.