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 (46 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	5	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3630.2.a.a	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓				330.2.a.c	$1$	$0$	$-1$	$-1$	$-1$	$-4$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-4q^{7}+\cdots$
3630.2.a.b	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.b	$1$	$0$	$-1$	$-1$	$-1$	$-3$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-3q^{7}+\cdots$
3630.2.a.c	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.c	$1$	$0$	$-1$	$-1$	$-1$	$-1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
3630.2.a.d	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.d	$1$	$1$	$-1$	$-1$	$1$	$-3$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-3q^{7}+\cdots$
3630.2.a.e	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.e	$1$	$1$	$-1$	$-1$	$1$	$-1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
3630.2.a.f	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓				330.2.a.d	$1$	$1$	$-1$	$-1$	$1$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots$
3630.2.a.g	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.g	$1$	$1$	$-1$	$1$	$-1$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
3630.2.a.h	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.h	$1$	$1$	$-1$	$1$	$-1$	$1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
3630.2.a.i	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.i	$1$	$0$	$-1$	$1$	$-1$	$2$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots$
3630.2.a.j	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.j	$1$	$1$	$-1$	$1$	$1$	$-2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots$
3630.2.a.k	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓				330.2.a.e	$1$	$0$	$-1$	$1$	$1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
3630.2.a.l	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.l	$1$	$0$	$-1$	$1$	$1$	$3$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots$
3630.2.a.m	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.m	$1$	$0$	$-1$	$1$	$1$	$5$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+5q^{7}+\cdots$
3630.2.a.n	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓				330.2.a.a	$1$	$1$	$1$	$-1$	$-1$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
3630.2.a.o	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.c	$1$	$1$	$1$	$-1$	$-1$	$1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
3630.2.a.p	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.b	$1$	$1$	$1$	$-1$	$-1$	$3$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+3q^{7}+\cdots$
3630.2.a.q	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.e	$1$	$0$	$1$	$-1$	$1$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
3630.2.a.r	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.d	$1$	$0$	$1$	$-1$	$1$	$3$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots$
3630.2.a.s	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓				330.2.a.b	$1$	$0$	$1$	$-1$	$1$	$4$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots$
3630.2.a.t	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.i	$1$	$1$	$1$	$1$	$-1$	$-2$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots$
3630.2.a.u	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.h	$1$	$0$	$1$	$1$	$-1$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
3630.2.a.v	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.g	$1$	$0$	$1$	$1$	$-1$	$1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
3630.2.a.w	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓				30.2.a.a	$1$	$0$	$1$	$1$	$-1$	$4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+4q^{7}+\cdots$
3630.2.a.x	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.m	$1$	$1$	$1$	$1$	$1$	$-5$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-5q^{7}+\cdots$
3630.2.a.y	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.l	$1$	$1$	$1$	$1$	$1$	$-3$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-3q^{7}+\cdots$
3630.2.a.z	$3630$	$2$	3630.a	1.a	$1$	$1$	$1$	$28.986$	$\Q$	None	✓	✓			3630.2.a.j	$1$	$0$	$1$	$1$	$1$	$2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+2q^{7}+\cdots$
3630.2.a.ba	$3630$	$2$	3630.a	1.a	$1$	$2$	$2$	$28.986$	$\Q(\sqrt{3}) $	None	✓	✓			3630.2.a.ba	$1$	$1$	$-2$	$-2$	$-2$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+\beta q^{7}+\cdots$
3630.2.a.bb	$3630$	$2$	3630.a	1.a	$1$	$2$	$2$	$28.986$	$\Q(\sqrt{5}) $	None	✓		✓		330.2.m.b	$1$	$0$	$-2$	$-2$	$-2$	$2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2\beta q^{7}+\cdots$
3630.2.a.bc	$3630$	$2$	3630.a	1.a	$1$	$2$	$2$	$28.986$	$\Q(\sqrt{5}) $	None	✓				330.2.m.d	$1$	$1$	$-2$	$-2$	$-2$	$5$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(3-\beta )q^{7}+\cdots$
3630.2.a.bd	$3630$	$2$	3630.a	1.a	$1$	$2$	$2$	$28.986$	$\Q(\sqrt{3}) $	None	✓	✓			3630.2.a.bd	$1$	$0$	$-2$	$-2$	$2$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+\beta q^{7}+\cdots$
3630.2.a.be	$3630$	$2$	3630.a	1.a	$1$	$2$	$2$	$28.986$	$\Q(\sqrt{5}) $	None	✓				330.2.m.c	$1$	$0$	$-2$	$-2$	$2$	$2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+2\beta q^{7}+\cdots$
3630.2.a.bf	$3630$	$2$	3630.a	1.a	$1$	$2$	$2$	$28.986$	$\Q(\sqrt{5}) $	None	✓		✓		330.2.m.a	$1$	$1$	$-2$	$-2$	$2$	$5$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(3-\beta )q^{7}+\cdots$
3630.2.a.bg	$3630$	$2$	3630.a	1.a	$1$	$2$	$2$	$28.986$	$\Q(\sqrt{3}) $	None	✓	✓			3630.2.a.bg	$1$	$0$	$-2$	$2$	$-2$	$4$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(2+\beta )q^{7}+\cdots$
3630.2.a.bh	$3630$	$2$	3630.a	1.a	$1$	$2$	$2$	$28.986$	$\Q(\sqrt{3}) $	None	✓	✓	✓		3630.2.a.bh	$1$	$1$	$-2$	$2$	$2$	$-4$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots$
3630.2.a.bi	$3630$	$2$	3630.a	1.a	$1$	$2$	$2$	$28.986$	$\Q(\sqrt{5}) $	None	✓		✓		330.2.m.d	$1$	$1$	$2$	$-2$	$-2$	$-5$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots$
3630.2.a.bj	$3630$	$2$	3630.a	1.a	$1$	$2$	$2$	$28.986$	$\Q(\sqrt{5}) $	None	✓				330.2.m.b	$1$	$0$	$2$	$-2$	$-2$	$-2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-2\beta q^{7}+\cdots$
3630.2.a.bk	$3630$	$2$	3630.a	1.a	$1$	$2$	$2$	$28.986$	$\Q(\sqrt{3}) $	None	✓	✓			3630.2.a.ba	$1$	$0$	$2$	$-2$	$-2$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+\beta q^{7}+\cdots$
3630.2.a.bl	$3630$	$2$	3630.a	1.a	$1$	$2$	$2$	$28.986$	$\Q(\sqrt{5}) $	None	✓				330.2.m.a	$1$	$1$	$2$	$-2$	$2$	$-5$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots$
3630.2.a.bm	$3630$	$2$	3630.a	1.a	$1$	$2$	$2$	$28.986$	$\Q(\sqrt{5}) $	None	✓		✓		330.2.m.c	$1$	$0$	$2$	$-2$	$2$	$-2$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2\beta q^{7}+\cdots$
3630.2.a.bn	$3630$	$2$	3630.a	1.a	$1$	$2$	$2$	$28.986$	$\Q(\sqrt{3}) $	None	✓	✓			3630.2.a.bd	$1$	$1$	$2$	$-2$	$2$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+\beta q^{7}+\cdots$
3630.2.a.bo	$3630$	$2$	3630.a	1.a	$1$	$2$	$2$	$28.986$	$\Q(\sqrt{3}) $	None	✓	✓	✓		3630.2.a.bg	$1$	$1$	$2$	$2$	$-2$	$-4$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
3630.2.a.bp	$3630$	$2$	3630.a	1.a	$1$	$2$	$2$	$28.986$	$\Q(\sqrt{3}) $	None	✓	✓			3630.2.a.bh	$1$	$0$	$2$	$2$	$2$	$4$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(2+\beta )q^{7}+\cdots$
3630.2.a.bq	$3630$	$2$	3630.a	1.a	$1$	$4$	$4$	$28.986$	4.4.52625.1	None	✓		✓		330.2.m.f	$1$	$0$	$-4$	$4$	$-4$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+\beta _{3}q^{7}+\cdots$
3630.2.a.br	$3630$	$2$	3630.a	1.a	$1$	$4$	$4$	$28.986$	4.4.43025.1	None	✓		✓		330.2.m.e	$1$	$0$	$-4$	$4$	$4$	$-1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-\beta _{1}q^{7}+\cdots$
3630.2.a.bs	$3630$	$2$	3630.a	1.a	$1$	$4$	$4$	$28.986$	4.4.52625.1	None	✓		✓		330.2.m.f	$1$	$0$	$4$	$4$	$-4$	$1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(-\beta _{2}+\cdots)q^{7}+\cdots$
3630.2.a.bt	$3630$	$2$	3630.a	1.a	$1$	$4$	$4$	$28.986$	4.4.43025.1	None	✓		✓		330.2.m.e	$1$	$0$	$4$	$4$	$4$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+\beta _{1}q^{7}+\cdots$

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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.