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 73 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3450.2.a.a	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓	✓			3450.2.a.a	$1$	$2$	$-1$	$-1$	$0$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-5q^{7}-q^{8}+\cdots$
3450.2.a.b	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓				690.2.a.j	$1$	$0$	$-1$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
3450.2.a.c	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓				690.2.a.i	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
3450.2.a.d	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓				690.2.a.k	$1$	$0$	$-1$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
3450.2.a.e	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓	✓			3450.2.a.e	$1$	$1$	$-1$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots$
3450.2.a.f	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓	✓			3450.2.a.f	$1$	$0$	$-1$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots$
3450.2.a.g	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓	✓			3450.2.a.g	$1$	$1$	$-1$	$-1$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+3q^{7}-q^{8}+\cdots$
3450.2.a.h	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓	✓			3450.2.a.h	$1$	$1$	$-1$	$1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots$
3450.2.a.i	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓	✓			3450.2.a.i	$1$	$1$	$-1$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
3450.2.a.j	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓				690.2.a.h	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
3450.2.a.k	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓				138.2.a.c	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
3450.2.a.l	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓				690.2.a.g	$1$	$0$	$-1$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots$
3450.2.a.m	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓	✓			3450.2.a.m	$1$	$0$	$-1$	$1$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+5q^{7}-q^{8}+\cdots$
3450.2.a.n	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓	✓			3450.2.a.m	$1$	$0$	$1$	$-1$	$0$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-5q^{7}+q^{8}+\cdots$
3450.2.a.o	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓				138.2.a.b	$1$	$1$	$1$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots$
3450.2.a.p	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓				690.2.a.e	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
3450.2.a.q	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓				690.2.a.f	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
3450.2.a.r	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓	✓			3450.2.a.i	$1$	$1$	$1$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
3450.2.a.s	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓	✓			3450.2.a.h	$1$	$1$	$1$	$-1$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+3q^{7}+q^{8}+\cdots$
3450.2.a.t	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓				690.2.a.b	$1$	$1$	$1$	$1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots$
3450.2.a.u	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓				690.2.a.d	$1$	$0$	$1$	$1$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots$
3450.2.a.v	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓	✓	✓	✓	3450.2.a.g	$1$	$1$	$1$	$1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots$
3450.2.a.w	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓	✓			3450.2.a.e	$1$	$1$	$1$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots$
3450.2.a.x	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓	✓			3450.2.a.f	$1$	$0$	$1$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots$
3450.2.a.y	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓				138.2.a.a	$1$	$0$	$1$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots$
3450.2.a.z	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓				690.2.a.c	$1$	$0$	$1$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots$
3450.2.a.ba	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓				690.2.a.a	$1$	$0$	$1$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots$
3450.2.a.bb	$3450$	$2$	3450.a	1.a	$1$	$1$	$1$	$27.548$	$\Q$	None	✓	✓			3450.2.a.a	$1$	$0$	$1$	$1$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+5q^{7}+q^{8}+\cdots$
3450.2.a.bc	$3450$	$2$	3450.a	1.a	$1$	$2$	$2$	$27.548$	$\Q(\sqrt{5}) $	None	✓				690.2.d.a	$1$	$1$	$-2$	$-2$	$0$	$-8$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots$
3450.2.a.bd	$3450$	$2$	3450.a	1.a	$1$	$2$	$2$	$27.548$	$\Q(\sqrt{57}) $	None	✓	✓	✓		3450.2.a.bd	$1$	$0$	$-2$	$-2$	$0$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots$
3450.2.a.be	$3450$	$2$	3450.a	1.a	$1$	$2$	$2$	$27.548$	$\Q(\sqrt{5}) $	None	✓		✓		138.2.a.d	$1$	$1$	$-2$	$-2$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-2\beta q^{7}-q^{8}+\cdots$
3450.2.a.bf	$3450$	$2$	3450.a	1.a	$1$	$2$	$2$	$27.548$	$\Q(\sqrt{6}) $	None	✓	✓	✓		3450.2.a.bf	$1$	$0$	$-2$	$-2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+(1+\beta )q^{7}+\cdots$
3450.2.a.bg	$3450$	$2$	3450.a	1.a	$1$	$2$	$2$	$27.548$	$\Q(\sqrt{2}) $	None	✓				690.2.d.b	$1$	$1$	$-2$	$-2$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots$
3450.2.a.bh	$3450$	$2$	3450.a	1.a	$1$	$2$	$2$	$27.548$	$\Q(\sqrt{73}) $	None	✓	✓			3450.2.a.bh	$1$	$0$	$-2$	$2$	$0$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots$
3450.2.a.bi	$3450$	$2$	3450.a	1.a	$1$	$2$	$2$	$27.548$	$\Q(\sqrt{17}) $	None	✓				690.2.a.l	$1$	$0$	$-2$	$2$	$0$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+(1+\beta )q^{7}+\cdots$
3450.2.a.bj	$3450$	$2$	3450.a	1.a	$1$	$2$	$2$	$27.548$	$\Q(\sqrt{73}) $	None	✓	✓	✓		3450.2.a.bh	$1$	$0$	$2$	$-2$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+3q^{7}+q^{8}+\cdots$
3450.2.a.bk	$3450$	$2$	3450.a	1.a	$1$	$2$	$2$	$27.548$	$\Q(\sqrt{2}) $	None	✓				690.2.d.b	$1$	$0$	$2$	$2$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots$
3450.2.a.bl	$3450$	$2$	3450.a	1.a	$1$	$2$	$2$	$27.548$	$\Q(\sqrt{6}) $	None	✓	✓	✓		3450.2.a.bf	$1$	$0$	$2$	$2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+(-1+\beta )q^{7}+\cdots$
3450.2.a.bm	$3450$	$2$	3450.a	1.a	$1$	$2$	$2$	$27.548$	$\Q(\sqrt{57}) $	None	✓	✓			3450.2.a.bd	$1$	$0$	$2$	$2$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots$
3450.2.a.bn	$3450$	$2$	3450.a	1.a	$1$	$2$	$2$	$27.548$	$\Q(\sqrt{5}) $	None	✓				690.2.d.a	$1$	$0$	$2$	$2$	$0$	$8$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots$
3450.2.a.bo	$3450$	$2$	3450.a	1.a	$1$	$3$	$3$	$27.548$	3.3.148.1	None	✓		✓		690.2.d.c	$1$	$1$	$-3$	$3$	$0$	$-2$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
3450.2.a.bp	$3450$	$2$	3450.a	1.a	$1$	$3$	$3$	$27.548$	3.3.3368.1	None	✓	✓	✓		3450.2.a.bp	$1$	$0$	$-3$	$3$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+\beta _{1}q^{7}-q^{8}+\cdots$
3450.2.a.bq	$3450$	$2$	3450.a	1.a	$1$	$3$	$3$	$27.548$	3.3.568.1	None	✓		✓		690.2.d.d	$1$	$0$	$-3$	$3$	$0$	$6$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots$
3450.2.a.br	$3450$	$2$	3450.a	1.a	$1$	$3$	$3$	$27.548$	3.3.568.1	None	✓		✓		690.2.d.d	$1$	$1$	$3$	$-3$	$0$	$-6$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots$
3450.2.a.bs	$3450$	$2$	3450.a	1.a	$1$	$3$	$3$	$27.548$	3.3.3368.1	None	✓	✓			3450.2.a.bp	$1$	$0$	$3$	$-3$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-\beta _{1}q^{7}+q^{8}+\cdots$
3450.2.a.bt	$3450$	$2$	3450.a	1.a	$1$	$3$	$3$	$27.548$	3.3.148.1	None	✓				690.2.d.c	$1$	$0$	$3$	$-3$	$0$	$2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+(1+\beta _{1})q^{7}+\cdots$
3450.2.d.a	$3450$	$2$	3450.d	5.b	$2$	$2$	$2$	$27.548$	$\Q(\sqrt{-1}) $	None					690.2.a.e	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-i q^{3}-q^{4}-q^{6}+i q^{8}+\cdots$
3450.2.d.b	$3450$	$2$	3450.d	5.b	$2$	$2$	$2$	$27.548$	$\Q(\sqrt{-1}) $	None		✓			3450.2.a.h	$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+i q^{3}-q^{4}-q^{6}+3 i q^{7}+\cdots$
3450.2.d.c	$3450$	$2$	3450.d	5.b	$2$	$2$	$2$	$27.548$	$\Q(\sqrt{-1}) $	None		✓			3450.2.a.i	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+i q^{3}-q^{4}-q^{6}+i q^{7}+\cdots$
3450.2.d.d	$3450$	$2$	3450.d	5.b	$2$	$2$	$2$	$27.548$	$\Q(\sqrt{-1}) $	None					690.2.a.g	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-i q^{3}-q^{4}-q^{6}+2 i q^{7}+\cdots$

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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.