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 76 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
4752.2.a.a	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				2376.2.a.a	$1$	$1$	$0$	$0$	$-3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-4q^{7}-q^{11}+3q^{13}+3q^{17}+\cdots$
4752.2.a.b	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				594.2.a.a	$1$	$1$	$0$	$0$	$-3$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+4q^{7}+q^{11}+5q^{13}-3q^{17}+\cdots$
4752.2.a.c	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				297.2.a.a	$1$	$0$	$0$	$0$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}-q^{11}-5q^{13}-2q^{17}+\cdots$
4752.2.a.d	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				594.2.a.c	$1$	$0$	$0$	$0$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}+q^{11}-2q^{13}-q^{17}+\cdots$
4752.2.a.e	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				1188.2.a.a	$1$	$1$	$0$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}-q^{11}+3q^{13}-2q^{17}+\cdots$
4752.2.a.f	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				594.2.a.b	$1$	$0$	$0$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}-q^{11}+6q^{13}-5q^{17}+\cdots$
4752.2.a.g	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				297.2.a.b	$1$	$0$	$0$	$0$	$-2$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+5q^{7}-q^{11}-2q^{13}+7q^{17}+\cdots$
4752.2.a.h	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				594.2.a.d	$1$	$0$	$0$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}-q^{11}+q^{13}-5q^{17}+\cdots$
4752.2.a.i	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				2376.2.a.b	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-q^{11}-3q^{13}+5q^{19}+4q^{23}+\cdots$
4752.2.a.j	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				2376.2.a.b	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+q^{11}-3q^{13}+5q^{19}-4q^{23}+\cdots$
4752.2.a.k	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				1188.2.a.b	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-q^{11}-4q^{13}-3q^{17}+4q^{19}+\cdots$
4752.2.a.l	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				1188.2.a.b	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+q^{11}-4q^{13}+3q^{17}+4q^{19}+\cdots$
4752.2.a.m	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				594.2.a.d	$1$	$1$	$0$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{7}+q^{11}+q^{13}+5q^{17}+\cdots$
4752.2.a.n	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				594.2.a.c	$1$	$0$	$0$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}-q^{11}-2q^{13}+q^{17}+\cdots$
4752.2.a.o	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				297.2.a.a	$1$	$1$	$0$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}+q^{11}-5q^{13}+2q^{17}+\cdots$
4752.2.a.p	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				1188.2.a.a	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}+q^{11}+3q^{13}+2q^{17}+\cdots$
4752.2.a.q	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				594.2.a.b	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}+q^{11}+6q^{13}+5q^{17}+\cdots$
4752.2.a.r	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				297.2.a.b	$1$	$0$	$0$	$0$	$2$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+5q^{7}+q^{11}-2q^{13}-7q^{17}+\cdots$
4752.2.a.s	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				2376.2.a.a	$1$	$0$	$0$	$0$	$3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-4q^{7}+q^{11}+3q^{13}-3q^{17}+\cdots$
4752.2.a.t	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	$\Q$	None	✓				594.2.a.a	$1$	$0$	$0$	$0$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+4q^{7}-q^{11}+5q^{13}+3q^{17}+\cdots$
4752.2.a.u	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	$\Q(\sqrt{10}) $	None	✓				594.2.a.i	$1$	$1$	$0$	$0$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{5}-2q^{7}-q^{11}+(1+\beta )q^{13}+\cdots$
4752.2.a.v	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	$\Q(\sqrt{7}) $	None	✓				1188.2.a.e	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{5}+\beta q^{7}+q^{11}-\beta q^{13}+\cdots$
4752.2.a.w	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	$\Q(\sqrt{3}) $	None	✓				297.2.a.e	$1$	$0$	$0$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{5}+(2+\beta )q^{7}+q^{11}+(-2+\cdots)q^{13}+\cdots$
4752.2.a.x	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	$\Q(\sqrt{7}) $	None	✓				2376.2.a.i	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{7}-q^{11}+(2-\beta )q^{17}-2\beta q^{19}+\cdots$
4752.2.a.y	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	$\Q(\sqrt{7}) $	None	✓				2376.2.a.i	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{7}+q^{11}+(-2-\beta )q^{17}+2\beta q^{19}+\cdots$
4752.2.a.z	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	$\Q(\sqrt{2}) $	None	✓				2376.2.a.e	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{5}+(1+\beta )q^{7}-q^{11}+(-4-2\beta )q^{13}+\cdots$
4752.2.a.ba	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	$\Q(\sqrt{2}) $	None	✓				2376.2.a.f	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(1-\beta )q^{7}-q^{11}+(-1-\beta )q^{13}+\cdots$
4752.2.a.bb	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	$\Q(\sqrt{2}) $	None	✓				2376.2.a.e	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{5}+(1-\beta )q^{7}+q^{11}+(-4+2\beta )q^{13}+\cdots$
4752.2.a.bc	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	$\Q(\sqrt{2}) $	None	✓				2376.2.a.f	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(1+\beta )q^{7}+q^{11}+(-1+\beta )q^{13}+\cdots$
4752.2.a.bd	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	$\Q(\sqrt{10}) $	None	✓				594.2.a.i	$1$	$0$	$0$	$0$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}-2q^{7}+q^{11}+(1-\beta )q^{13}+\cdots$
4752.2.a.be	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	$\Q(\sqrt{7}) $	None	✓				1188.2.a.e	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}-\beta q^{7}-q^{11}+\beta q^{13}+\cdots$
4752.2.a.bf	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	$\Q(\sqrt{3}) $	None	✓				297.2.a.e	$1$	$1$	$0$	$0$	$2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+(2-\beta )q^{7}-q^{11}+(-2+\cdots)q^{13}+\cdots$
4752.2.a.bg	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.564.1	None	✓		✓		297.2.a.g	$1$	$1$	$0$	$0$	$-2$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{5}+(-2-\beta _{1})q^{7}+q^{11}+\cdots$
4752.2.a.bh	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.788.1	None	✓				2376.2.a.l	$1$	$0$	$0$	$0$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{5}-\beta _{1}q^{7}+q^{11}+(1+\cdots)q^{13}+\cdots$
4752.2.a.bi	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.1016.1	None	✓		✓		2376.2.a.m	$1$	$1$	$0$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}+(-\beta _{1}-\beta _{2})q^{7}+q^{11}+\cdots$
4752.2.a.bj	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.564.1	None	✓				2376.2.a.k	$1$	$0$	$0$	$0$	$-2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+\cdots$
4752.2.a.bk	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.7032.1	None	✓				2376.2.a.n	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+(1-\beta _{1})q^{7}+q^{11}+(-1+\cdots)q^{13}+\cdots$
4752.2.a.bl	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.3124.1	None	✓		✓		1188.2.a.g	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+\beta _{2}q^{7}-q^{11}+(2-\beta _{1})q^{13}+\cdots$
4752.2.a.bm	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.3124.1	None	✓		✓		1188.2.a.g	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+\beta _{2}q^{7}+q^{11}+(2-\beta _{1})q^{13}+\cdots$
4752.2.a.bn	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.7032.1	None	✓		✓		2376.2.a.n	$1$	$1$	$0$	$0$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+(1-\beta _{1})q^{7}-q^{11}+(-1+\cdots)q^{13}+\cdots$
4752.2.a.bo	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.564.1	None	✓		✓		297.2.a.g	$1$	$1$	$0$	$0$	$2$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{5}+(-2-\beta _{1})q^{7}-q^{11}+\cdots$
4752.2.a.bp	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.788.1	None	✓				2376.2.a.l	$1$	$0$	$0$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{5}-\beta _{1}q^{7}-q^{11}+(1-2\beta _{1}+\cdots)q^{13}+\cdots$
4752.2.a.bq	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.1016.1	None	✓				2376.2.a.m	$1$	$0$	$0$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}+(-\beta _{1}-\beta _{2})q^{7}-q^{11}+\cdots$
4752.2.a.br	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.564.1	None	✓				2376.2.a.k	$1$	$0$	$0$	$0$	$2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+q^{11}+\cdots$
4752.2.b.a	$4752$	$2$	4752.b	33.d	$2$	$4$	$4$	$37.945$	$\Q(\sqrt{-3}, \sqrt{-35})$	None					594.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{3})q^{5}-\beta _{2}q^{7}+(-1-\beta _{2}+\cdots)q^{11}+\cdots$
4752.2.b.b	$4752$	$2$	4752.b	33.d	$2$	$4$	$4$	$37.945$	$\Q(\sqrt{-2}, \sqrt{3})$	None					594.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(\beta _{1}+\beta _{3})q^{7}+(2\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
4752.2.b.c	$4752$	$2$	4752.b	33.d	$2$	$4$	$4$	$37.945$	$\Q(\sqrt{-2}, \sqrt{3})$	None					594.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+(2\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$
4752.2.b.d	$4752$	$2$	4752.b	33.d	$2$	$4$	$4$	$37.945$	$\Q(\sqrt{-3}, \sqrt{-35})$	None					594.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}+(1-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
4752.2.b.e	$4752$	$2$	4752.b	33.d	$2$	$8$	$8$	$37.945$	8.0.$\cdots$.14	None					297.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{5}-\beta _{3}q^{7}+(-\beta _{1}+\beta _{7})q^{11}+\cdots$
4752.2.b.f	$4752$	$2$	4752.b	33.d	$2$	$8$	$8$	$37.945$	8.0.3317760000.8	None					1188.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{3}-\beta _{4})q^{5}-\beta _{5}q^{7}+(-\beta _{4}-\beta _{6}+\cdots)q^{11}+\cdots$

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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.