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 58 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	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4725.2.a.a	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓	✓			4725.2.a.a	$1$	$1$	$-2$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{7}-3q^{13}+2q^{14}+\cdots$
4725.2.a.b	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓	✓			4725.2.a.a	$1$	$0$	$-2$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+q^{7}+3q^{13}-2q^{14}+\cdots$
4725.2.a.c	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓				189.2.a.a	$1$	$0$	$-2$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+q^{7}+4q^{11}+2q^{13}+\cdots$
4725.2.a.d	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓	✓			4725.2.a.d	$1$	$1$	$-1$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{7}+3q^{8}+3q^{11}-3q^{13}+\cdots$
4725.2.a.e	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓				945.2.d.a	$1$	$0$	$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{7}+3q^{8}+3q^{11}+7q^{13}+\cdots$
4725.2.a.f	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓				945.2.d.a	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{7}+3q^{8}-3q^{11}-7q^{13}+\cdots$
4725.2.a.g	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓	✓			4725.2.a.d	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{7}+3q^{8}-3q^{11}+3q^{13}+\cdots$
4725.2.a.h	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓	✓			4725.2.a.h	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{7}-6q^{11}+q^{13}+4q^{16}+\cdots$
4725.2.a.i	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓				189.2.a.b	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{7}-6q^{11}+4q^{13}+4q^{16}+\cdots$
4725.2.a.j	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓	✓			4725.2.a.h	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{7}+6q^{11}+q^{13}+4q^{16}+\cdots$
4725.2.a.k	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓				189.2.a.b	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{7}+6q^{11}+4q^{13}+4q^{16}+\cdots$
4725.2.a.l	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓	✓			4725.2.a.h	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{7}-6q^{11}-q^{13}+4q^{16}+\cdots$
4725.2.a.m	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓	✓			4725.2.a.h	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{7}+6q^{11}-q^{13}+4q^{16}+\cdots$
4725.2.a.n	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓	✓			4725.2.a.d	$1$	$0$	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{7}-3q^{8}-3q^{11}-3q^{13}+\cdots$
4725.2.a.o	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓				945.2.d.a	$1$	$1$	$1$	$0$	$0$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{7}-3q^{8}-3q^{11}+7q^{13}+\cdots$
4725.2.a.p	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓				945.2.d.a	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}+3q^{11}-7q^{13}+\cdots$
4725.2.a.q	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓	✓			4725.2.a.d	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}+3q^{11}+3q^{13}+\cdots$
4725.2.a.r	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓	✓			4725.2.a.a	$1$	$1$	$2$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-q^{7}-3q^{13}-2q^{14}+\cdots$
4725.2.a.s	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓				189.2.a.a	$1$	$1$	$2$	$0$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{7}-4q^{11}+2q^{13}+\cdots$
4725.2.a.t	$4725$	$2$	4725.a	1.a	$1$	$1$	$1$	$37.729$	$\Q$	None	✓	✓			4725.2.a.a	$1$	$0$	$2$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{7}+3q^{13}+2q^{14}+\cdots$
4725.2.a.u	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	$\Q(\sqrt{5}) $	None	✓				945.2.a.a	$1$	$0$	$-3$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+3\beta q^{4}-q^{7}+(-1+\cdots)q^{8}+\cdots$
4725.2.a.v	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	$\Q(\sqrt{2}) $	None	✓				945.2.a.b	$1$	$1$	$-2$	$0$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{7}+(-3+\cdots)q^{8}+\cdots$
4725.2.a.w	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	$\Q(\sqrt{5}) $	None	✓				945.2.a.e	$1$	$1$	$-1$	$0$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(-1+2\beta )q^{8}+\cdots$
4725.2.a.x	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	$\Q(\sqrt{5}) $	None	✓				945.2.a.d	$1$	$0$	$-1$	$0$	$0$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(-1+2\beta )q^{8}+\cdots$
4725.2.a.y	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	$\Q(\sqrt{5}) $	None	✓				945.2.a.c	$1$	$1$	$-1$	$0$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(-1+2\beta )q^{8}+\cdots$
4725.2.a.z	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	$\Q(\sqrt{13}) $	None	✓				945.2.a.f	$1$	$1$	$-1$	$0$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1+\beta )q^{4}-q^{7}-3q^{8}+3q^{11}+\cdots$
4725.2.a.ba	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	$\Q(\sqrt{3}) $	None	✓				189.2.a.e	$2$	$0$	$0$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-q^{7}-\beta q^{8}+\beta q^{11}+\cdots$
4725.2.a.bb	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	$\Q(\sqrt{7}) $	None	✓				189.2.a.f	$2$	$0$	$0$	$0$	$0$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+5q^{4}+q^{7}+3\beta q^{8}+\beta q^{11}+\cdots$
4725.2.a.bc	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	$\Q(\sqrt{5}) $	None	✓				945.2.a.d	$1$	$0$	$1$	$0$	$0$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(1-2\beta )q^{8}+\cdots$
4725.2.a.bd	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	$\Q(\sqrt{5}) $	None	✓				945.2.a.c	$1$	$0$	$1$	$0$	$0$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(1-2\beta )q^{8}+\cdots$
4725.2.a.be	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	$\Q(\sqrt{5}) $	None	✓				945.2.a.e	$1$	$1$	$1$	$0$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(1-2\beta )q^{8}+\cdots$
4725.2.a.bf	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	$\Q(\sqrt{13}) $	None	✓				945.2.a.f	$1$	$1$	$1$	$0$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}-q^{7}+3q^{8}-3q^{11}+\cdots$
4725.2.a.bg	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	$\Q(\sqrt{2}) $	None	✓				945.2.a.b	$1$	$0$	$2$	$0$	$0$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{7}+(3+\beta )q^{8}+\cdots$
4725.2.a.bh	$4725$	$2$	4725.a	1.a	$1$	$2$	$2$	$37.729$	$\Q(\sqrt{5}) $	None	✓				945.2.a.a	$1$	$0$	$3$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}-q^{7}+(1+4\beta )q^{8}+\cdots$
4725.2.a.bi	$4725$	$2$	4725.a	1.a	$1$	$3$	$3$	$37.729$	3.3.257.1	None	✓	✓			4725.2.a.bi	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}-q^{7}+(-3+\cdots)q^{8}+\cdots$
4725.2.a.bj	$4725$	$2$	4725.a	1.a	$1$	$3$	$3$	$37.729$	3.3.257.1	None	✓	✓			4725.2.a.bi	$1$	$0$	$0$	$0$	$0$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}-q^{7}+(3+\cdots)q^{8}+\cdots$
4725.2.a.bk	$4725$	$2$	4725.a	1.a	$1$	$3$	$3$	$37.729$	3.3.257.1	None	✓	✓			4725.2.a.bi	$1$	$1$	$0$	$0$	$0$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+q^{7}+(-3+\cdots)q^{8}+\cdots$
4725.2.a.bl	$4725$	$2$	4725.a	1.a	$1$	$3$	$3$	$37.729$	3.3.257.1	None	✓	✓			4725.2.a.bi	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+q^{7}+(3+\cdots)q^{8}+\cdots$
4725.2.a.bm	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	4.4.15529.1	None	✓	✓			4725.2.a.bm	$1$	$1$	$-3$	$0$	$0$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots$
4725.2.a.bn	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	4.4.15529.1	None	✓	✓			4725.2.a.bm	$1$	$1$	$-3$	$0$	$0$	$4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots$
4725.2.a.bo	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	4.4.144344.1	None	✓		✓		945.2.a.m	$1$	$1$	$-1$	$0$	$0$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{7}+(-1-2\beta _{1}+\cdots)q^{8}+\cdots$
4725.2.a.bp	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	$\Q(\sqrt{2}, \sqrt{29})$	None	✓	✓			4725.2.a.bp	$2$	$0$	$0$	$0$	$0$	$-4$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{7}-2\beta _{1}q^{8}-\beta _{2}q^{11}+\cdots$
4725.2.a.bq	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	$\Q(\sqrt{2}, \sqrt{29})$	None	✓	✓			4725.2.a.bp	$2$	$1$	$0$	$0$	$0$	$4$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{7}-2\beta _{1}q^{8}+\beta _{2}q^{11}+\cdots$
4725.2.a.br	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓				945.2.d.c	$2$	$1$	$0$	$0$	$0$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}-\beta _{2}q^{4}-q^{7}+(\beta _{1}+\beta _{3})q^{8}+\cdots$
4725.2.a.bs	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓				945.2.d.c	$2$	$1$	$0$	$0$	$0$	$4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}-\beta _{2}q^{4}+q^{7}+(\beta _{1}+\beta _{3})q^{8}+\cdots$
4725.2.a.bt	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	$\Q(\sqrt{2}, \sqrt{5})$	None	✓	✓			4725.2.a.bt	$2$	$1$	$0$	$0$	$0$	$-4$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}-q^{7}+2\beta _{2}q^{8}+\cdots$
4725.2.a.bu	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	$\Q(\sqrt{2}, \sqrt{5})$	None	✓	✓			4725.2.a.bu	$2$	$0$	$0$	$0$	$0$	$-4$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}-q^{7}+2\beta _{2}q^{8}+\cdots$
4725.2.a.bv	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	$\Q(\sqrt{2}, \sqrt{5})$	None	✓	✓			4725.2.a.bu	$2$	$1$	$0$	$0$	$0$	$4$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+q^{7}+2\beta _{2}q^{8}+\cdots$
4725.2.a.bw	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	$\Q(\sqrt{2}, \sqrt{5})$	None	✓	✓			4725.2.a.bt	$2$	$0$	$0$	$0$	$0$	$4$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+q^{7}+2\beta _{2}q^{8}+\cdots$
4725.2.a.bx	$4725$	$2$	4725.a	1.a	$1$	$4$	$4$	$37.729$	4.4.144344.1	None	✓				945.2.a.m	$1$	$0$	$1$	$0$	$0$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{7}+(1+2\beta _{1}+\cdots)q^{8}+\cdots$

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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.