LMFDB - Newform search results

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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 64 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9747.2.a.a	$9747$	$2$	9747.a	1.a	$1$	$1$	$1$	$77.830$	$\Q$	None	✓	$1$	$2$	$-2$	$0$	$-4$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-4q^{5}+8q^{10}-6q^{11}+\cdots$
9747.2.a.b	$9747$	$2$	9747.a	1.a	$1$	$1$	$1$	$77.830$	$\Q$	None	✓	$1$	$0$	$-2$	$0$	$4$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+4q^{5}-8q^{10}+6q^{11}+\cdots$
9747.2.a.c	$9747$	$2$	9747.a	1.a	$1$	$1$	$1$	$77.830$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$-2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{7}+3q^{8}-5q^{11}+\cdots$
9747.2.a.d	$9747$	$2$	9747.a	1.a	$1$	$1$	$1$	$77.830$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$2$	$0$	$0$	$0$	$-4$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-4q^{7}-7q^{13}+4q^{16}-5q^{25}+\cdots$
9747.2.a.e	$9747$	$2$	9747.a	1.a	$1$	$1$	$1$	$77.830$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$0$	$0$	$-4$	$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-4q^{7}+7q^{13}+4q^{16}-5q^{25}+\cdots$
9747.2.a.f	$9747$	$2$	9747.a	1.a	$1$	$1$	$1$	$77.830$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$0$	$0$	$-1$	$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}-q^{7}-5q^{13}+4q^{16}-5q^{25}+\cdots$
9747.2.a.g	$9747$	$2$	9747.a	1.a	$1$	$1$	$1$	$77.830$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$0$	$0$	$5$	$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+5q^{7}-2q^{13}+4q^{16}-5q^{25}+\cdots$
9747.2.a.h	$9747$	$2$	9747.a	1.a	$1$	$1$	$1$	$77.830$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$0$	$0$	$5$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+5q^{7}+2q^{13}+4q^{16}-5q^{25}+\cdots$
9747.2.a.i	$9747$	$2$	9747.a	1.a	$1$	$1$	$1$	$77.830$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$-2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-2q^{7}-3q^{8}+5q^{11}+\cdots$
9747.2.a.j	$9747$	$2$	9747.a	1.a	$1$	$1$	$1$	$77.830$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$-4$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-4q^{5}-8q^{10}-6q^{11}+\cdots$
9747.2.a.k	$9747$	$2$	9747.a	1.a	$1$	$1$	$1$	$77.830$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$4$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+4q^{5}+8q^{10}+6q^{11}+\cdots$
9747.2.a.l	$9747$	$2$	9747.a	1.a	$1$	$2$	$2$	$77.830$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-3$	$0$	$-5$	$1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+3\beta q^{4}+(-3+\beta )q^{5}+\cdots$
9747.2.a.m	$9747$	$2$	9747.a	1.a	$1$	$2$	$2$	$77.830$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-3$	$0$	$5$	$1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+3\beta q^{4}+(3-\beta )q^{5}+\cdots$
9747.2.a.n	$9747$	$2$	9747.a	1.a	$1$	$2$	$2$	$77.830$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-1$	$0$	$-1$	$-3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}-\beta q^{5}-3\beta q^{7}+\cdots$
9747.2.a.o	$9747$	$2$	9747.a	1.a	$1$	$2$	$2$	$77.830$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-1$	$0$	$1$	$-3$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+\beta q^{5}-3\beta q^{7}+\cdots$
9747.2.a.p	$9747$	$2$	9747.a	1.a	$1$	$2$	$2$	$77.830$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-8$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+2\beta q^{5}-4q^{7}-\beta q^{8}+\cdots$
9747.2.a.q	$9747$	$2$	9747.a	1.a	$1$	$2$	$2$	$77.830$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$1$	$0$	$-1$	$-3$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}-\beta q^{5}-3\beta q^{7}+\cdots$
9747.2.a.r	$9747$	$2$	9747.a	1.a	$1$	$2$	$2$	$77.830$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$1$	$0$	$1$	$-3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+\beta q^{5}-3\beta q^{7}+\cdots$
9747.2.a.s	$9747$	$2$	9747.a	1.a	$1$	$2$	$2$	$77.830$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$3$	$0$	$-5$	$1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}+(-3+\beta )q^{5}+\cdots$
9747.2.a.t	$9747$	$2$	9747.a	1.a	$1$	$2$	$2$	$77.830$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$3$	$0$	$5$	$1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}+(3-\beta )q^{5}+(1+\cdots)q^{7}+\cdots$
9747.2.a.u	$9747$	$2$	9747.a	1.a	$1$	$3$	$3$	$77.830$	$\Q(\zeta_{18})^+$	None	✓	$1$	$2$	$-3$	$0$	$-3$	$-9$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots$
9747.2.a.v	$9747$	$2$	9747.a	1.a	$1$	$3$	$3$	$77.830$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$-3$	$0$	$3$	$-9$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots$
9747.2.a.w	$9747$	$2$	9747.a	1.a	$1$	$3$	$3$	$77.830$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$-3$	$0$	$3$	$-3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots$
9747.2.a.x	$9747$	$2$	9747.a	1.a	$1$	$3$	$3$	$77.830$	3.3.321.1	None	✓	$1$	$0$	$-1$	$0$	$5$	$1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots$
9747.2.a.y	$9747$	$2$	9747.a	1.a	$1$	$3$	$3$	$77.830$	$\Q(\zeta_{18})^+$	$\Q(\sqrt{-3}) $	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+(-2\beta _{1}-\beta _{2})q^{7}+(4\beta _{1}-3\beta _{2})q^{13}+\cdots$
9747.2.a.z	$9747$	$2$	9747.a	1.a	$1$	$3$	$3$	$77.830$	$\Q(\zeta_{18})^+$	$\Q(\sqrt{-3}) $	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+(-2\beta _{1}-\beta _{2})q^{7}+(-4\beta _{1}+\cdots)q^{13}+\cdots$
9747.2.a.ba	$9747$	$2$	9747.a	1.a	$1$	$3$	$3$	$77.830$	3.3.321.1	None	✓	$1$	$1$	$1$	$0$	$-5$	$1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots$
9747.2.a.bb	$9747$	$2$	9747.a	1.a	$1$	$3$	$3$	$77.830$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$3$	$0$	$-3$	$-9$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
9747.2.a.bc	$9747$	$2$	9747.a	1.a	$1$	$3$	$3$	$77.830$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$3$	$0$	$-3$	$-3$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
9747.2.a.bd	$9747$	$2$	9747.a	1.a	$1$	$3$	$3$	$77.830$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$3$	$0$	$3$	$-9$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
9747.2.a.be	$9747$	$2$	9747.a	1.a	$1$	$4$	$4$	$77.830$	4.4.27648.1	None	✓	$2$	$1$	$0$	$0$	$0$	$8$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+(2-\beta _{2}+\cdots)q^{7}+\cdots$
9747.2.a.bf	$9747$	$2$	9747.a	1.a	$1$	$4$	$4$	$77.830$	4.4.29952.1	None	✓	$2$	$0$	$0$	$0$	$0$	$12$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+(3+\beta _{2}+\cdots)q^{7}+\cdots$
9747.2.a.bg	$9747$	$2$	9747.a	1.a	$1$	$4$	$4$	$77.830$	4.4.7600.1	None	✓	$2$	$0$	$0$	$0$	$0$	$2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+\beta _{3}q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots$
9747.2.a.bh	$9747$	$2$	9747.a	1.a	$1$	$4$	$4$	$77.830$	4.4.7600.1	None	✓	$2$	$1$	$0$	$0$	$0$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}-\beta _{3}q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots$
9747.2.a.bi	$9747$	$2$	9747.a	1.a	$1$	$4$	$4$	$77.830$	4.4.25088.1	None	✓	$2$	$0$	$0$	$0$	$0$	$4$	$+$	$-$	$-$	$3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(3-\beta _{2})q^{4}+\beta _{1}q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots$
9747.2.a.bj	$9747$	$2$	9747.a	1.a	$1$	$4$	$4$	$77.830$	4.4.25088.1	None	✓	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(3-\beta _{2})q^{4}-\beta _{1}q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots$
9747.2.a.bk	$9747$	$2$	9747.a	1.a	$1$	$6$	$6$	$77.830$	6.6.1272367936.1	None	✓	$2$	$1$	$-2$	$0$	$0$	$-2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(1+\beta _{5})q^{4}+\beta _{1}q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots$
9747.2.a.bl	$9747$	$2$	9747.a	1.a	$1$	$6$	$6$	$77.830$	6.6.54265221.1	None	✓	$1$	$1$	$-1$	$0$	$-5$	$1$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{5})q^{5}+\cdots$
9747.2.a.bm	$9747$	$2$	9747.a	1.a	$1$	$6$	$6$	$77.830$	6.6.54265221.1	None	✓	$1$	$0$	$-1$	$0$	$5$	$1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(1+\beta _{5})q^{5}+\cdots$
9747.2.a.bn	$9747$	$2$	9747.a	1.a	$1$	$6$	$6$	$77.830$	6.6.74097664.1	None	✓	$2$	$1$	$0$	$0$	$0$	$4$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+(1-\beta _{5})q^{7}+\cdots$
9747.2.a.bo	$9747$	$2$	9747.a	1.a	$1$	$6$	$6$	$77.830$	6.6.74097664.1	None	✓	$2$	$0$	$0$	$0$	$0$	$4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+(1-\beta _{5})q^{7}+\cdots$
9747.2.a.bp	$9747$	$2$	9747.a	1.a	$1$	$6$	$6$	$77.830$	6.6.61074432.1	None	✓	$2$	$1$	$0$	$0$	$0$	$-8$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots$
9747.2.a.bq	$9747$	$2$	9747.a	1.a	$1$	$6$	$6$	$77.830$	6.6.61074432.1	None	✓	$2$	$1$	$0$	$0$	$0$	$-8$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots$
9747.2.a.br	$9747$	$2$	9747.a	1.a	$1$	$6$	$6$	$77.830$	6.6.54265221.1	None	✓	$1$	$1$	$1$	$0$	$-5$	$1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{5})q^{5}+\cdots$
9747.2.a.bs	$9747$	$2$	9747.a	1.a	$1$	$6$	$6$	$77.830$	6.6.54265221.1	None	✓	$1$	$0$	$1$	$0$	$5$	$1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(1+\beta _{5})q^{5}+\cdots$
9747.2.a.bt	$9747$	$2$	9747.a	1.a	$1$	$6$	$6$	$77.830$	6.6.1272367936.1	None	✓	$2$	$0$	$2$	$0$	$0$	$-2$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(1+\beta _{5})q^{4}-\beta _{1}q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots$
9747.2.a.bu	$9747$	$2$	9747.a	1.a	$1$	$12$	$12$	$77.830$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$-4$	$0$	$-1$	$1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
9747.2.a.bv	$9747$	$2$	9747.a	1.a	$1$	$12$	$12$	$77.830$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$-4$	$0$	$1$	$1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(\beta _{1}+\beta _{7}+\cdots)q^{5}+\cdots$
9747.2.a.bw	$9747$	$2$	9747.a	1.a	$1$	$12$	$12$	$77.830$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$1$	$0$	$0$	$0$	$-2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots$
9747.2.a.bx	$9747$	$2$	9747.a	1.a	$1$	$12$	$12$	$77.830$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$-2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{4}-\beta _{11})q^{5}+\cdots$

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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.