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 (48 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	97	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8730.2.a.a	$8730$	$2$	8730.a	1.a	$1$	$1$	$1$	$69.709$	$\Q$	None	✓				970.2.a.b	$1$	$1$	$-1$	$0$	$-1$	$-4$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots$
8730.2.a.b	$8730$	$2$	8730.a	1.a	$1$	$1$	$1$	$69.709$	$\Q$	None	✓				2910.2.a.k	$1$	$1$	$-1$	$0$	$-1$	$-4$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots$
8730.2.a.c	$8730$	$2$	8730.a	1.a	$1$	$1$	$1$	$69.709$	$\Q$	None	✓				2910.2.a.h	$1$	$0$	$-1$	$0$	$-1$	$-2$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots$
8730.2.a.d	$8730$	$2$	8730.a	1.a	$1$	$1$	$1$	$69.709$	$\Q$	None	✓				2910.2.a.i	$1$	$1$	$-1$	$0$	$-1$	$2$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots$
8730.2.a.e	$8730$	$2$	8730.a	1.a	$1$	$1$	$1$	$69.709$	$\Q$	None	✓	✓			8730.2.a.e	$1$	$1$	$-1$	$0$	$1$	$-4$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots$
8730.2.a.f	$8730$	$2$	8730.a	1.a	$1$	$1$	$1$	$69.709$	$\Q$	None	✓				2910.2.a.g	$1$	$0$	$-1$	$0$	$1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+4q^{11}+\cdots$
8730.2.a.g	$8730$	$2$	8730.a	1.a	$1$	$1$	$1$	$69.709$	$\Q$	None	✓				2910.2.a.j	$1$	$0$	$-1$	$0$	$1$	$2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots$
8730.2.a.h	$8730$	$2$	8730.a	1.a	$1$	$1$	$1$	$69.709$	$\Q$	None	✓	✓			8730.2.a.e	$1$	$1$	$1$	$0$	$-1$	$-4$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots$
8730.2.a.i	$8730$	$2$	8730.a	1.a	$1$	$1$	$1$	$69.709$	$\Q$	None	✓				2910.2.a.f	$1$	$0$	$1$	$0$	$-1$	$2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots$
8730.2.a.j	$8730$	$2$	8730.a	1.a	$1$	$1$	$1$	$69.709$	$\Q$	None	✓				2910.2.a.c	$1$	$0$	$1$	$0$	$-1$	$2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots$
8730.2.a.k	$8730$	$2$	8730.a	1.a	$1$	$1$	$1$	$69.709$	$\Q$	None	✓				2910.2.a.b	$1$	$0$	$1$	$0$	$-1$	$2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots$
8730.2.a.l	$8730$	$2$	8730.a	1.a	$1$	$1$	$1$	$69.709$	$\Q$	None	✓				2910.2.a.d	$1$	$1$	$1$	$0$	$1$	$-2$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots$
8730.2.a.m	$8730$	$2$	8730.a	1.a	$1$	$1$	$1$	$69.709$	$\Q$	None	✓				970.2.a.a	$1$	$1$	$1$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-3q^{11}+\cdots$
8730.2.a.n	$8730$	$2$	8730.a	1.a	$1$	$1$	$1$	$69.709$	$\Q$	None	✓				2910.2.a.e	$1$	$1$	$1$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-2q^{13}+\cdots$
8730.2.a.o	$8730$	$2$	8730.a	1.a	$1$	$1$	$1$	$69.709$	$\Q$	None	✓				2910.2.a.a	$1$	$1$	$1$	$0$	$1$	$2$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots$
8730.2.a.p	$8730$	$2$	8730.a	1.a	$1$	$2$	$2$	$69.709$	$\Q(\sqrt{5}) $	None	✓				970.2.a.c	$1$	$0$	$-2$	$0$	$-2$	$-4$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots$
8730.2.a.q	$8730$	$2$	8730.a	1.a	$1$	$2$	$2$	$69.709$	$\Q(\sqrt{6}) $	None	✓				2910.2.a.n	$1$	$0$	$-2$	$0$	$-2$	$-4$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots$
8730.2.a.r	$8730$	$2$	8730.a	1.a	$1$	$2$	$2$	$69.709$	$\Q(\sqrt{13}) $	None	✓	✓			8730.2.a.r	$1$	$0$	$-2$	$0$	$-2$	$-1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-\beta q^{7}-q^{8}+q^{10}+\cdots$
8730.2.a.s	$8730$	$2$	8730.a	1.a	$1$	$2$	$2$	$69.709$	$\Q(\sqrt{5}) $	None	✓				970.2.a.d	$1$	$0$	$-2$	$0$	$2$	$-2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-2\beta q^{7}-q^{8}-q^{10}+\cdots$
8730.2.a.t	$8730$	$2$	8730.a	1.a	$1$	$2$	$2$	$69.709$	$\Q(\sqrt{5}) $	None	✓	✓			8730.2.a.t	$1$	$1$	$-2$	$0$	$2$	$-2$	$+$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+(-1-\beta )q^{7}-q^{8}+\cdots$
8730.2.a.u	$8730$	$2$	8730.a	1.a	$1$	$2$	$2$	$69.709$	$\Q(\sqrt{5}) $	None	✓	✓			8730.2.a.t	$1$	$1$	$2$	$0$	$-2$	$-2$	$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+(-1-\beta )q^{7}+q^{8}+\cdots$
8730.2.a.v	$8730$	$2$	8730.a	1.a	$1$	$2$	$2$	$69.709$	$\Q(\sqrt{2}) $	None	✓				2910.2.a.m	$1$	$1$	$2$	$0$	$-2$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+(2-2\beta )q^{11}+\cdots$
8730.2.a.w	$8730$	$2$	8730.a	1.a	$1$	$2$	$2$	$69.709$	$\Q(\sqrt{13}) $	None	✓				2910.2.a.l	$1$	$1$	$2$	$0$	$2$	$-1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-\beta q^{7}+q^{8}+q^{10}+\cdots$
8730.2.a.x	$8730$	$2$	8730.a	1.a	$1$	$2$	$2$	$69.709$	$\Q(\sqrt{13}) $	None	✓	✓			8730.2.a.r	$1$	$0$	$2$	$0$	$2$	$-1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-\beta q^{7}+q^{8}+q^{10}+\cdots$
8730.2.a.y	$8730$	$2$	8730.a	1.a	$1$	$3$	$3$	$69.709$	3.3.316.1	None	✓				2910.2.a.o	$1$	$0$	$-3$	$0$	$3$	$-2$	$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+(-1-\beta _{1}-\beta _{2})q^{7}+\cdots$
8730.2.a.z	$8730$	$2$	8730.a	1.a	$1$	$3$	$3$	$69.709$	3.3.229.1	None	✓				970.2.a.f	$1$	$1$	$3$	$0$	$-3$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+(-\beta _{1}+\cdots)q^{11}+\cdots$
8730.2.a.ba	$8730$	$2$	8730.a	1.a	$1$	$3$	$3$	$69.709$	3.3.229.1	None	✓		✓		970.2.a.e	$1$	$1$	$3$	$0$	$3$	$-4$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+(-2-2\beta _{2})q^{7}+\cdots$
8730.2.a.bb	$8730$	$2$	8730.a	1.a	$1$	$4$	$4$	$69.709$	4.4.13025.1	None	✓				2910.2.a.q	$1$	$1$	$-4$	$0$	$-4$	$1$	$+$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+(\beta _{1}-\beta _{3})q^{7}-q^{8}+\cdots$
8730.2.a.bc	$8730$	$2$	8730.a	1.a	$1$	$4$	$4$	$69.709$	$\Q(\zeta_{16})^+$	None	✓				2910.2.a.r	$1$	$1$	$-4$	$0$	$4$	$-8$	$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+(-2+\beta _{1})q^{7}-q^{8}+\cdots$
8730.2.a.bd	$8730$	$2$	8730.a	1.a	$1$	$4$	$4$	$69.709$	4.4.39528.1	None	✓				2910.2.a.p	$1$	$1$	$-4$	$0$	$4$	$1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-\beta _{3}q^{7}-q^{8}-q^{10}+\cdots$
8730.2.a.be	$8730$	$2$	8730.a	1.a	$1$	$4$	$4$	$69.709$	4.4.2225.1	None	✓	✓	✓		8730.2.a.be	$1$	$1$	$-4$	$0$	$4$	$1$	$+$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{7}+\cdots$
8730.2.a.bf	$8730$	$2$	8730.a	1.a	$1$	$4$	$4$	$69.709$	4.4.31225.1	None	✓		✓		2910.2.a.s	$1$	$0$	$-4$	$0$	$4$	$3$	$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+(1-\beta _{1})q^{7}-q^{8}+\cdots$
8730.2.a.bg	$8730$	$2$	8730.a	1.a	$1$	$4$	$4$	$69.709$	4.4.2225.1	None	✓	✓	✓		8730.2.a.be	$1$	$1$	$4$	$0$	$-4$	$1$	$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{7}+\cdots$
8730.2.a.bh	$8730$	$2$	8730.a	1.a	$1$	$4$	$4$	$69.709$	4.4.5744.1	None	✓				970.2.a.g	$1$	$0$	$4$	$0$	$4$	$2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+(\beta _{1}+\beta _{2})q^{7}+q^{8}+\cdots$
8730.2.a.bi	$8730$	$2$	8730.a	1.a	$1$	$5$	$5$	$69.709$	5.5.1287152.1	None	✓		✓		970.2.a.j	$1$	$1$	$-5$	$0$	$-5$	$8$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+(1+\beta _{1}-\beta _{4})q^{7}+\cdots$
8730.2.a.bj	$8730$	$2$	8730.a	1.a	$1$	$5$	$5$	$69.709$	5.5.516112.1	None	✓		✓		970.2.a.i	$1$	$1$	$-5$	$0$	$5$	$2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-\beta _{4}q^{7}-q^{8}-q^{10}+\cdots$
8730.2.a.bk	$8730$	$2$	8730.a	1.a	$1$	$5$	$5$	$69.709$	5.5.809024.1	None	✓				970.2.a.h	$1$	$0$	$5$	$0$	$-5$	$-6$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+(-1-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
8730.2.a.bl	$8730$	$2$	8730.a	1.a	$1$	$5$	$5$	$69.709$	5.5.4442688.1	None	✓				2910.2.a.t	$1$	$0$	$5$	$0$	$5$	$2$	$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+\beta _{4}q^{7}+q^{8}+q^{10}+\cdots$
8730.2.a.bm	$8730$	$2$	8730.a	1.a	$1$	$5$	$5$	$69.709$	5.5.4363144.1	None	✓				2910.2.a.u	$1$	$0$	$5$	$0$	$5$	$7$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+(1+\beta _{2})q^{7}+q^{8}+\cdots$
8730.2.a.bn	$8730$	$2$	8730.a	1.a	$1$	$6$	$6$	$69.709$	6.6.4222000.1	None	✓	✓	✓	✓	8730.2.a.bn	$1$	$1$	$-6$	$0$	$-6$	$-5$	$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+(-1+\beta _{2}-\beta _{5})q^{7}+\cdots$
8730.2.a.bo	$8730$	$2$	8730.a	1.a	$1$	$6$	$6$	$69.709$	6.6.742608384.1	None	✓		✓		2910.2.a.v	$1$	$1$	$6$	$0$	$-6$	$-3$	$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+(-1-\beta _{3})q^{7}+q^{8}+\cdots$
8730.2.a.bp	$8730$	$2$	8730.a	1.a	$1$	$6$	$6$	$69.709$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓		✓		2910.2.a.w	$1$	$0$	$6$	$0$	$-6$	$1$	$-$	$-$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-\beta _{5}q^{7}+q^{8}-q^{10}+\cdots$
8730.2.a.bq	$8730$	$2$	8730.a	1.a	$1$	$6$	$6$	$69.709$	6.6.4222000.1	None	✓	✓	✓	✓	8730.2.a.bn	$1$	$1$	$6$	$0$	$6$	$-5$	$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+(-1+\beta _{2}-\beta _{5})q^{7}+\cdots$
8730.2.a.br	$8730$	$2$	8730.a	1.a	$1$	$7$	$7$	$69.709$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		2910.2.a.x	$1$	$0$	$-7$	$0$	$-7$	$7$	$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+(1-\beta _{1})q^{7}-q^{8}+\cdots$
8730.2.a.bs	$8730$	$2$	8730.a	1.a	$1$	$8$	$8$	$69.709$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓	✓	8730.2.a.bs	$1$	$0$	$-8$	$0$	$8$	$5$	$+$	$+$	$-$	$+$	$-$	$2\cdot 5$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+(1-\beta _{6})q^{7}-q^{8}+\cdots$
8730.2.a.bt	$8730$	$2$	8730.a	1.a	$1$	$8$	$8$	$69.709$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓	✓	8730.2.a.bs	$1$	$0$	$8$	$0$	$-8$	$5$	$-$	$+$	$+$	$+$	$-$	$2\cdot 5$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+(1-\beta _{6})q^{7}+q^{8}+\cdots$
8730.2.a.bu	$8730$	$2$	8730.a	1.a	$1$	$9$	$9$	$69.709$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓		8730.2.a.bu	$1$	$0$	$-9$	$0$	$-9$	$6$	$+$	$+$	$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+(1-\beta _{2})q^{7}-q^{8}+\cdots$
8730.2.a.bv	$8730$	$2$	8730.a	1.a	$1$	$9$	$9$	$69.709$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓		8730.2.a.bu	$1$	$0$	$9$	$0$	$9$	$6$	$-$	$+$	$-$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+(1-\beta _{2})q^{7}+q^{8}+\cdots$

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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.