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 51 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
8280.2.a.a	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓				2760.2.a.j	$1$	$0$	$0$	$0$	$-1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{7}+4q^{11}-3q^{17}-4q^{19}+\cdots$
8280.2.a.b	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓	✓			8280.2.a.b	$1$	$0$	$0$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}-2q^{13}-6q^{17}+q^{23}+\cdots$
8280.2.a.c	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓	✓			8280.2.a.c	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}-2q^{13}+2q^{17}-4q^{19}+\cdots$
8280.2.a.d	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓				920.2.a.a	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+q^{13}-q^{23}+q^{25}+\cdots$
8280.2.a.e	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓				920.2.a.b	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{11}-5q^{13}+4q^{17}-2q^{19}+\cdots$
8280.2.a.f	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓				2760.2.a.k	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{11}-6q^{17}+8q^{19}+q^{23}+\cdots$
8280.2.a.g	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓				2760.2.a.e	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{11}-2q^{13}-2q^{17}+4q^{19}+\cdots$
8280.2.a.h	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓	✓			8280.2.a.h	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{11}+4q^{13}+4q^{17}+4q^{19}+\cdots$
8280.2.a.i	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓				2760.2.a.f	$1$	$1$	$0$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}-4q^{13}+q^{17}-q^{23}+\cdots$
8280.2.a.j	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓				920.2.a.c	$1$	$1$	$0$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}+6q^{11}-2q^{13}+3q^{17}+\cdots$
8280.2.a.k	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓	✓			8280.2.a.k	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-4q^{11}+2q^{13}+2q^{17}+\cdots$
8280.2.a.l	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓				2760.2.a.g	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}+2q^{11}+2q^{13}+8q^{17}+\cdots$
8280.2.a.m	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓	✓			8280.2.a.c	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-2q^{13}-2q^{17}-4q^{19}+\cdots$
8280.2.a.n	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓	✓			8280.2.a.b	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-2q^{13}+6q^{17}-q^{23}+\cdots$
8280.2.a.o	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓				920.2.a.d	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}+q^{13}+4q^{17}-4q^{19}+\cdots$
8280.2.a.p	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓				2760.2.a.a	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{11}+2q^{13}-2q^{17}+q^{23}+\cdots$
8280.2.a.q	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓	✓			8280.2.a.h	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{11}+4q^{13}-4q^{17}+4q^{19}+\cdots$
8280.2.a.r	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓				2760.2.a.h	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{13}+6q^{17}+q^{23}+q^{25}+\cdots$
8280.2.a.s	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓	✓			8280.2.a.k	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}+4q^{11}+2q^{13}-2q^{17}+\cdots$
8280.2.a.t	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓				2760.2.a.b	$1$	$0$	$0$	$0$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+3q^{7}+2q^{11}+2q^{13}+q^{17}+\cdots$
8280.2.a.u	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓				2760.2.a.i	$1$	$0$	$0$	$0$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+3q^{7}+6q^{11}-2q^{13}-3q^{17}+\cdots$
8280.2.a.v	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓				2760.2.a.d	$1$	$0$	$0$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{7}-4q^{11}+6q^{13}+2q^{17}+\cdots$
8280.2.a.w	$8280$	$2$	8280.a	1.a	$1$	$1$	$1$	$66.116$	$\Q$	None	✓				2760.2.a.c	$1$	$0$	$0$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{7}+6q^{11}-4q^{13}-2q^{17}+\cdots$
8280.2.a.x	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	$\Q(\sqrt{2}) $	None	✓				2760.2.a.n	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(-1+2\beta )q^{7}+\beta q^{11}+(2-\beta )q^{13}+\cdots$
8280.2.a.y	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	$\Q(\sqrt{2}) $	None	✓				2760.2.a.q	$1$	$0$	$0$	$0$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}+(2-3\beta )q^{11}+(-4-\beta )q^{13}+\cdots$
8280.2.a.z	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	$\Q(\sqrt{33}) $	None	✓				2760.2.a.o	$1$	$0$	$0$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+\beta q^{7}-4q^{11}+(-2+2\beta )q^{13}+\cdots$
8280.2.a.ba	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	$\Q(\sqrt{6}) $	None	✓	✓	✓		8280.2.a.ba	$1$	$0$	$0$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(1+\beta )q^{7}+\beta q^{11}+(-2-\beta )q^{13}+\cdots$
8280.2.a.bb	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	$\Q(\sqrt{17}) $	None	✓				920.2.a.f	$1$	$0$	$0$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2\beta q^{7}+4q^{11}+(2-\beta )q^{13}+\cdots$
8280.2.a.bc	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	$\Q(\sqrt{11}) $	None	✓				2760.2.a.l	$1$	$0$	$0$	$0$	$2$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{7}+(1+\beta )q^{11}+(1-\beta )q^{13}+\cdots$
8280.2.a.bd	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	$\Q(\sqrt{17}) $	None	✓				2760.2.a.m	$1$	$1$	$0$	$0$	$2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(-1-\beta )q^{7}-2q^{11}-2q^{13}+\cdots$
8280.2.a.be	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	$\Q(\sqrt{17}) $	None	✓				2760.2.a.p	$1$	$1$	$0$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-\beta q^{7}+2\beta q^{11}+2q^{13}+(-2+\cdots)q^{17}+\cdots$
8280.2.a.bf	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	$\Q(\sqrt{17}) $	None	✓				920.2.a.e	$1$	$1$	$0$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-\beta q^{7}+2q^{11}+(-1-\beta )q^{13}+\cdots$
8280.2.a.bg	$8280$	$2$	8280.a	1.a	$1$	$2$	$2$	$66.116$	$\Q(\sqrt{6}) $	None	✓	✓	✓		8280.2.a.ba	$1$	$1$	$0$	$0$	$2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(1+\beta )q^{7}-\beta q^{11}+(-2-\beta )q^{13}+\cdots$
8280.2.a.bh	$8280$	$2$	8280.a	1.a	$1$	$3$	$3$	$66.116$	3.3.229.1	None	✓		✓		2760.2.a.t	$1$	$1$	$0$	$0$	$-3$	$1$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{5}-\beta _{1}q^{7}+(1-\beta _{2})q^{13}+(-2+\cdots)q^{17}+\cdots$
8280.2.a.bi	$8280$	$2$	8280.a	1.a	$1$	$3$	$3$	$66.116$	3.3.568.1	None	✓		✓		2760.2.a.u	$1$	$1$	$0$	$0$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(1-2\beta _{1}-\beta _{2})q^{7}+(-2-\beta _{1}+\cdots)q^{11}+\cdots$
8280.2.a.bj	$8280$	$2$	8280.a	1.a	$1$	$3$	$3$	$66.116$	3.3.2597.1	None	✓		✓		920.2.a.h	$1$	$0$	$0$	$0$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(1-\beta _{1})q^{7}+(-2-\beta _{1})q^{11}+\cdots$
8280.2.a.bk	$8280$	$2$	8280.a	1.a	$1$	$3$	$3$	$66.116$	3.3.568.1	None	✓	✓	✓		8280.2.a.bk	$1$	$1$	$0$	$0$	$-3$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(1+\beta _{1})q^{7}+(-2-\beta _{1}-\beta _{2})q^{11}+\cdots$
8280.2.a.bl	$8280$	$2$	8280.a	1.a	$1$	$3$	$3$	$66.116$	3.3.229.1	None	✓				920.2.a.i	$1$	$0$	$0$	$0$	$-3$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(2-\beta _{2})q^{7}+(-1-\beta _{1})q^{11}+\cdots$
8280.2.a.bm	$8280$	$2$	8280.a	1.a	$1$	$3$	$3$	$66.116$	3.3.316.1	None	✓				2760.2.a.r	$1$	$0$	$0$	$0$	$3$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(-2+\beta _{2})q^{7}+(-1+\beta _{1}+\beta _{2})q^{11}+\cdots$
8280.2.a.bn	$8280$	$2$	8280.a	1.a	$1$	$3$	$3$	$66.116$	3.3.1436.1	None	✓				2760.2.a.s	$1$	$1$	$0$	$0$	$3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(-1+\beta _{2})q^{7}+(-1-\beta _{1}-\beta _{2})q^{11}+\cdots$
8280.2.a.bo	$8280$	$2$	8280.a	1.a	$1$	$3$	$3$	$66.116$	3.3.621.1	None	✓				920.2.a.g	$1$	$0$	$0$	$0$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(1+\beta _{1})q^{7}+(-1+\beta _{1}-\beta _{2})q^{11}+\cdots$
8280.2.a.bp	$8280$	$2$	8280.a	1.a	$1$	$3$	$3$	$66.116$	3.3.568.1	None	✓	✓	✓		8280.2.a.bk	$1$	$0$	$0$	$0$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(1+\beta _{1})q^{7}+(2+\beta _{1}+\beta _{2})q^{11}+\cdots$
8280.2.a.bq	$8280$	$2$	8280.a	1.a	$1$	$4$	$4$	$66.116$	4.4.54764.1	None	✓		✓		2760.2.a.v	$1$	$1$	$0$	$0$	$4$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{5}-\beta _{1}q^{7}+\beta _{3}q^{11}+(-1+\beta _{1}+\cdots)q^{13}+\cdots$
8280.2.a.br	$8280$	$2$	8280.a	1.a	$1$	$5$	$5$	$66.116$	5.5.20087896.1	None	✓		✓		2760.2.a.w	$1$	$0$	$0$	$0$	$-5$	$-4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{5}+(-1+\beta _{1})q^{7}+(1-\beta _{2})q^{11}+\cdots$
8280.2.a.bs	$8280$	$2$	8280.a	1.a	$1$	$5$	$5$	$66.116$	5.5.13955077.1	None	✓		✓		920.2.a.j	$1$	$0$	$0$	$0$	$5$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(-\beta _{3}-\beta _{4})q^{7}+(-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$
8280.2.a.bt	$8280$	$2$	8280.a	1.a	$1$	$6$	$6$	$66.116$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓	✓		8280.2.a.bt	$1$	$1$	$0$	$0$	$-6$	$-2$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{5}-\beta _{2}q^{7}+(1+\beta _{3})q^{11}+\beta _{4}q^{13}+\cdots$
8280.2.a.bu	$8280$	$2$	8280.a	1.a	$1$	$6$	$6$	$66.116$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓	✓		8280.2.a.bt	$1$	$0$	$0$	$0$	$6$	$-2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{5}-\beta _{2}q^{7}+(-1-\beta _{3})q^{11}+\beta _{4}q^{13}+\cdots$
8280.2.a.bv	$8280$	$2$	8280.a	1.a	$1$	$7$	$7$	$66.116$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	8280.2.a.bv	$1$	$0$	$0$	$0$	$-7$	$-6$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{5}+(-1+\beta _{4})q^{7}+\beta _{3}q^{11}+(-2+\cdots)q^{13}+\cdots$
8280.2.a.bw	$8280$	$2$	8280.a	1.a	$1$	$7$	$7$	$66.116$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	8280.2.a.bv	$1$	$1$	$0$	$0$	$7$	$-6$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+q^{5}+(-1+\beta _{4})q^{7}-\beta _{3}q^{11}+(-2+\cdots)q^{13}+\cdots$
8280.2.p.a	$8280$	$2$	8280.p	69.c	$2$	$48$	$48$	$66.116$		None		✓			8280.2.p.a	$2$	$0$	$0$	$0$	$-48$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.