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 (47 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	11	47	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9306.2.a.a	$9306$	$2$	9306.a	1.a	$1$	$1$	$1$	$74.309$	$\Q$	None	✓				3102.2.a.i	$1$	$1$	$-1$	$0$	$-2$	$-4$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-4q^{7}-q^{8}+2q^{10}+\cdots$
9306.2.a.b	$9306$	$2$	9306.a	1.a	$1$	$1$	$1$	$74.309$	$\Q$	None	✓	✓			9306.2.a.b	$1$	$2$	$-1$	$0$	$-2$	$-2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-2q^{7}-q^{8}+2q^{10}+\cdots$
9306.2.a.c	$9306$	$2$	9306.a	1.a	$1$	$1$	$1$	$74.309$	$\Q$	None	✓				1034.2.a.c	$1$	$1$	$-1$	$0$	$0$	$-5$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-5q^{7}-q^{8}-q^{11}+q^{13}+\cdots$
9306.2.a.d	$9306$	$2$	9306.a	1.a	$1$	$1$	$1$	$74.309$	$\Q$	None	✓				3102.2.a.j	$1$	$0$	$-1$	$0$	$0$	$-2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}+q^{11}-4q^{13}+\cdots$
9306.2.a.e	$9306$	$2$	9306.a	1.a	$1$	$1$	$1$	$74.309$	$\Q$	None	✓	✓			9306.2.a.e	$1$	$0$	$-1$	$0$	$0$	$-2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}+q^{11}-2q^{13}+\cdots$
9306.2.a.f	$9306$	$2$	9306.a	1.a	$1$	$1$	$1$	$74.309$	$\Q$	None	✓				1034.2.a.b	$1$	$1$	$-1$	$0$	$2$	$1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots$
9306.2.a.g	$9306$	$2$	9306.a	1.a	$1$	$1$	$1$	$74.309$	$\Q$	None	✓				3102.2.a.h	$1$	$1$	$-1$	$0$	$4$	$2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}+2q^{7}-q^{8}-4q^{10}+\cdots$
9306.2.a.h	$9306$	$2$	9306.a	1.a	$1$	$1$	$1$	$74.309$	$\Q$	None	✓				3102.2.a.b	$1$	$1$	$1$	$0$	$-2$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}+q^{11}+\cdots$
9306.2.a.i	$9306$	$2$	9306.a	1.a	$1$	$1$	$1$	$74.309$	$\Q$	None	✓				3102.2.a.f	$1$	$0$	$1$	$0$	$0$	$-3$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{7}+q^{8}+q^{11}+q^{13}+\cdots$
9306.2.a.j	$9306$	$2$	9306.a	1.a	$1$	$1$	$1$	$74.309$	$\Q$	None	✓	✓			9306.2.a.e	$1$	$1$	$1$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}-q^{11}-2q^{13}+\cdots$
9306.2.a.k	$9306$	$2$	9306.a	1.a	$1$	$1$	$1$	$74.309$	$\Q$	None	✓				3102.2.a.g	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}+q^{11}-4q^{13}+\cdots$
9306.2.a.l	$9306$	$2$	9306.a	1.a	$1$	$1$	$1$	$74.309$	$\Q$	None	✓				1034.2.a.a	$1$	$0$	$1$	$0$	$2$	$-5$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}-5q^{7}+q^{8}+2q^{10}+\cdots$
9306.2.a.m	$9306$	$2$	9306.a	1.a	$1$	$1$	$1$	$74.309$	$\Q$	None	✓	✓			9306.2.a.b	$1$	$1$	$1$	$0$	$2$	$-2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}-2q^{7}+q^{8}+2q^{10}+\cdots$
9306.2.a.n	$9306$	$2$	9306.a	1.a	$1$	$1$	$1$	$74.309$	$\Q$	None	✓				3102.2.a.e	$1$	$0$	$1$	$0$	$2$	$4$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+4q^{7}+q^{8}+2q^{10}+\cdots$
9306.2.a.o	$9306$	$2$	9306.a	1.a	$1$	$1$	$1$	$74.309$	$\Q$	None	✓				3102.2.a.a	$1$	$0$	$1$	$0$	$4$	$-3$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{5}-3q^{7}+q^{8}+4q^{10}+\cdots$
9306.2.a.p	$9306$	$2$	9306.a	1.a	$1$	$1$	$1$	$74.309$	$\Q$	None	✓				3102.2.a.c	$1$	$0$	$1$	$0$	$4$	$-2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{5}-2q^{7}+q^{8}+4q^{10}+\cdots$
9306.2.a.q	$9306$	$2$	9306.a	1.a	$1$	$1$	$1$	$74.309$	$\Q$	None	✓				3102.2.a.d	$1$	$0$	$1$	$0$	$4$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{5}+q^{8}+4q^{10}-q^{11}+\cdots$
9306.2.a.r	$9306$	$2$	9306.a	1.a	$1$	$2$	$2$	$74.309$	$\Q(\sqrt{2}) $	None	✓				3102.2.a.l	$1$	$0$	$-2$	$0$	$4$	$-4$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2+\beta )q^{5}+(-2+\beta )q^{7}+\cdots$
9306.2.a.s	$9306$	$2$	9306.a	1.a	$1$	$2$	$2$	$74.309$	$\Q(\sqrt{2}) $	None	✓				1034.2.a.d	$1$	$1$	$-2$	$0$	$4$	$-2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2+\beta )q^{5}+(-1-\beta )q^{7}+\cdots$
9306.2.a.t	$9306$	$2$	9306.a	1.a	$1$	$2$	$2$	$74.309$	$\Q(\sqrt{3}) $	None	✓				3102.2.a.k	$1$	$1$	$2$	$0$	$2$	$-2$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1+\beta )q^{5}+(-1-\beta )q^{7}+\cdots$
9306.2.a.u	$9306$	$2$	9306.a	1.a	$1$	$3$	$3$	$74.309$	3.3.961.1	None	✓				3102.2.a.m	$1$	$1$	$-3$	$0$	$0$	$1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{1}q^{7}-q^{8}+q^{11}+(-2+\cdots)q^{13}+\cdots$
9306.2.a.v	$9306$	$2$	9306.a	1.a	$1$	$3$	$3$	$74.309$	3.3.148.1	None	✓				3102.2.a.n	$1$	$0$	$-3$	$0$	$4$	$-4$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{1})q^{5}+(-2+2\beta _{1}+\cdots)q^{7}+\cdots$
9306.2.a.w	$9306$	$2$	9306.a	1.a	$1$	$3$	$3$	$74.309$	3.3.148.1	None	✓				1034.2.a.e	$1$	$1$	$3$	$0$	$0$	$-1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{7}+q^{8}+\cdots$
9306.2.a.x	$9306$	$2$	9306.a	1.a	$1$	$3$	$3$	$74.309$	3.3.148.1	None	✓				1034.2.a.f	$1$	$1$	$3$	$0$	$2$	$-3$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1-\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+\cdots$
9306.2.a.y	$9306$	$2$	9306.a	1.a	$1$	$4$	$4$	$74.309$	4.4.37108.1	None	✓				3102.2.a.r	$1$	$1$	$-4$	$0$	$2$	$-3$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
9306.2.a.z	$9306$	$2$	9306.a	1.a	$1$	$4$	$4$	$74.309$	4.4.25808.1	None	✓				3102.2.a.s	$1$	$0$	$-4$	$0$	$2$	$4$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
9306.2.a.ba	$9306$	$2$	9306.a	1.a	$1$	$4$	$4$	$74.309$	4.4.15188.1	None	✓				3102.2.a.p	$1$	$0$	$4$	$0$	$-2$	$-5$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{2})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots$
9306.2.a.bb	$9306$	$2$	9306.a	1.a	$1$	$4$	$4$	$74.309$	4.4.33428.1	None	✓				3102.2.a.o	$1$	$1$	$4$	$0$	$-2$	$-4$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
9306.2.a.bc	$9306$	$2$	9306.a	1.a	$1$	$4$	$4$	$74.309$	4.4.16448.1	None	✓				3102.2.a.q	$1$	$1$	$4$	$0$	$-2$	$2$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{3}q^{5}+\beta _{1}q^{7}+q^{8}+\cdots$
9306.2.a.bd	$9306$	$2$	9306.a	1.a	$1$	$5$	$5$	$74.309$	5.5.4695248.1	None	✓		✓		3102.2.a.w	$1$	$1$	$-5$	$0$	$-4$	$1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
9306.2.a.be	$9306$	$2$	9306.a	1.a	$1$	$5$	$5$	$74.309$	5.5.2949696.1	None	✓				3102.2.a.v	$1$	$0$	$-5$	$0$	$-2$	$6$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta _{1}q^{5}+(1+\beta _{3})q^{7}-q^{8}+\cdots$
9306.2.a.bf	$9306$	$2$	9306.a	1.a	$1$	$5$	$5$	$74.309$	5.5.1280720.1	None	✓		✓		3102.2.a.u	$1$	$1$	$5$	$0$	$-6$	$-4$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{4})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
9306.2.a.bg	$9306$	$2$	9306.a	1.a	$1$	$5$	$5$	$74.309$	5.5.10976256.1	None	✓				3102.2.a.t	$1$	$0$	$5$	$0$	$-2$	$8$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots$
9306.2.a.bh	$9306$	$2$	9306.a	1.a	$1$	$6$	$6$	$74.309$	6.6.143539456.1	None	✓		✓		3102.2.a.x	$1$	$1$	$-6$	$0$	$-6$	$7$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta _{5})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
9306.2.a.bi	$9306$	$2$	9306.a	1.a	$1$	$6$	$6$	$74.309$	6.6.373410513.1	None	✓				1034.2.a.g	$1$	$0$	$6$	$0$	$-3$	$8$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{5})q^{5}+(1-\beta _{3}+\cdots)q^{7}+\cdots$
9306.2.a.bj	$9306$	$2$	9306.a	1.a	$1$	$7$	$7$	$74.309$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓		9306.2.a.bj	$1$	$0$	$-7$	$0$	$4$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1-\beta _{1}-\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
9306.2.a.bk	$9306$	$2$	9306.a	1.a	$1$	$7$	$7$	$74.309$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓		9306.2.a.bk	$1$	$0$	$-7$	$0$	$8$	$-4$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{1})q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots$
9306.2.a.bl	$9306$	$2$	9306.a	1.a	$1$	$7$	$7$	$74.309$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓		9306.2.a.bk	$1$	$1$	$7$	$0$	$-8$	$-4$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{1})q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots$
9306.2.a.bm	$9306$	$2$	9306.a	1.a	$1$	$7$	$7$	$74.309$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓		9306.2.a.bj	$1$	$1$	$7$	$0$	$-4$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
9306.2.a.bn	$9306$	$2$	9306.a	1.a	$1$	$7$	$7$	$74.309$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		3102.2.a.y	$1$	$0$	$7$	$0$	$0$	$3$	$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta _{1}q^{5}+\beta _{2}q^{7}+q^{8}+\cdots$
9306.2.a.bo	$9306$	$2$	9306.a	1.a	$1$	$7$	$7$	$74.309$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		1034.2.a.h	$1$	$0$	$7$	$0$	$3$	$5$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{2}q^{5}+(1-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots$
9306.2.a.bp	$9306$	$2$	9306.a	1.a	$1$	$8$	$8$	$74.309$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓		✓		1034.2.a.i	$1$	$0$	$-8$	$0$	$-3$	$2$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{6}q^{5}-\beta _{3}q^{7}-q^{8}+\cdots$
9306.2.a.bq	$9306$	$2$	9306.a	1.a	$1$	$9$	$9$	$74.309$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓		✓		1034.2.a.j	$1$	$0$	$-9$	$0$	$-5$	$8$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta _{3})q^{5}+(1+\beta _{6}+\cdots)q^{7}+\cdots$
9306.2.a.br	$9306$	$2$	9306.a	1.a	$1$	$11$	$11$	$74.309$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓	✓	9306.2.a.br	$1$	$1$	$-11$	$0$	$-6$	$4$	$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta _{1})q^{5}+\beta _{4}q^{7}+\cdots$
9306.2.a.bs	$9306$	$2$	9306.a	1.a	$1$	$11$	$11$	$74.309$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓	✓	9306.2.a.bs	$1$	$1$	$-11$	$0$	$-4$	$0$	$+$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta _{1}q^{5}+\beta _{2}q^{7}-q^{8}+\cdots$
9306.2.a.bt	$9306$	$2$	9306.a	1.a	$1$	$11$	$11$	$74.309$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓	✓	9306.2.a.bs	$1$	$0$	$11$	$0$	$4$	$0$	$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{1}q^{5}+\beta _{2}q^{7}+q^{8}+\cdots$
9306.2.a.bu	$9306$	$2$	9306.a	1.a	$1$	$11$	$11$	$74.309$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓	✓	9306.2.a.br	$1$	$0$	$11$	$0$	$6$	$4$	$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1-\beta _{1})q^{5}+\beta _{4}q^{7}+q^{8}+\cdots$

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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.