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 (50 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	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4275.2.a.a	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	$\Q$	None	✓				57.2.a.b	$1$	$0$	$-2$	$0$	$0$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-3q^{7}+3q^{11}+6q^{13}+\cdots$
4275.2.a.b	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	$\Q$	None	✓				57.2.a.a	$1$	$0$	$-2$	$0$	$0$	$5$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+5q^{7}-q^{11}-2q^{13}+\cdots$
4275.2.a.c	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	$\Q$	None	✓				1425.2.a.e	$1$	$1$	$-1$	$0$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-4q^{7}+3q^{8}-3q^{11}+\cdots$
4275.2.a.d	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	$\Q$	None	✓				855.2.c.a	$1$	$1$	$-1$	$0$	$0$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{7}+3q^{8}-2q^{11}+\cdots$
4275.2.a.e	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	$\Q$	None	✓				95.2.b.a	$1$	$0$	$-1$	$0$	$0$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{7}+3q^{8}+4q^{11}+\cdots$
4275.2.a.f	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	$\Q$	None	✓				1425.2.a.b	$1$	$0$	$-1$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}-5q^{11}-4q^{13}+\cdots$
4275.2.a.g	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	$\Q$	None	✓				855.2.c.a	$1$	$1$	$-1$	$0$	$0$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+2q^{7}+3q^{8}+2q^{11}+\cdots$
4275.2.a.h	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	$\Q$	None	✓				285.2.a.a	$1$	$1$	$-1$	$0$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+2q^{7}+3q^{8}+6q^{11}+\cdots$
4275.2.a.i	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	$\Q$	None	✓				19.2.a.a	$1$	$1$	$0$	$0$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{7}-3q^{11}+4q^{13}+4q^{16}+\cdots$
4275.2.a.j	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	$\Q$	None	✓				285.2.a.c	$1$	$0$	$1$	$0$	$0$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-4q^{7}-3q^{8}-4q^{11}+\cdots$
4275.2.a.k	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	$\Q$	None	✓				855.2.c.a	$1$	$1$	$1$	$0$	$0$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-2q^{7}-3q^{8}+2q^{11}+\cdots$
4275.2.a.l	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	$\Q$	None	✓				1425.2.a.b	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-3q^{8}-5q^{11}+4q^{13}+\cdots$
4275.2.a.m	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	$\Q$	None	✓				57.2.a.c	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-3q^{8}-6q^{13}-q^{16}+\cdots$
4275.2.a.n	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	$\Q$	None	✓				855.2.c.a	$1$	$1$	$1$	$0$	$0$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{7}-3q^{8}-2q^{11}+\cdots$
4275.2.a.o	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	$\Q$	None	✓				285.2.a.b	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{7}-3q^{8}+2q^{11}+\cdots$
4275.2.a.p	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	$\Q$	None	✓				95.2.b.a	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{7}-3q^{8}+4q^{11}+\cdots$
4275.2.a.q	$4275$	$2$	4275.a	1.a	$1$	$1$	$1$	$34.136$	$\Q$	None	✓				1425.2.a.e	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+4q^{7}-3q^{8}-3q^{11}+\cdots$
4275.2.a.r	$4275$	$2$	4275.a	1.a	$1$	$2$	$2$	$34.136$	$\Q(\sqrt{5}) $	None	✓				1425.2.a.m	$1$	$1$	$-1$	$0$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+(-1-2\beta )q^{7}+\cdots$
4275.2.a.s	$4275$	$2$	4275.a	1.a	$1$	$2$	$2$	$34.136$	$\Q(\sqrt{5}) $	None	✓				1425.2.a.n	$1$	$0$	$-1$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots$
4275.2.a.t	$4275$	$2$	4275.a	1.a	$1$	$2$	$2$	$34.136$	$\Q(\sqrt{3}) $	None	✓				285.2.a.e	$1$	$1$	$0$	$0$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+(1-\beta )q^{7}-\beta q^{8}+(-3+\cdots)q^{11}+\cdots$
4275.2.a.u	$4275$	$2$	4275.a	1.a	$1$	$2$	$2$	$34.136$	$\Q(\sqrt{7}) $	None	✓				285.2.a.d	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+5q^{4}+(1+\beta )q^{7}+3\beta q^{8}+\cdots$
4275.2.a.v	$4275$	$2$	4275.a	1.a	$1$	$2$	$2$	$34.136$	$\Q(\sqrt{5}) $	None	✓				1425.2.a.n	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(1-2\beta )q^{7}+\cdots$
4275.2.a.w	$4275$	$2$	4275.a	1.a	$1$	$2$	$2$	$34.136$	$\Q(\sqrt{5}) $	None	✓				1425.2.a.m	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(1+2\beta )q^{7}+\cdots$
4275.2.a.x	$4275$	$2$	4275.a	1.a	$1$	$2$	$2$	$34.136$	$\Q(\sqrt{2}) $	None	✓				285.2.a.f	$1$	$1$	$2$	$0$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(-2-\beta )q^{7}+\cdots$
4275.2.a.y	$4275$	$2$	4275.a	1.a	$1$	$2$	$2$	$34.136$	$\Q(\sqrt{2}) $	None	✓				285.2.a.g	$1$	$0$	$2$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+\beta q^{7}+(3+\cdots)q^{8}+\cdots$
4275.2.a.z	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	$\Q(\zeta_{14})^+$	None	✓				475.2.a.d	$1$	$1$	$-4$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+\cdots$
4275.2.a.ba	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.169.1	None	✓				475.2.a.e	$1$	$1$	$-2$	$0$	$0$	$4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
4275.2.a.bb	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.148.1	None	✓				855.2.a.h	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{2}q^{7}+(-1+\cdots)q^{8}+\cdots$
4275.2.a.bc	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.148.1	None	✓				855.2.a.j	$1$	$0$	$-1$	$0$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(2-2\beta _{1}-\beta _{2})q^{7}+\cdots$
4275.2.a.bd	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.148.1	None	✓				285.2.c.a	$1$	$1$	$-1$	$0$	$0$	$8$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(3-\beta _{1})q^{7}+\cdots$
4275.2.a.be	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.621.1	None	✓				1425.2.a.u	$1$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}-\beta _{2}q^{7}+\cdots$
4275.2.a.bf	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.837.1	None	✓				1425.2.a.t	$1$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}+\beta _{2})q^{7}+\cdots$
4275.2.a.bg	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.837.1	None	✓				1425.2.a.t	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}-\beta _{2})q^{7}+\cdots$
4275.2.a.bh	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.621.1	None	✓				1425.2.a.u	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+\beta _{2}q^{7}+\cdots$
4275.2.a.bi	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.148.1	None	✓				285.2.c.a	$1$	$1$	$1$	$0$	$0$	$-8$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-3+\beta _{1}+\cdots)q^{7}+\cdots$
4275.2.a.bj	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.148.1	None	✓				855.2.a.h	$1$	$1$	$1$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{2}q^{7}+(1+\cdots)q^{8}+\cdots$
4275.2.a.bk	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.148.1	None	✓				95.2.a.a	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-2\beta _{2}q^{7}+(1+\cdots)q^{8}+\cdots$
4275.2.a.bl	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.148.1	None	✓				855.2.a.j	$1$	$0$	$1$	$0$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(2-2\beta _{1}-\beta _{2})q^{7}+\cdots$
4275.2.a.bm	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	3.3.169.1	None	✓				475.2.a.e	$1$	$0$	$2$	$0$	$0$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{7}+\cdots$
4275.2.a.bn	$4275$	$2$	4275.a	1.a	$1$	$3$	$3$	$34.136$	$\Q(\zeta_{14})^+$	None	✓				475.2.a.d	$1$	$0$	$4$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{7}+\cdots$
4275.2.a.bo	$4275$	$2$	4275.a	1.a	$1$	$4$	$4$	$34.136$	4.4.11344.1	None	✓		✓		95.2.a.b	$1$	$1$	$-2$	$0$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-2+2\beta _{1}+\cdots)q^{7}+\cdots$
4275.2.a.bp	$4275$	$2$	4275.a	1.a	$1$	$4$	$4$	$34.136$	4.4.13068.1	None	✓				171.2.a.e	$2$	$0$	$0$	$0$	$0$	$-2$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{3})q^{4}+(-1+\beta _{3})q^{7}+\cdots$
4275.2.a.bq	$4275$	$2$	4275.a	1.a	$1$	$6$	$6$	$34.136$	6.6.15044092.1	None	✓	✓	✓		4275.2.a.bq	$2$	$1$	$0$	$0$	$0$	$-8$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(1+\beta _{5})q^{4}+(-1+\beta _{1}-\beta _{5})q^{7}+\cdots$
4275.2.a.br	$4275$	$2$	4275.a	1.a	$1$	$6$	$6$	$34.136$	6.6.66064384.1	None	✓		✓		95.2.b.b	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}+(1-\beta _{3})q^{4}+(\beta _{4}+\beta _{5})q^{7}+\cdots$
4275.2.a.bs	$4275$	$2$	4275.a	1.a	$1$	$6$	$6$	$34.136$	6.6.16717036.1	None	✓	✓	✓		4275.2.a.bs	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots$
4275.2.a.bt	$4275$	$2$	4275.a	1.a	$1$	$6$	$6$	$34.136$	6.6.16717036.1	None	✓	✓			4275.2.a.bs	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{2}-\beta _{4})q^{7}+\cdots$
4275.2.a.bu	$4275$	$2$	4275.a	1.a	$1$	$6$	$6$	$34.136$	6.6.15044092.1	None	✓	✓	✓		4275.2.a.bq	$2$	$0$	$0$	$0$	$0$	$8$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(1+\beta _{5})q^{4}+(1-\beta _{1}+\beta _{5})q^{7}+\cdots$
4275.2.a.bv	$4275$	$2$	4275.a	1.a	$1$	$7$	$7$	$34.136$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓				285.2.c.b	$1$	$0$	$-3$	$0$	$0$	$8$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{4})q^{7}+\cdots$
4275.2.a.bw	$4275$	$2$	4275.a	1.a	$1$	$7$	$7$	$34.136$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓				285.2.c.b	$1$	$0$	$3$	$0$	$0$	$-8$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{4})q^{7}+\cdots$
4275.2.a.bx	$4275$	$2$	4275.a	1.a	$1$	$12$	$12$	$34.136$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓		✓		855.2.c.f	$4$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$2^{11}$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{2}+(1+\beta _{6})q^{4}+\beta _{3}q^{7}+(\beta _{2}+\cdots)q^{8}+\cdots$

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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.