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 126 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	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
1776.1.n.a	$1776$	$1$	1776.n	111.d	$2$	$1$	$1$	$0.886$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-111}) $	$\Q(\sqrt{37}) $	✓				111.1.d.a	$4$	$0$	$0$	$-1$	$0$	$2$		$1$		$q-q^{3}+2q^{7}+q^{9}-2q^{21}-q^{25}+\cdots$
1776.1.n.b	$1776$	$1$	1776.n	111.d	$2$	$2$	$2$	$0.886$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{37}) $					444.1.h.a	$4$	$0$	$0$	$1$	$0$	$-2$		$1$		$q-\zeta_{6}^{2}q^{3}-q^{7}-\zeta_{6}q^{9}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{11}+\cdots$
1776.1.n.c	$1776$	$1$	1776.n	111.d	$2$	$2$	$2$	$0.886$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-111}) $	None	✓				111.1.d.b	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+q^{3}-\beta q^{5}+q^{9}-\beta q^{15}+\beta q^{17}+\cdots$
1776.1.w.a	$1776$	$1$	1776.w	444.j	$4$	$2$	$1$	$0.886$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		✓			1776.1.w.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-q^{3}-2 i q^{7}+q^{9}+(-i-1)q^{13}+\cdots$
1776.1.w.b	$1776$	$1$	1776.w	444.j	$4$	$2$	$1$	$0.886$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		✓			1776.1.w.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+q^{3}+2 i q^{7}+q^{9}+(-i-1)q^{13}+\cdots$
1776.1.z.a	$1776$	$1$	1776.z	1776.z	$4$	$4$	$2$	$0.886$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			1776.1.z.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}-q^{4}+(-1+\zeta_{8}^{2}+\cdots)q^{5}+\cdots$
1776.1.z.b	$1776$	$1$	1776.z	1776.z	$4$	$4$	$2$	$0.886$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			1776.1.z.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}-q^{4}+(1-\zeta_{8}^{2}+\cdots)q^{5}+\cdots$
1776.1.z.c	$1776$	$1$	1776.z	1776.z	$4$	$16$	$8$	$0.886$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-111}) $	None		✓	✓		1776.1.z.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{32}^{3}q^{2}+\zeta_{32}^{4}q^{3}+\zeta_{32}^{6}q^{4}+\cdots$
1776.1.bq.a	$1776$	$1$	1776.bq	111.h	$6$	$2$	$1$	$0.886$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None			✓	✓	111.1.h.a	$4$	$0$	$0$	$1$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+(-1+\cdots)q^{13}+\cdots$
1776.1.bw.a	$1776$	$1$	1776.bw	111.i	$6$	$2$	$1$	$0.886$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None			✓	✓	111.1.i.a	$4$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+\zeta_{6}q^{3}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{13}+\cdots$
1776.1.cr.a	$1776$	$1$	1776.cr	444.x	$12$	$4$	$1$	$0.886$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓			1776.1.cr.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+\zeta_{12}^{4}q^{3}+\zeta_{12}q^{7}-\zeta_{12}^{2}q^{9}+(\zeta_{12}^{2}+\cdots)q^{13}+\cdots$
1776.1.cr.b	$1776$	$1$	1776.cr	444.x	$12$	$4$	$1$	$0.886$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓			1776.1.cr.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\zeta_{12}^{4}q^{3}-\zeta_{12}q^{7}-\zeta_{12}^{2}q^{9}+(\zeta_{12}^{2}+\cdots)q^{13}+\cdots$
1776.1.dk.a	$1776$	$1$	1776.dk	111.n	$18$	$6$	$1$	$0.886$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None			✓	✓	444.1.bc.a	$4$	$0$	$0$	$0$	$0$	$-3$		$1$		$q+\zeta_{18}^{7}q^{3}+(-\zeta_{18}^{5}+\zeta_{18}^{6})q^{7}+\cdots$
1776.1.dr.a	$1776$	$1$	1776.dr	111.p	$18$	$6$	$1$	$0.886$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None			✓	✓	444.1.bf.a	$4$	$0$	$0$	$0$	$0$	$3$		$1$		$q+\zeta_{18}q^{3}+(-\zeta_{18}^{2}-\zeta_{18}^{6})q^{7}+\zeta_{18}^{2}q^{9}+\cdots$
1776.1.em.a	$1776$	$1$	1776.em	444.ai	$36$	$12$	$1$	$0.886$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-3}) $	None		✓			1776.1.em.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{36}^{16}q^{3}+(-\zeta_{36}^{5}+\zeta_{36}^{15})q^{7}+\cdots$
1776.1.em.b	$1776$	$1$	1776.em	444.ai	$36$	$12$	$1$	$0.886$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-3}) $	None		✓			1776.1.em.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{36}^{16}q^{3}+(\zeta_{36}^{5}-\zeta_{36}^{15})q^{7}+\cdots$
1776.2.a.a	$1776$	$2$	1776.a	1.a	$1$	$1$	$1$	$14.181$	$\Q$	$_{}$	None	None	✓				888.2.a.c	$1$	$0$	$0$	$-1$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
1776.2.a.b	$1776$	$2$	1776.a	1.a	$1$	$1$	$1$	$14.181$	$\Q$	$_{}$	None	None	✓				444.2.a.b	$1$	$0$	$0$	$-1$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots$
1776.2.a.c	$1776$	$2$	1776.a	1.a	$1$	$1$	$1$	$14.181$	$\Q$	$_{}$	None	None	✓				222.2.a.e	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-3q^{11}-q^{13}-3q^{17}+\cdots$
1776.2.a.d	$1776$	$2$	1776.a	1.a	$1$	$1$	$1$	$14.181$	$\Q$	$_{}$	None	None	✓				888.2.a.d	$1$	$0$	$0$	$-1$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{5}+q^{9}+2q^{13}-4q^{15}+\cdots$
1776.2.a.e	$1776$	$2$	1776.a	1.a	$1$	$1$	$1$	$14.181$	$\Q$	$_{}$	None	None	✓				222.2.a.c	$1$	$0$	$0$	$-1$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{5}+q^{7}+q^{9}+q^{11}-3q^{13}+\cdots$
1776.2.a.f	$1776$	$2$	1776.a	1.a	$1$	$1$	$1$	$14.181$	$\Q$	$_{}$	None	None	✓				222.2.a.a	$1$	$0$	$0$	$1$	$-4$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}-3q^{7}+q^{9}-5q^{11}+\cdots$
1776.2.a.g	$1776$	$2$	1776.a	1.a	$1$	$1$	$1$	$14.181$	$\Q$	$_{}$	None	None	✓				888.2.a.a	$1$	$1$	$0$	$1$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}+q^{7}+q^{9}+3q^{11}-5q^{13}+\cdots$
1776.2.a.h	$1776$	$2$	1776.a	1.a	$1$	$1$	$1$	$14.181$	$\Q$	$_{}$	None	None	✓				222.2.a.d	$1$	$1$	$0$	$1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{7}+q^{9}-q^{11}+q^{13}-3q^{17}+\cdots$
1776.2.a.i	$1776$	$2$	1776.a	1.a	$1$	$1$	$1$	$14.181$	$\Q$	$_{}$	None	None	✓				444.2.a.a	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}-4q^{11}-2q^{13}-6q^{19}+\cdots$
1776.2.a.j	$1776$	$2$	1776.a	1.a	$1$	$1$	$1$	$14.181$	$\Q$	$_{}$	None	None	✓				888.2.a.b	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}-6q^{13}-4q^{17}-4q^{19}+\cdots$
1776.2.a.k	$1776$	$2$	1776.a	1.a	$1$	$1$	$1$	$14.181$	$\Q$	$_{}$	None	None	✓				222.2.a.b	$1$	$0$	$0$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots$
1776.2.a.l	$1776$	$2$	1776.a	1.a	$1$	$2$	$2$	$14.181$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				888.2.a.g	$1$	$1$	$0$	$-2$	$-4$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-2+\beta )q^{5}+(2+2\beta )q^{7}+q^{9}+\cdots$
1776.2.a.m	$1776$	$2$	1776.a	1.a	$1$	$2$	$2$	$14.181$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓		✓		444.2.a.d	$1$	$1$	$0$	$-2$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}-2q^{7}+q^{9}+(2-2\beta )q^{13}+\cdots$
1776.2.a.n	$1776$	$2$	1776.a	1.a	$1$	$2$	$2$	$14.181$	$\Q(\sqrt{41}) $	$_{}$	None	None	✓		✓		888.2.a.h	$1$	$0$	$0$	$-2$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta )q^{7}+q^{9}+(-1-\beta )q^{11}+\cdots$
1776.2.a.o	$1776$	$2$	1776.a	1.a	$1$	$2$	$2$	$14.181$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				444.2.a.c	$1$	$0$	$0$	$2$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta )q^{5}+2\beta q^{7}+q^{9}+\cdots$
1776.2.a.p	$1776$	$2$	1776.a	1.a	$1$	$2$	$2$	$14.181$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		✓		888.2.a.f	$1$	$1$	$0$	$2$	$2$	$-8$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{5}-4q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
1776.2.a.q	$1776$	$2$	1776.a	1.a	$1$	$2$	$2$	$14.181$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				888.2.a.e	$1$	$0$	$0$	$2$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{5}+2q^{7}+q^{9}+(2+2\beta )q^{11}+\cdots$
1776.2.a.r	$1776$	$2$	1776.a	1.a	$1$	$3$	$3$	$14.181$	3.3.568.1	$_{}$	None	None	✓		✓		888.2.a.j	$1$	$1$	$0$	$-3$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots$
1776.2.a.s	$1776$	$2$	1776.a	1.a	$1$	$3$	$3$	$14.181$	3.3.316.1	$_{}$	None	None	✓		✓		888.2.a.i	$1$	$0$	$0$	$3$	$2$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(1+2\beta _{1}+\cdots)q^{7}+\cdots$
1776.2.a.t	$1776$	$2$	1776.a	1.a	$1$	$3$	$3$	$14.181$	3.3.148.1	$_{}$	None	None	✓		✓		111.2.a.a	$1$	$0$	$0$	$3$	$4$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta _{2})q^{5}+(2-\beta _{1}-\beta _{2})q^{7}+\cdots$
1776.2.a.u	$1776$	$2$	1776.a	1.a	$1$	$4$	$4$	$14.181$	4.4.6224.1	$_{}$	None	None	✓		✓		111.2.a.b	$1$	$0$	$0$	$-4$	$-2$	$-4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta _{3})q^{5}+(-2+\beta _{2}+\beta _{3})q^{7}+\cdots$
1776.2.e.a	$1776$	$2$	1776.e	12.b	$2$	$2$	$2$	$14.181$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1776.2.e.a	$2$	$1$	$0$	$-3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\zeta_{6})q^{3}+(2-4\zeta_{6})q^{5}+(1-2\zeta_{6})q^{7}+\cdots$
1776.2.e.b	$1776$	$2$	1776.e	12.b	$2$	$2$	$2$	$14.181$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1776.2.e.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}-2\beta q^{5}-2\beta q^{7}-3 q^{9}+\cdots$
1776.2.e.c	$1776$	$2$	1776.e	12.b	$2$	$2$	$2$	$14.181$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1776.2.e.b	$2$	$1$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-2\beta q^{5}+2\beta q^{7}-3 q^{9}+\cdots$
1776.2.e.d	$1776$	$2$	1776.e	12.b	$2$	$2$	$2$	$14.181$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1776.2.e.a	$2$	$0$	$0$	$3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{6})q^{3}+(2-4\zeta_{6})q^{5}+(-1+2\zeta_{6})q^{7}+\cdots$
1776.2.e.e	$1776$	$2$	1776.e	12.b	$2$	$8$	$8$	$14.181$	8.0.8275904784.2	$_{}$	None	None		✓			1776.2.e.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(2\beta _{3}-2\beta _{5}-\beta _{6})q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots$
1776.2.e.f	$1776$	$2$	1776.e	12.b	$2$	$12$	$12$	$14.181$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			1776.2.e.f	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{10}q^{3}-\beta _{1}q^{5}+(-\beta _{6}-\beta _{10})q^{7}+\cdots$
1776.2.e.g	$1776$	$2$	1776.e	12.b	$2$	$12$	$12$	$14.181$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			1776.2.e.g	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{3}+\beta _{10}q^{5}-\beta _{11}q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots$
1776.2.e.h	$1776$	$2$	1776.e	12.b	$2$	$16$	$16$	$14.181$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1776.2.e.h	$4$	$0$	$0$	$0$	$0$	$0$		$2^{16}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}+\beta _{6}q^{5}-\beta _{2}q^{9}+(\beta _{5}+\beta _{12}+\cdots)q^{11}+\cdots$
1776.2.e.i	$1776$	$2$	1776.e	12.b	$2$	$16$	$16$	$14.181$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1776.2.e.i	$4$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{7}q^{5}+(-\beta _{1}-\beta _{3}-\beta _{13}+\cdots)q^{7}+\cdots$
1776.2.h.a	$1776$	$2$	1776.h	37.b	$2$	$2$	$2$	$14.181$	$\Q(\sqrt{-1}) $	$_{}$	None	None					222.2.c.a	$2$	$0$	$0$	$-2$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+2 i q^{5}-3 q^{7}+q^{9}+3 q^{11}+\cdots$
1776.2.h.b	$1776$	$2$	1776.h	37.b	$2$	$2$	$2$	$14.181$	$\Q(\sqrt{-1}) $	$_{}$	None	None					888.2.h.a	$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+q^{9}-4 q^{11}-2\beta q^{13}+2\beta q^{17}+\cdots$
1776.2.h.c	$1776$	$2$	1776.h	37.b	$2$	$2$	$2$	$14.181$	$\Q(\sqrt{-1}) $	$_{}$	None	None					111.2.c.a	$2$	$0$	$0$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta q^{5}+q^{9}+\beta q^{15}-\beta q^{17}+\cdots$
1776.2.h.d	$1776$	$2$	1776.h	37.b	$2$	$4$	$4$	$14.181$	$\Q(\sqrt{-5 + \sqrt{13}})$	$_{}$	None	None					444.2.e.b	$2$	$0$	$0$	$-4$	$0$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+\beta _{1}q^{5}+(1-\beta _{2})q^{7}+q^{9}+2\beta _{1}q^{13}+\cdots$

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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.