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 89 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
1425.1.j.a	$1425$	$1$	1425.j	285.j	$4$	$2$	$1$	$0.711$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-95}) $	None		✓			1425.1.j.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q+(-i-1)q^{2}-i q^{3}+i q^{4}+(i-1)q^{6}+\cdots$
1425.1.j.b	$1425$	$1$	1425.j	285.j	$4$	$2$	$1$	$0.711$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-95}) $	None		✓			1425.1.j.a	$4$	$0$	$-2$	$2$	$0$	$0$		$1$		$q+(-i-1)q^{2}+q^{3}+i q^{4}+(-i-1)q^{6}+\cdots$
1425.1.j.c	$1425$	$1$	1425.j	285.j	$4$	$2$	$1$	$0.711$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-95}) $	None		✓			1425.1.j.a	$4$	$0$	$2$	$-2$	$0$	$0$		$1$		$q+(i+1)q^{2}-q^{3}+i q^{4}+(-i-1)q^{6}+\cdots$
1425.1.j.d	$1425$	$1$	1425.j	285.j	$4$	$2$	$1$	$0.711$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-95}) $	None		✓			1425.1.j.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+(i+1)q^{2}+i q^{3}+i q^{4}+(i-1)q^{6}+\cdots$
1425.1.j.e	$1425$	$1$	1425.j	285.j	$4$	$4$	$2$	$0.711$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{285}) $		✓			1425.1.j.e	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{9}+\zeta_{8}q^{12}+\cdots$
1425.1.j.f	$1425$	$1$	1425.j	285.j	$4$	$4$	$2$	$0.711$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{57}) $		✓			1425.1.j.f	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}+\zeta_{8}q^{3}-3\zeta_{8}^{2}q^{4}+2q^{6}+\cdots$
1425.1.j.g	$1425$	$1$	1425.j	285.j	$4$	$8$	$4$	$0.711$	$\Q(\zeta_{24})$	$D_{6}$	None	$\Q(\sqrt{57}) $		✓	✓		1425.1.j.g	$16$	$0$	$0$	$0$	$0$	$0$		$2^{4}$		$q-\zeta_{24}^{9}q^{2}-\zeta_{24}^{3}q^{3}-q^{6}+(-\zeta_{24}^{7}+\cdots)q^{7}+\cdots$
1425.1.o.a	$1425$	$1$	1425.o	285.n	$6$	$4$	$2$	$0.711$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-3}) $	None			✓	✓	57.1.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{7}+\cdots$
1425.1.t.a	$1425$	$1$	1425.t	57.h	$6$	$2$	$1$	$0.711$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					57.1.h.a	$4$	$0$	$0$	$1$	$0$	$2$		$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+q^{7}-\zeta_{6}q^{9}-q^{12}+\cdots$
1425.1.t.b	$1425$	$1$	1425.t	57.h	$6$	$4$	$2$	$0.711$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-15}) $	None			✓		285.1.n.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{6}+\cdots$
1425.1.be.a	$1425$	$1$	1425.be	285.w	$12$	$8$	$2$	$0.711$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1425.1.be.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{3}+\zeta_{24}^{2}q^{4}+(-\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{7}+\cdots$
1425.1.be.b	$1425$	$1$	1425.be	285.w	$12$	$8$	$2$	$0.711$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓			1425.1.be.b	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{2}+\zeta_{24}q^{3}-\zeta_{24}^{8}q^{6}-\zeta_{24}^{9}q^{8}+\cdots$
1425.1.bk.a	$1425$	$1$	1425.bk	57.l	$18$	$6$	$1$	$0.711$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		✓			1425.1.bk.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{5}q^{3}-\zeta_{18}^{7}q^{4}+(\zeta_{18}^{2}+\zeta_{18}^{4}+\cdots)q^{7}+\cdots$
1425.1.bk.b	$1425$	$1$	1425.bk	57.l	$18$	$6$	$1$	$0.711$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		✓			1425.1.bk.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{5}q^{3}-\zeta_{18}^{7}q^{4}+(-\zeta_{18}^{2}-\zeta_{18}^{4}+\cdots)q^{7}+\cdots$
1425.1.bk.c	$1425$	$1$	1425.bk	57.l	$18$	$12$	$2$	$0.711$	$\Q(\zeta_{36})$	$D_{9}$	$\Q(\sqrt{-15}) $	None			✓		285.1.bd.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{36}^{3}-\zeta_{36}^{11})q^{2}-\zeta_{36}q^{3}+\cdots$
1425.1.bm.a	$1425$	$1$	1425.bm	285.ad	$18$	$12$	$2$	$0.711$	$\Q(\zeta_{36})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	1425.1.bk.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{36}^{7}q^{3}-\zeta_{36}^{8}q^{4}+(-\zeta_{36}+\zeta_{36}^{11}+\cdots)q^{7}+\cdots$
1425.1.cd.a	$1425$	$1$	1425.cd	285.aj	$36$	$24$	$2$	$0.711$	$\Q(\zeta_{72})$	$D_{18}$	$\Q(\sqrt{-15}) $	None		✓			1425.1.cd.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{72}^{3}+\zeta_{72}^{35})q^{2}+\zeta_{72}^{13}q^{3}+\cdots$
1425.1.cd.b	$1425$	$1$	1425.cd	285.aj	$36$	$24$	$2$	$0.711$	$\Q(\zeta_{72})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		✓			1425.1.cd.b	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{72}^{31}q^{3}+\zeta_{72}^{2}q^{4}+(\zeta_{72}^{5}+\zeta_{72}^{25}+\cdots)q^{7}+\cdots$
1425.2.a.a	$1425$	$2$	1425.a	1.a	$1$	$1$	$1$	$11.379$	$\Q$	$_{}$	None	None	✓				57.2.a.c	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{8}+q^{9}+\cdots$
1425.2.a.b	$1425$	$2$	1425.a	1.a	$1$	$1$	$1$	$11.379$	$\Q$	$_{}$	None	None	✓	✓			1425.2.a.b	$1$	$0$	$-1$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{8}+q^{9}+\cdots$
1425.2.a.c	$1425$	$2$	1425.a	1.a	$1$	$1$	$1$	$11.379$	$\Q$	$_{}$	None	None	✓				285.2.a.c	$1$	$0$	$-1$	$1$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}-4q^{7}+3q^{8}+\cdots$
1425.2.a.d	$1425$	$2$	1425.a	1.a	$1$	$1$	$1$	$11.379$	$\Q$	$_{}$	None	None	✓				285.2.a.b	$1$	$0$	$-1$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}+2q^{7}+3q^{8}+\cdots$
1425.2.a.e	$1425$	$2$	1425.a	1.a	$1$	$1$	$1$	$11.379$	$\Q$	$_{}$	None	None	✓	✓			1425.2.a.e	$1$	$0$	$-1$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}+4q^{7}+3q^{8}+\cdots$
1425.2.a.f	$1425$	$2$	1425.a	1.a	$1$	$1$	$1$	$11.379$	$\Q$	$_{}$	None	None	✓	✓			1425.2.a.e	$1$	$0$	$1$	$-1$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}-4q^{7}-3q^{8}+\cdots$
1425.2.a.g	$1425$	$2$	1425.a	1.a	$1$	$1$	$1$	$11.379$	$\Q$	$_{}$	None	None	✓				285.2.a.a	$1$	$0$	$1$	$-1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}+2q^{7}-3q^{8}+\cdots$
1425.2.a.h	$1425$	$2$	1425.a	1.a	$1$	$1$	$1$	$11.379$	$\Q$	$_{}$	None	None	✓	✓			1425.2.a.b	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots$
1425.2.a.i	$1425$	$2$	1425.a	1.a	$1$	$1$	$1$	$11.379$	$\Q$	$_{}$	None	None	✓				57.2.a.b	$1$	$1$	$2$	$-1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-2q^{6}-3q^{7}+\cdots$
1425.2.a.j	$1425$	$2$	1425.a	1.a	$1$	$1$	$1$	$11.379$	$\Q$	$_{}$	None	None	✓				57.2.a.a	$1$	$0$	$2$	$1$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+2q^{6}+5q^{7}+\cdots$
1425.2.a.k	$1425$	$2$	1425.a	1.a	$1$	$2$	$2$	$11.379$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				285.2.a.g	$1$	$1$	$-2$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+(1+\cdots)q^{6}+\cdots$
1425.2.a.l	$1425$	$2$	1425.a	1.a	$1$	$2$	$2$	$11.379$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				285.2.a.f	$1$	$1$	$-2$	$2$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots$
1425.2.a.m	$1425$	$2$	1425.a	1.a	$1$	$2$	$2$	$11.379$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			1425.2.a.m	$1$	$1$	$-1$	$-2$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots$
1425.2.a.n	$1425$	$2$	1425.a	1.a	$1$	$2$	$2$	$11.379$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			1425.2.a.n	$1$	$1$	$-1$	$2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots$
1425.2.a.o	$1425$	$2$	1425.a	1.a	$1$	$2$	$2$	$11.379$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				285.2.a.e	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+q^{4}-\beta q^{6}+(1+\beta )q^{7}+\cdots$
1425.2.a.p	$1425$	$2$	1425.a	1.a	$1$	$2$	$2$	$11.379$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓				285.2.a.d	$1$	$0$	$0$	$2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+5q^{4}+\beta q^{6}+(1-\beta )q^{7}+\cdots$
1425.2.a.q	$1425$	$2$	1425.a	1.a	$1$	$2$	$2$	$11.379$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			1425.2.a.n	$1$	$1$	$1$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots$
1425.2.a.r	$1425$	$2$	1425.a	1.a	$1$	$2$	$2$	$11.379$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			1425.2.a.m	$1$	$1$	$1$	$2$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots$
1425.2.a.s	$1425$	$2$	1425.a	1.a	$1$	$3$	$3$	$11.379$	3.3.148.1	$_{}$	None	None	✓		✓		285.2.c.a	$1$	$1$	$-1$	$3$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
1425.2.a.t	$1425$	$2$	1425.a	1.a	$1$	$3$	$3$	$11.379$	3.3.837.1	$_{}$	None	None	✓	✓			1425.2.a.t	$1$	$0$	$0$	$-3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
1425.2.a.u	$1425$	$2$	1425.a	1.a	$1$	$3$	$3$	$11.379$	3.3.621.1	$_{}$	None	None	✓	✓	✓		1425.2.a.u	$1$	$0$	$0$	$-3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
1425.2.a.v	$1425$	$2$	1425.a	1.a	$1$	$3$	$3$	$11.379$	3.3.621.1	$_{}$	None	None	✓	✓			1425.2.a.u	$1$	$0$	$0$	$3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
1425.2.a.w	$1425$	$2$	1425.a	1.a	$1$	$3$	$3$	$11.379$	3.3.837.1	$_{}$	None	None	✓	✓	✓		1425.2.a.t	$1$	$0$	$0$	$3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
1425.2.a.x	$1425$	$2$	1425.a	1.a	$1$	$3$	$3$	$11.379$	3.3.148.1	$_{}$	None	None	✓				285.2.c.a	$1$	$0$	$1$	$-3$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
1425.2.a.y	$1425$	$2$	1425.a	1.a	$1$	$7$	$7$	$11.379$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓		✓		285.2.c.b	$1$	$1$	$-3$	$-7$	$0$	$-8$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
1425.2.a.z	$1425$	$2$	1425.a	1.a	$1$	$7$	$7$	$11.379$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓		✓		285.2.c.b	$1$	$0$	$3$	$7$	$0$	$8$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
1425.2.c.a	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	$\Q(\sqrt{-1}) $	$_{}$	None	None					57.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{2}+i q^{3}-2 q^{4}-2 q^{6}-3 i q^{7}+\cdots$
1425.2.c.b	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	$\Q(\sqrt{-1}) $	$_{}$	None	None					57.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{2}-i q^{3}-2 q^{4}+2 q^{6}+5 i q^{7}+\cdots$
1425.2.c.c	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	$\Q(\sqrt{-1}) $	$_{}$	None	None					285.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+i q^{3}+q^{4}-q^{6}+2 i q^{7}+\cdots$
1425.2.c.d	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	$\Q(\sqrt{-1}) $	$_{}$	None	None					285.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+i q^{3}+q^{4}-q^{6}-2 i q^{7}+\cdots$
1425.2.c.e	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1425.2.a.e	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+i q^{3}+q^{4}-q^{6}-4 i q^{7}+\cdots$
1425.2.c.f	$1425$	$2$	1425.c	5.b	$2$	$2$	$2$	$11.379$	$\Q(\sqrt{-1}) $	$_{}$	None	None					285.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+i q^{3}+q^{4}-q^{6}+4 i q^{7}+\cdots$

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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.