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 156 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
1216.1.e.a	$1216$	$1$	1216.e	19.b	$2$	$1$	$1$	$0.607$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	✓				76.1.c.a	$2$	$0$	$0$	$0$	$1$	$-1$		$1$		$q+q^{5}-q^{7}+q^{9}+q^{11}-q^{17}-q^{19}+\cdots$
1216.1.e.b	$1216$	$1$	1216.e	19.b	$2$	$1$	$1$	$0.607$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	✓				76.1.c.a	$2$	$0$	$0$	$0$	$1$	$1$		$1$		$q+q^{5}+q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots$
1216.1.g.a	$1216$	$1$	1216.g	152.g	$2$	$2$	$2$	$0.607$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-19}) $	$\Q(\sqrt{38}) $		✓			1216.1.g.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{9}-2 i q^{11}+2 q^{17}-i q^{19}+\cdots$
1216.1.g.b	$1216$	$1$	1216.g	152.g	$2$	$4$	$4$	$0.607$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-19}) $	None		✓	✓		1216.1.g.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{5}+(\zeta_{12}-\zeta_{12}^{5}+\cdots)q^{7}+\cdots$
1216.1.p.a	$1216$	$1$	1216.p	152.l	$6$	$4$	$2$	$0.607$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-2}) $	None		✓	✓	✓	1216.1.p.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+(-1-\zeta_{12}^{2}+\cdots)q^{9}+\cdots$
1216.1.q.a	$1216$	$1$	1216.q	76.g	$6$	$4$	$2$	$0.607$	$\Q(\zeta_{12})$	$A_{4}$	None	None			✓	✓	608.1.q.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+\zeta_{12}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{2}q^{13}+\cdots$
1216.1.bi.a	$1216$	$1$	1216.bi	152.s	$18$	$12$	$2$	$0.607$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-2}) $	None		✓	✓	✓	1216.1.bi.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{36}^{13}+\zeta_{36}^{15})q^{3}+(-\zeta_{36}^{8}-\zeta_{36}^{10}+\cdots)q^{9}+\cdots$
1216.2.a.a	$1216$	$2$	1216.a	1.a	$1$	$1$	$1$	$9.710$	$\Q$	$_{}$	None	None	✓				608.2.a.a	$1$	$1$	$0$	$-3$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{7}+6q^{9}-2q^{11}+q^{13}+\cdots$
1216.2.a.b	$1216$	$2$	1216.a	1.a	$1$	$1$	$1$	$9.710$	$\Q$	$_{}$	None	None	✓				19.2.a.a	$1$	$1$	$0$	$-2$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-3q^{5}+q^{7}+q^{9}+3q^{11}+\cdots$
1216.2.a.c	$1216$	$2$	1216.a	1.a	$1$	$1$	$1$	$9.710$	$\Q$	$_{}$	None	None	✓				76.2.a.a	$1$	$0$	$0$	$-2$	$1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}-3q^{7}+q^{9}-5q^{11}+\cdots$
1216.2.a.d	$1216$	$2$	1216.a	1.a	$1$	$1$	$1$	$9.710$	$\Q$	$_{}$	None	None	✓				152.2.a.a	$1$	$0$	$0$	$-2$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+3q^{7}+q^{9}-3q^{11}+\cdots$
1216.2.a.e	$1216$	$2$	1216.a	1.a	$1$	$1$	$1$	$9.710$	$\Q$	$_{}$	None	None	✓				38.2.a.a	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}-2q^{9}+6q^{11}-5q^{13}+\cdots$
1216.2.a.f	$1216$	$2$	1216.a	1.a	$1$	$1$	$1$	$9.710$	$\Q$	$_{}$	None	None	✓				152.2.a.b	$1$	$1$	$0$	$-1$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{7}-2q^{9}-2q^{11}-q^{13}+\cdots$
1216.2.a.g	$1216$	$2$	1216.a	1.a	$1$	$1$	$1$	$9.710$	$\Q$	$_{}$	None	None	✓				38.2.a.b	$1$	$0$	$0$	$-1$	$4$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{5}-3q^{7}-2q^{9}+2q^{11}+\cdots$
1216.2.a.h	$1216$	$2$	1216.a	1.a	$1$	$1$	$1$	$9.710$	$\Q$	$_{}$	None	None	✓				608.2.a.d	$1$	$0$	$0$	$0$	$-3$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-5q^{7}-3q^{9}+5q^{11}+4q^{13}+\cdots$
1216.2.a.i	$1216$	$2$	1216.a	1.a	$1$	$1$	$1$	$9.710$	$\Q$	$_{}$	None	None	✓				608.2.a.d	$1$	$1$	$0$	$0$	$-3$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+5q^{7}-3q^{9}-5q^{11}+4q^{13}+\cdots$
1216.2.a.j	$1216$	$2$	1216.a	1.a	$1$	$1$	$1$	$9.710$	$\Q$	$_{}$	None	None	✓				608.2.a.b	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}-3q^{9}-3q^{11}+4q^{13}+\cdots$
1216.2.a.k	$1216$	$2$	1216.a	1.a	$1$	$1$	$1$	$9.710$	$\Q$	$_{}$	None	None	✓				608.2.a.b	$1$	$0$	$0$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}-3q^{9}+3q^{11}+4q^{13}+\cdots$
1216.2.a.l	$1216$	$2$	1216.a	1.a	$1$	$1$	$1$	$9.710$	$\Q$	$_{}$	None	None	✓				152.2.a.b	$1$	$1$	$0$	$1$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{7}-2q^{9}+2q^{11}-q^{13}+\cdots$
1216.2.a.m	$1216$	$2$	1216.a	1.a	$1$	$1$	$1$	$9.710$	$\Q$	$_{}$	None	None	✓				38.2.a.a	$1$	$1$	$0$	$1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}-2q^{9}-6q^{11}-5q^{13}+\cdots$
1216.2.a.n	$1216$	$2$	1216.a	1.a	$1$	$1$	$1$	$9.710$	$\Q$	$_{}$	None	None	✓				38.2.a.b	$1$	$0$	$0$	$1$	$4$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+3q^{7}-2q^{9}-2q^{11}+\cdots$
1216.2.a.o	$1216$	$2$	1216.a	1.a	$1$	$1$	$1$	$9.710$	$\Q$	$_{}$	None	None	✓				19.2.a.a	$1$	$1$	$0$	$2$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-3q^{5}-q^{7}+q^{9}-3q^{11}+\cdots$
1216.2.a.p	$1216$	$2$	1216.a	1.a	$1$	$1$	$1$	$9.710$	$\Q$	$_{}$	None	None	✓				152.2.a.a	$1$	$0$	$0$	$2$	$1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}-3q^{7}+q^{9}+3q^{11}+\cdots$
1216.2.a.q	$1216$	$2$	1216.a	1.a	$1$	$1$	$1$	$9.710$	$\Q$	$_{}$	None	None	✓				76.2.a.a	$1$	$0$	$0$	$2$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+3q^{7}+q^{9}+5q^{11}+\cdots$
1216.2.a.r	$1216$	$2$	1216.a	1.a	$1$	$1$	$1$	$9.710$	$\Q$	$_{}$	None	None	✓				608.2.a.a	$1$	$0$	$0$	$3$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{7}+6q^{9}+2q^{11}+q^{13}+\cdots$
1216.2.a.s	$1216$	$2$	1216.a	1.a	$1$	$2$	$2$	$9.710$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				608.2.a.g	$1$	$0$	$0$	$-1$	$1$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1-\beta )q^{5}+3q^{7}+(1+\beta )q^{9}+\cdots$
1216.2.a.t	$1216$	$2$	1216.a	1.a	$1$	$2$	$2$	$9.710$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		✓		608.2.a.g	$1$	$1$	$0$	$1$	$1$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1-\beta )q^{5}-3q^{7}+(1+\beta )q^{9}+\cdots$
1216.2.a.u	$1216$	$2$	1216.a	1.a	$1$	$3$	$3$	$9.710$	3.3.961.1	$_{}$	None	None	✓				152.2.a.c	$1$	$0$	$0$	$-1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{2}q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots$
1216.2.a.v	$1216$	$2$	1216.a	1.a	$1$	$3$	$3$	$9.710$	3.3.961.1	$_{}$	None	None	✓		✓		152.2.a.c	$1$	$0$	$0$	$1$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots$
1216.2.a.w	$1216$	$2$	1216.a	1.a	$1$	$4$	$4$	$9.710$	$\Q(\sqrt{11 +2 \sqrt{17}})$	$_{}$	None	None	✓		✓		608.2.a.i	$1$	$1$	$0$	$-2$	$-1$	$-1$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+\beta _{1}q^{5}+(\beta _{2}-\beta _{3})q^{7}+\cdots$
1216.2.a.x	$1216$	$2$	1216.a	1.a	$1$	$4$	$4$	$9.710$	$\Q(\sqrt{11 +2 \sqrt{17}})$	$_{}$	None	None	✓		✓		608.2.a.i	$1$	$0$	$0$	$2$	$-1$	$1$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(-\beta _{1}+\beta _{2})q^{5}-\beta _{3}q^{7}+\cdots$
1216.2.b.a	$1216$	$2$	1216.b	152.b	$2$	$4$	$4$	$9.710$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			1216.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta_1 q^{3}+\beta_{2} q^{5}+\beta_1 q^{7}-q^{9}+\cdots$
1216.2.b.b	$1216$	$2$	1216.b	152.b	$2$	$4$	$4$	$9.710$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			1216.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta_1 q^{3}-\beta_{2} q^{5}-\beta_1 q^{7}-q^{9}+\cdots$
1216.2.b.c	$1216$	$2$	1216.b	152.b	$2$	$4$	$4$	$9.710$	$\Q(i, \sqrt{19})$	$_{}$	$\Q(\sqrt{-19}) $	None		✓			1216.2.b.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{3}q^{5}-3\beta _{1}q^{7}+3q^{9}+\beta _{2}q^{11}+\cdots$
1216.2.b.d	$1216$	$2$	1216.b	152.b	$2$	$8$	$8$	$9.710$	$\Q(i, \sqrt{3}, \sqrt{7})$	$_{}$	None	None		✓			1216.2.b.d	$8$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{3}q^{5}+\beta _{2}q^{7}-4q^{9}-\beta _{7}q^{13}+\cdots$
1216.2.b.e	$1216$	$2$	1216.b	152.b	$2$	$8$	$8$	$9.710$	$\Q(i, \sqrt{3}, \sqrt{19})$	$_{}$	$\Q(\sqrt{-19}) $	None		✓			1216.2.b.e	$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{3}q^{5}+\beta _{6}q^{7}+3q^{9}+(-2\beta _{1}+\beta _{5}+\cdots)q^{11}+\cdots$
1216.2.b.f	$1216$	$2$	1216.b	152.b	$2$	$12$	$12$	$9.710$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	$\Q(\sqrt{-38}) $	None		✓	✓		1216.2.b.f	$8$	$0$	$0$	$0$	$0$	$0$		$2^{14}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{4}q^{3}+\beta _{7}q^{7}+(-3+\beta _{2})q^{9}+\beta _{5}q^{13}+\cdots$
1216.2.c.a	$1216$	$2$	1216.c	8.b	$2$	$2$	$2$	$9.710$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1216.2.c.a	$2$	$0$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}-3 q^{7}+2 q^{9}-3 i q^{13}+\cdots$
1216.2.c.b	$1216$	$2$	1216.c	8.b	$2$	$2$	$2$	$9.710$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1216.2.c.b	$2$	$1$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{3}-4 i q^{5}-q^{7}-6 q^{9}+5 i q^{13}+\cdots$
1216.2.c.c	$1216$	$2$	1216.c	8.b	$2$	$2$	$2$	$9.710$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1216.2.c.b	$2$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{3}+4 i q^{5}+q^{7}-6 q^{9}-5 i q^{13}+\cdots$
1216.2.c.d	$1216$	$2$	1216.c	8.b	$2$	$2$	$2$	$9.710$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1216.2.c.a	$2$	$0$	$0$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+3 q^{7}+2 q^{9}+3 i q^{13}+\cdots$
1216.2.c.e	$1216$	$2$	1216.c	8.b	$2$	$4$	$4$	$9.710$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			1216.2.c.e	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta_1 q^{3}-\beta_{2} q^{5}+\beta_{3} q^{7}-q^{9}+\cdots$
1216.2.c.f	$1216$	$2$	1216.c	8.b	$2$	$4$	$4$	$9.710$	$\Q(i, \sqrt{11})$	$_{}$	None	None		✓			1216.2.c.f	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-2\beta _{1}q^{3}-\beta _{3}q^{5}+\beta _{2}q^{7}-q^{9}-5\beta _{1}q^{11}+\cdots$
1216.2.c.g	$1216$	$2$	1216.c	8.b	$2$	$4$	$4$	$9.710$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			1216.2.c.g	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{3}+2\beta_{2} q^{5}-\beta_{3} q^{7}+2 q^{9}+\cdots$
1216.2.c.h	$1216$	$2$	1216.c	8.b	$2$	$8$	$8$	$9.710$	$\Q(i, \sqrt{3}, \sqrt{11})$	$_{}$	None	None		✓			1216.2.c.h	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+\beta _{1}q^{5}+(-\beta _{3}+2\beta _{6})q^{7}+\cdots$
1216.2.c.i	$1216$	$2$	1216.c	8.b	$2$	$8$	$8$	$9.710$	$\Q(i, \sqrt{3}, \sqrt{19})$	$_{}$	None	None		✓			1216.2.c.i	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{5}+\beta _{5}q^{7}+3q^{9}+(-\beta _{2}-2\beta _{4}+\cdots)q^{11}+\cdots$
1216.2.h.a	$1216$	$2$	1216.h	76.d	$2$	$2$	$2$	$9.710$	$\Q(\sqrt{-19}) $	$_{}$	$\Q(\sqrt{-19}) $	None					304.2.h.a	$4$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+q^{5}+\beta q^{7}-3q^{9}-\beta q^{11}+7q^{17}+\cdots$
1216.2.h.b	$1216$	$2$	1216.h	76.d	$2$	$4$	$4$	$9.710$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	$\Q(\sqrt{-19}) $	None					304.2.h.c	$4$	$0$	$0$	$0$	$-2$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(-1+\beta _{2})q^{5}+(2\beta _{1}+\beta _{3})q^{7}-3q^{9}+\cdots$
1216.2.h.c	$1216$	$2$	1216.h	76.d	$2$	$4$	$4$	$9.710$	$\Q(\sqrt{-3}, \sqrt{7})$	$_{}$	None	None					304.2.h.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{7}+4q^{9}+2\beta _{2}q^{11}+\cdots$
1216.2.h.d	$1216$	$2$	1216.h	76.d	$2$	$8$	$8$	$9.710$	8.0.$\cdots$.1	$_{}$	None	None					76.2.d.a	$4$	$0$	$0$	$0$	$4$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(1+\beta _{1})q^{5}-\beta _{7}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$

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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.