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 152 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
216.1.h.a	$216$	$1$	216.h	24.h	$2$	$1$	$1$	$0.108$	$\Q$	$D_{3}$	$\Q(\sqrt{-6}) $	None	✓	✓			216.1.h.a	$2$	$0$	$-1$	$0$	$1$	$-1$		$1$		$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
216.1.h.b	$216$	$1$	216.h	24.h	$2$	$1$	$1$	$0.108$	$\Q$	$D_{3}$	$\Q(\sqrt{-6}) $	None	✓	✓			216.1.h.a	$2$	$0$	$1$	$0$	$-1$	$-1$		$1$		$q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots$
216.1.p.a	$216$	$1$	216.p	72.p	$6$	$2$	$1$	$0.108$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None			✓	✓	72.1.p.a	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+\zeta_{6}^{2}q^{11}+\cdots$
216.1.r.a	$216$	$1$	216.r	216.r	$18$	$6$	$1$	$0.108$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		✓	✓	✓	216.1.r.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{2}q^{2}+\zeta_{18}^{8}q^{3}+\zeta_{18}^{4}q^{4}+\cdots$
216.2.a.a	$216$	$2$	216.a	1.a	$1$	$1$	$1$	$1.725$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	216.2.a.a	$1$	$1$	$0$	$0$	$-4$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-3q^{7}-4q^{11}+q^{13}+4q^{17}+\cdots$
216.2.a.b	$216$	$2$	216.a	1.a	$1$	$1$	$1$	$1.725$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	216.2.a.b	$1$	$0$	$0$	$0$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+3q^{7}+5q^{11}+4q^{13}-8q^{17}+\cdots$
216.2.a.c	$216$	$2$	216.a	1.a	$1$	$1$	$1$	$1.725$	$\Q$	$_{}$	None	None	✓	✓			216.2.a.b	$1$	$0$	$0$	$0$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+3q^{7}-5q^{11}+4q^{13}+8q^{17}+\cdots$
216.2.a.d	$216$	$2$	216.a	1.a	$1$	$1$	$1$	$1.725$	$\Q$	$_{}$	None	None	✓	✓			216.2.a.a	$1$	$0$	$0$	$0$	$4$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-3q^{7}+4q^{11}+q^{13}-4q^{17}+\cdots$
216.2.d.a	$216$	$2$	216.d	8.b	$2$	$4$	$4$	$1.725$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-6}) $	None		✓			216.2.d.a	$4$	$0$	$0$	$0$	$0$	$-4$		$2\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta_{2} q^{2}-2 q^{4}+(-\beta_{2}+\beta_1)q^{5}+\cdots$
216.2.d.b	$216$	$2$	216.d	8.b	$2$	$4$	$4$	$1.725$	$\Q(i, \sqrt{7})$	$_{}$	None	None		✓			216.2.d.b	$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+q^{7}+\cdots$
216.2.d.c	$216$	$2$	216.d	8.b	$2$	$8$	$8$	$1.725$	8.0.629407744.1	$_{}$	None	None		✓	✓		216.2.d.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{4}q^{5}+(-\beta _{2}-\beta _{6}+\cdots)q^{7}+\cdots$
216.2.f.a	$216$	$2$	216.f	24.f	$2$	$8$	$8$	$1.725$	8.0.$\cdots$.3	$_{}$	None	None		✓			216.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(-1-\beta _{1}-\beta _{4})q^{4}+\beta _{2}q^{5}+\cdots$
216.2.f.b	$216$	$2$	216.f	24.f	$2$	$8$	$8$	$1.725$	8.0.170772624.1	$_{}$	None	None		✓			216.2.f.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-\beta _{3}q^{4}+\beta _{2}q^{5}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots$
216.2.i.a	$216$	$2$	216.i	9.c	$3$	$2$	$1$	$1.725$	$\Q(\sqrt{-3}) $	$_{}$	None	None					72.2.i.a	$2$	$0$	$0$	$0$	$-1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots$
216.2.i.b	$216$	$2$	216.i	9.c	$3$	$4$	$2$	$1.725$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None			✓		72.2.i.b	$2$	$0$	$0$	$0$	$-1$	$-3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{3})q^{5}+(-2+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
216.2.l.a	$216$	$2$	216.l	72.l	$6$	$4$	$2$	$1.725$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-2}) $	None					72.2.l.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+2\beta _{3}q^{8}+(3-\beta _{1}+\cdots)q^{11}+\cdots$
216.2.l.b	$216$	$2$	216.l	72.l	$6$	$16$	$8$	$1.725$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None			✓		72.2.l.b	$4$	$0$	$3$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{11}q^{2}+(-1-\beta _{1}+\beta _{2}-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots$
216.2.n.a	$216$	$2$	216.n	72.n	$6$	$4$	$2$	$1.725$	$\Q(\zeta_{12})$	$_{}$	None	None					72.2.n.a	$4$	$0$	$2$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots$
216.2.n.b	$216$	$2$	216.n	72.n	$6$	$16$	$8$	$1.725$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None			✓		72.2.n.b	$4$	$0$	$-1$	$0$	$0$	$6$		$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{7}q^{2}+(\beta _{4}-\beta _{9})q^{4}+(\beta _{5}-\beta _{6}-\beta _{8}+\cdots)q^{5}+\cdots$
216.2.q.a	$216$	$2$	216.q	27.e	$9$	$24$	$4$	$1.725$		$_{}$	None	None		✓			216.2.q.a	$2$	$0$	$0$	$0$	$0$	$-3$			$\mathrm{SU}(2)[C_{9}]$
216.2.q.b	$216$	$2$	216.q	27.e	$9$	$30$	$5$	$1.725$		$_{}$	None	None		✓	✓		216.2.q.b	$2$	$0$	$0$	$0$	$0$	$3$			$\mathrm{SU}(2)[C_{9}]$
216.2.t.a	$216$	$2$	216.t	216.t	$18$	$204$	$34$	$1.725$		$_{}$	None	None		✓	✓	✓	216.2.t.a	$4$	$0$	$-6$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{18}]$
216.2.v.a	$216$	$2$	216.v	216.v	$18$	$12$	$2$	$1.725$	12.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-2}) $	None		✓			216.2.v.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{18}]$	$q-\beta _{11}q^{2}+(\beta _{5}-\beta _{8}-\beta _{11})q^{3}-2\beta _{4}q^{4}+\cdots$
216.2.v.b	$216$	$2$	216.v	216.v	$18$	$192$	$32$	$1.725$		$_{}$	None	None		✓	✓		216.2.v.b	$4$	$0$	$-6$	$-12$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
216.3.b.a	$216$	$3$	216.b	8.d	$2$	$16$	$16$	$5.886$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			216.3.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{14}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{7}q^{5}-\beta _{6}q^{7}+\cdots$
216.3.b.b	$216$	$3$	216.b	8.d	$2$	$16$	$16$	$5.886$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			216.3.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{12}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{6}q^{5}-\beta _{14}q^{7}+\cdots$
216.3.e.a	$216$	$3$	216.e	3.b	$2$	$2$	$2$	$5.886$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			216.3.e.a	$2$	$0$	$0$	$0$	$0$	$-6$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-3q^{7}+7\beta q^{11}+7q^{13}+5\beta q^{17}+\cdots$
216.3.e.b	$216$	$3$	216.e	3.b	$2$	$2$	$2$	$5.886$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			216.3.e.b	$2$	$0$	$0$	$0$	$0$	$6$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}+3q^{7}+\beta q^{11}-17q^{13}+5\beta q^{17}+\cdots$
216.3.e.c	$216$	$3$	216.e	3.b	$2$	$4$	$4$	$5.886$	$\Q(\zeta_{8})$	$_{}$	None	None		✓	✓		216.3.e.c	$2$	$0$	$0$	$0$	$0$	$-12$		$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{2}-\beta_1)q^{5}+(\beta_{3}-3)q^{7}+(-2\beta_{2}+3\beta_1)q^{11}+\cdots$
216.3.h.a	$216$	$3$	216.h	24.h	$2$	$2$	$2$	$5.886$	$\Q(\sqrt{2}) $	$_{}$	$\Q(\sqrt{-6}) $	None	✓	✓			216.3.h.a	$2$	$0$	$-4$	$0$	$-2$	$10$		$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+4q^{4}+(-1+\beta )q^{5}+(5+\beta )q^{7}+\cdots$
216.3.h.b	$216$	$3$	216.h	24.h	$2$	$2$	$2$	$5.886$	$\Q(\sqrt{2}) $	$_{}$	$\Q(\sqrt{-6}) $	None	✓	✓			216.3.h.a	$2$	$0$	$4$	$0$	$2$	$10$		$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+4q^{4}+(1+\beta )q^{5}+(5-\beta )q^{7}+\cdots$
216.3.h.c	$216$	$3$	216.h	24.h	$2$	$6$	$6$	$5.886$	6.0.121670000.1	$_{}$	None	None		✓			216.3.h.c	$2$	$0$	$-1$	$0$	$-2$	$-10$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots$
216.3.h.d	$216$	$3$	216.h	24.h	$2$	$6$	$6$	$5.886$	6.0.121670000.1	$_{}$	None	None		✓			216.3.h.c	$2$	$0$	$1$	$0$	$2$	$-10$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots$
216.3.h.e	$216$	$3$	216.h	24.h	$2$	$8$	$8$	$5.886$	8.0.629407744.1	$_{}$	None	None		✓			216.3.h.e	$4$	$0$	$0$	$0$	$0$	$-48$		$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{5}+\beta _{7})q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots$
216.3.h.f	$216$	$3$	216.h	24.h	$2$	$8$	$8$	$5.886$	8.0.$\cdots$.11	$_{}$	None	None		✓			216.3.h.f	$4$	$0$	$0$	$0$	$0$	$48$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}-\beta _{5})q^{5}+(6+\cdots)q^{7}+\cdots$
216.3.j.a	$216$	$3$	216.j	72.j	$6$	$44$	$22$	$5.886$		$_{}$	None	None			✓	✓	72.3.j.a	$4$	$0$	$3$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{6}]$
216.3.m.a	$216$	$3$	216.m	9.d	$6$	$4$	$2$	$5.886$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None					72.3.m.a	$2$	$0$	$0$	$0$	$-6$	$-6$		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}-3\beta _{2}+\cdots)q^{7}+\cdots$
216.3.m.b	$216$	$3$	216.m	9.d	$6$	$8$	$4$	$5.886$	8.0.$\cdots$.9	$_{}$	None	None			✓		72.3.m.b	$2$	$0$	$0$	$0$	$6$	$6$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{1}-\beta _{2}+\beta _{4})q^{5}+(1-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots$
216.3.p.a	$216$	$3$	216.p	72.p	$6$	$4$	$2$	$5.886$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-2}) $	None					72.3.p.a	$4$	$0$	$-4$	$0$	$0$	$0$		$2^{2}\cdot 3^{3}$	$\mathrm{U}(1)[D_{6}]$	$q-2\beta _{1}q^{2}+(-4+4\beta _{1})q^{4}+8q^{8}+\cdots$
216.3.p.b	$216$	$3$	216.p	72.p	$6$	$40$	$20$	$5.886$		$_{}$	None	None			✓		72.3.p.b	$4$	$0$	$5$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
216.3.r.a	$216$	$3$	216.r	216.r	$18$	$12$	$2$	$5.886$	12.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-2}) $	None		✓			216.3.r.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{18}]$	$q+2\beta _{2}q^{2}+(\beta _{5}-\beta _{8}-\beta _{11})q^{3}+4\beta _{4}q^{4}+\cdots$
216.3.r.b	$216$	$3$	216.r	216.r	$18$	$408$	$68$	$5.886$		$_{}$	None	None		✓	✓		216.3.r.b	$4$	$0$	$-6$	$-12$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
216.3.u.a	$216$	$3$	216.u	27.f	$18$	$108$	$18$	$5.886$		$_{}$	None	None		✓	✓	✓	216.3.u.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
216.3.x.a	$216$	$3$	216.x	216.x	$18$	$420$	$70$	$5.886$		$_{}$	None	None		✓	✓	✓	216.3.x.a	$4$	$0$	$-6$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{18}]$
216.4.a.a	$216$	$4$	216.a	1.a	$1$	$1$	$1$	$12.744$	$\Q$	$_{}$	None	None	✓	✓			216.4.a.a	$1$	$1$	$0$	$0$	$-4$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+3q^{7}-28q^{11}-11q^{13}+\cdots$
216.4.a.b	$216$	$4$	216.a	1.a	$1$	$1$	$1$	$12.744$	$\Q$	$_{}$	None	None	✓	✓			216.4.a.b	$1$	$1$	$0$	$0$	$-1$	$-9$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-9q^{7}+17q^{11}-44q^{13}-56q^{17}+\cdots$
216.4.a.c	$216$	$4$	216.a	1.a	$1$	$1$	$1$	$12.744$	$\Q$	$_{}$	None	None	✓	✓			216.4.a.b	$1$	$1$	$0$	$0$	$1$	$-9$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-9q^{7}-17q^{11}-44q^{13}+56q^{17}+\cdots$
216.4.a.d	$216$	$4$	216.a	1.a	$1$	$1$	$1$	$12.744$	$\Q$	$_{}$	None	None	✓	✓			216.4.a.a	$1$	$0$	$0$	$0$	$4$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+3q^{7}+28q^{11}-11q^{13}+\cdots$
216.4.a.e	$216$	$4$	216.a	1.a	$1$	$2$	$2$	$12.744$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	✓			216.4.a.e	$1$	$0$	$0$	$0$	$-8$	$24$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	$q+(-4-\beta )q^{5}+(12+\beta )q^{7}-q^{11}+\cdots$
216.4.a.f	$216$	$4$	216.a	1.a	$1$	$2$	$2$	$12.744$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓		216.4.a.f	$1$	$1$	$0$	$0$	$-4$	$-6$	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	$q+(-2-\beta )q^{5}+(-3+2\beta )q^{7}+(-26+\cdots)q^{11}+\cdots$

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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.