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 158 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
333.1.i.a	$333$	$1$	333.i	37.d	$4$	$2$	$1$	$0.166$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	333.1.i.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{4}+(1-i)q^{13}-q^{16}+(-1+i+\cdots)q^{19}+\cdots$
333.1.p.a	$333$	$1$	333.p	111.i	$6$	$4$	$2$	$0.166$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		✓	✓	✓	333.1.p.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$
333.1.bb.a	$333$	$1$	333.bb	37.g	$12$	$4$	$1$	$0.166$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	333.1.bb.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{4}+(\zeta_{12}+\zeta_{12}^{3})q^{7}+(-\zeta_{12}^{3}+\cdots)q^{13}+\cdots$
333.2.a.a	$333$	$2$	333.a	1.a	$1$	$1$	$1$	$2.659$	$\Q$	$_{}$	None	None	✓	✓			333.2.a.a	$1$	$1$	$-1$	$0$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+2q^{5}-4q^{7}+3q^{8}-2q^{10}+\cdots$
333.2.a.b	$333$	$2$	333.a	1.a	$1$	$1$	$1$	$2.659$	$\Q$	$_{}$	None	None	✓				37.2.a.b	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{7}-3q^{11}-4q^{13}+4q^{16}+\cdots$
333.2.a.c	$333$	$2$	333.a	1.a	$1$	$1$	$1$	$2.659$	$\Q$	$_{}$	None	None	✓	✓			333.2.a.a	$1$	$1$	$1$	$0$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-2q^{5}-4q^{7}-3q^{8}-2q^{10}+\cdots$
333.2.a.d	$333$	$2$	333.a	1.a	$1$	$1$	$1$	$2.659$	$\Q$	$_{}$	None	None	✓				37.2.a.a	$1$	$0$	$2$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+2q^{5}-q^{7}+4q^{10}+\cdots$
333.2.a.e	$333$	$2$	333.a	1.a	$1$	$3$	$3$	$2.659$	3.3.148.1	$_{}$	None	None	✓		✓		111.2.a.a	$1$	$1$	$-3$	$0$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
333.2.a.f	$333$	$2$	333.a	1.a	$1$	$4$	$4$	$2.659$	4.4.27648.1	$_{}$	None	None	✓	✓	✓	✓	333.2.a.f	$2$	$0$	$0$	$0$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+2q^{7}+\cdots$
333.2.a.g	$333$	$2$	333.a	1.a	$1$	$4$	$4$	$2.659$	4.4.6224.1	$_{}$	None	None	✓		✓		111.2.a.b	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
333.2.c.a	$333$	$2$	333.c	37.b	$2$	$2$	$2$	$2.659$	$\Q(\sqrt{-1}) $	$_{}$	None	None					37.2.b.a	$2$	$0$	$0$	$0$	$0$	$6$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-2q^{4}-iq^{5}+3q^{7}+4q^{10}+\cdots$
333.2.c.b	$333$	$2$	333.c	37.b	$2$	$2$	$2$	$2.659$	$\Q(\sqrt{-1}) $	$_{}$	None	None					111.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{4}+2iq^{5}+3iq^{8}-2q^{10}+\cdots$
333.2.c.c	$333$	$2$	333.c	37.b	$2$	$4$	$4$	$2.659$	4.0.27648.1	$_{}$	None	None					111.2.c.b	$2$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{3}q^{5}-2q^{7}+\cdots$
333.2.c.d	$333$	$2$	333.c	37.b	$2$	$8$	$8$	$2.659$	8.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-111}) $	None		✓	✓		333.2.c.d	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{4}q^{2}+(-2+\beta _{7})q^{4}+\beta _{3}q^{5}-\beta _{1}q^{7}+\cdots$
333.2.e.a	$333$	$2$	333.e	9.c	$3$	$36$	$18$	$2.659$		$_{}$	None	None		✓			333.2.e.a	$2$	$0$	$-6$	$-1$	$-10$	$0$			$\mathrm{SU}(2)[C_{3}]$
333.2.e.b	$333$	$2$	333.e	9.c	$3$	$36$	$18$	$2.659$		$_{}$	None	None		✓			333.2.e.b	$2$	$0$	$4$	$-1$	$6$	$0$			$\mathrm{SU}(2)[C_{3}]$
333.2.f.a	$333$	$2$	333.f	37.c	$3$	$2$	$1$	$2.659$	$\Q(\sqrt{-3}) $	$_{}$	None	None					37.2.c.a	$2$	$0$	$1$	$0$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}-2\zeta_{6}q^{7}+\cdots$
333.2.f.b	$333$	$2$	333.f	37.c	$3$	$6$	$3$	$2.659$	6.0.1415907.1	$_{}$	None	None					111.2.e.a	$2$	$0$	$0$	$0$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{3}-\beta _{4}-\beta _{5})q^{4}+\cdots$
333.2.f.c	$333$	$2$	333.f	37.c	$3$	$10$	$5$	$2.659$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None					111.2.e.b	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(\beta _{2}-2\beta _{6}+\beta _{8})q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots$
333.2.f.d	$333$	$2$	333.f	37.c	$3$	$12$	$6$	$2.659$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓		333.2.f.d	$4$	$0$	$0$	$0$	$0$	$6$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-\beta _{5}+\beta _{9})q^{4}+\beta _{10}q^{5}+\cdots$
333.2.g.a	$333$	$2$	333.g	333.g	$3$	$72$	$36$	$2.659$		$_{}$	None	None		✓	✓	✓	333.2.g.a	$2$	$0$	$1$	$-2$	$-1$	$0$			$\mathrm{SU}(2)[C_{3}]$
333.2.h.a	$333$	$2$	333.h	333.h	$3$	$72$	$36$	$2.659$		$_{}$	None	None		✓	✓	✓	333.2.g.a	$2$	$0$	$-2$	$1$	$2$	$0$			$\mathrm{SU}(2)[C_{3}]$
333.2.j.a	$333$	$2$	333.j	111.g	$4$	$28$	$14$	$2.659$		$_{}$	None	None		✓	✓	✓	333.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
333.2.k.a	$333$	$2$	333.k	333.k	$6$	$2$	$1$	$2.659$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			333.2.k.a	$2$	$0$	$0$	$0$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-2\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+\cdots$
333.2.k.b	$333$	$2$	333.k	333.k	$6$	$4$	$2$	$2.659$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None		✓			333.2.k.b	$2$	$0$	$0$	$-6$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{3})q^{2}+(-1-\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots$
333.2.k.c	$333$	$2$	333.k	333.k	$6$	$66$	$33$	$2.659$		$_{}$	None	None		✓	✓		333.2.k.c	$2$	$0$	$0$	$3$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
333.2.q.a	$333$	$2$	333.q	333.q	$6$	$8$	$4$	$2.659$	8.0.592240896.6	$_{}$	None	None		✓			333.2.q.a	$4$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{2}+(-1+2\beta _{2})q^{3}-\beta _{1}q^{4}+\cdots$
333.2.q.b	$333$	$2$	333.q	333.q	$6$	$12$	$6$	$2.659$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			333.2.q.b	$4$	$0$	$0$	$-18$	$0$	$-2$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{5}q^{2}+(-2+\beta _{4})q^{3}+(2-2\beta _{4}+\cdots)q^{4}+\cdots$
333.2.q.c	$333$	$2$	333.q	333.q	$6$	$52$	$26$	$2.659$		$_{}$	None	None		✓	✓		333.2.q.c	$4$	$0$	$0$	$12$	$0$	$-2$			$\mathrm{SU}(2)[C_{6}]$
333.2.s.a	$333$	$2$	333.s	37.e	$6$	$2$	$1$	$2.659$	$\Q(\sqrt{-3}) $	$_{}$	None	None					111.2.j.a	$2$	$0$	$3$	$0$	$6$	$-1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+(4-2\zeta_{6})q^{5}+\cdots$
333.2.s.b	$333$	$2$	333.s	37.e	$6$	$4$	$2$	$2.659$	$\Q(\zeta_{12})$	$_{}$	None	None					37.2.e.a	$2$	$0$	$0$	$0$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}-\zeta_{12}^{2}q^{4}+(2-2\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
333.2.s.c	$333$	$2$	333.s	37.e	$6$	$4$	$2$	$2.659$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None					111.2.j.b	$2$	$0$	$3$	$0$	$-3$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-2\beta _{3})q^{4}+\cdots$
333.2.s.d	$333$	$2$	333.s	37.e	$6$	$6$	$3$	$2.659$	6.0.16553403.1	$_{}$	None	None					111.2.j.c	$2$	$0$	$0$	$0$	$-9$	$-3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{2}+(2-2\beta _{2}-\beta _{4}+\beta _{5})q^{4}+\cdots$
333.2.s.e	$333$	$2$	333.s	37.e	$6$	$8$	$4$	$2.659$	8.0.303595776.1	$_{}$	None	None		✓			333.2.s.e	$4$	$0$	$0$	$0$	$0$	$-6$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{5}q^{2}+(-1-\beta _{3})q^{4}+\beta _{7}q^{5}+(-2+\cdots)q^{7}+\cdots$
333.2.s.f	$333$	$2$	333.s	37.e	$6$	$8$	$4$	$2.659$	8.0.592240896.6	$_{}$	None	None		✓			333.2.s.f	$4$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{3}+\beta _{4})q^{2}+(-\beta _{1}+3\beta _{2})q^{4}+\cdots$
333.2.t.a	$333$	$2$	333.t	333.t	$6$	$2$	$1$	$2.659$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			333.2.k.a	$2$	$1$	$-3$	$-3$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2+\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}+(1+\cdots)q^{4}+\cdots$
333.2.t.b	$333$	$2$	333.t	333.t	$6$	$4$	$2$	$2.659$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None		✓			333.2.k.b	$2$	$1$	$-3$	$0$	$-9$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\beta _{1})q^{2}+(-1+2\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots$
333.2.t.c	$333$	$2$	333.t	333.t	$6$	$66$	$33$	$2.659$		$_{}$	None	None		✓	✓		333.2.k.c	$2$	$0$	$3$	$3$	$6$	$0$			$\mathrm{SU}(2)[C_{6}]$
333.2.w.a	$333$	$2$	333.w	333.w	$9$	$216$	$36$	$2.659$		$_{}$	None	None		✓	✓	✓	333.2.w.a	$2$	$0$	$-3$	$-12$	$-3$	$0$			$\mathrm{SU}(2)[C_{9}]$
333.2.x.a	$333$	$2$	333.x	37.f	$9$	$6$	$1$	$2.659$	$\Q(\zeta_{18})$	$_{}$	None	None					37.2.f.b	$2$	$1$	$-3$	$0$	$-6$	$-12$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-1+\zeta_{18}-\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{4}+\cdots)q^{2}+\cdots$
333.2.x.b	$333$	$2$	333.x	37.f	$9$	$6$	$1$	$2.659$	$\Q(\zeta_{18})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			333.2.x.b	$4$	$0$	$0$	$0$	$0$	$-3$		$1$	$\mathrm{U}(1)[D_{9}]$	$q+2\zeta_{18}^{5}q^{4}+(-2-2\zeta_{18}+3\zeta_{18}^{3}+\cdots)q^{7}+\cdots$
333.2.x.c	$333$	$2$	333.x	37.f	$9$	$6$	$1$	$2.659$	$\Q(\zeta_{18})$	$_{}$	None	None					37.2.f.a	$2$	$0$	$6$	$0$	$6$	$3$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(1-\zeta_{18}^{5})q^{2}+(1-\zeta_{18})q^{4}+(2\zeta_{18}^{3}+\cdots)q^{5}+\cdots$
333.2.x.d	$333$	$2$	333.x	37.f	$9$	$18$	$3$	$2.659$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None					111.2.k.a	$2$	$0$	$3$	$0$	$6$	$6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+\beta _{7}q^{2}+(\beta _{13}+\beta _{16})q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
333.2.x.e	$333$	$2$	333.x	37.f	$9$	$24$	$4$	$2.659$		$_{}$	None	None		✓			333.2.x.e	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{9}]$
333.2.x.f	$333$	$2$	333.x	37.f	$9$	$24$	$4$	$2.659$		$_{}$	None	None					111.2.k.b	$2$	$0$	$3$	$0$	$6$	$-9$			$\mathrm{SU}(2)[C_{9}]$
333.2.y.a	$333$	$2$	333.y	333.y	$9$	$216$	$36$	$2.659$		$_{}$	None	None		✓	✓	✓	333.2.w.a	$2$	$0$	$-3$	$-3$	$-3$	$0$			$\mathrm{SU}(2)[C_{9}]$
333.2.z.a	$333$	$2$	333.z	333.z	$12$	$144$	$36$	$2.659$		$_{}$	None	None		✓	✓	✓	333.2.z.a	$2$	$0$	$-6$	$-6$	$-6$	$2$			$\mathrm{SU}(2)[C_{12}]$
333.2.bc.a	$333$	$2$	333.bc	333.ac	$12$	$144$	$36$	$2.659$		$_{}$	None	None		✓	✓	✓	333.2.bc.a	$4$	$0$	$-6$	$0$	$-12$	$-4$			$\mathrm{SU}(2)[C_{12}]$
333.2.be.a	$333$	$2$	333.be	111.m	$12$	$56$	$14$	$2.659$		$_{}$	None	None		✓	✓	✓	333.2.be.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
333.2.bf.a	$333$	$2$	333.bf	333.af	$12$	$144$	$36$	$2.659$		$_{}$	None	None		✓	✓	✓	333.2.z.a	$2$	$0$	$-6$	$-6$	$0$	$-4$			$\mathrm{SU}(2)[C_{12}]$

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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.