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 189 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	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
182.2.a.a	$182$	$2$	182.a	1.a	$1$	$1$	$1$	$1.453$	$\Q$	None	✓	✓	✓	✓	182.2.a.a	$1$	$0$	$-1$	$1$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{7}+\cdots$
182.2.a.b	$182$	$2$	182.a	1.a	$1$	$1$	$1$	$1.453$	$\Q$	None	✓	✓	✓	✓	182.2.a.b	$1$	$0$	$-1$	$3$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-3q^{6}+q^{7}-q^{8}+\cdots$
182.2.a.c	$182$	$2$	182.a	1.a	$1$	$1$	$1$	$1.453$	$\Q$	None	✓	✓			182.2.a.c	$1$	$0$	$1$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}-3q^{9}+\cdots$
182.2.a.d	$182$	$2$	182.a	1.a	$1$	$1$	$1$	$1.453$	$\Q$	None	✓	✓	✓	✓	182.2.a.d	$1$	$0$	$1$	$1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots$
182.2.a.e	$182$	$2$	182.a	1.a	$1$	$1$	$1$	$1.453$	$\Q$	None	✓	✓			182.2.a.e	$1$	$0$	$1$	$3$	$-4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}-4q^{5}+3q^{6}-q^{7}+\cdots$
182.2.d.a	$182$	$2$	182.d	13.b	$2$	$2$	$2$	$1.453$	$\Q(\sqrt{-1}) $	None		✓			182.2.d.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{3}-q^{4}+2 i q^{5}-i q^{6}+\cdots$
182.2.d.b	$182$	$2$	182.d	13.b	$2$	$6$	$6$	$1.453$	6.0.30647296.1	None		✓	✓		182.2.d.b	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+\beta _{3}q^{3}-q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
182.2.e.a	$182$	$2$	182.e	91.h	$3$	$2$	$1$	$1.453$	$\Q(\sqrt{-3}) $	None		✓			182.2.e.a	$2$	$0$	$-2$	$-1$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}-\zeta_{6}q^{3}+q^{4}-\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots$
182.2.e.b	$182$	$2$	182.e	91.h	$3$	$2$	$1$	$1.453$	$\Q(\sqrt{-3}) $	None		✓			182.2.e.b	$2$	$0$	$-2$	$-1$	$3$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}-\zeta_{6}q^{3}+q^{4}+3\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots$
182.2.e.c	$182$	$2$	182.e	91.h	$3$	$6$	$3$	$1.453$	6.0.4740147.1	None		✓			182.2.e.c	$2$	$0$	$-6$	$1$	$0$	$-3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+\beta _{4}q^{3}+q^{4}+(\beta _{4}+\beta _{5})q^{5}+\cdots$
182.2.e.d	$182$	$2$	182.e	91.h	$3$	$10$	$5$	$1.453$	10.0.$\cdots$.1	None		✓	✓		182.2.e.d	$2$	$0$	$10$	$-1$	$-2$	$-3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}-\beta _{5}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{5}q^{6}+\cdots$
182.2.f.a	$182$	$2$	182.f	7.c	$3$	$2$	$1$	$1.453$	$\Q(\sqrt{-3}) $	None		✓			182.2.f.a	$2$	$0$	$1$	$0$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(2+\zeta_{6})q^{7}+\cdots$
182.2.f.b	$182$	$2$	182.f	7.c	$3$	$6$	$3$	$1.453$	6.0.309123.1	None		✓			182.2.f.b	$2$	$0$	$3$	$0$	$2$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$
182.2.f.c	$182$	$2$	182.f	7.c	$3$	$8$	$4$	$1.453$	8.0.8681953329.1	None		✓	✓		182.2.f.c	$2$	$0$	$-4$	$0$	$-2$	$7$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+(-\beta _{1}-\beta _{7})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots$
182.2.g.a	$182$	$2$	182.g	13.c	$3$	$2$	$1$	$1.453$	$\Q(\sqrt{-3}) $	None		✓			182.2.g.a	$2$	$0$	$1$	$-3$	$-6$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
182.2.g.b	$182$	$2$	182.g	13.c	$3$	$2$	$1$	$1.453$	$\Q(\sqrt{-3}) $	None		✓			182.2.g.b	$2$	$0$	$1$	$-1$	$6$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
182.2.g.c	$182$	$2$	182.g	13.c	$3$	$2$	$1$	$1.453$	$\Q(\sqrt{-3}) $	None		✓			182.2.g.c	$2$	$0$	$1$	$2$	$-6$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
182.2.g.d	$182$	$2$	182.g	13.c	$3$	$2$	$1$	$1.453$	$\Q(\sqrt{-3}) $	None		✓			182.2.g.d	$2$	$0$	$1$	$2$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
182.2.g.e	$182$	$2$	182.g	13.c	$3$	$4$	$2$	$1.453$	$\Q(\zeta_{12})$	None		✓	✓		182.2.g.e	$2$	$0$	$-2$	$0$	$8$	$2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_1 q^{2}+\beta_{2} q^{3}+(\beta_1-1)q^{4}+\cdots$
182.2.h.a	$182$	$2$	182.h	91.g	$3$	$2$	$1$	$1.453$	$\Q(\sqrt{-3}) $	None		✓			182.2.e.a	$2$	$0$	$1$	$2$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+q^{3}+(-1+\zeta_{6})q^{4}+(-1+\cdots)q^{5}+\cdots$
182.2.h.b	$182$	$2$	182.h	91.g	$3$	$2$	$1$	$1.453$	$\Q(\sqrt{-3}) $	None		✓			182.2.e.b	$2$	$0$	$1$	$2$	$3$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+q^{3}+(-1+\zeta_{6})q^{4}+(3-3\zeta_{6})q^{5}+\cdots$
182.2.h.c	$182$	$2$	182.h	91.g	$3$	$6$	$3$	$1.453$	6.0.4740147.1	None		✓			182.2.e.c	$2$	$0$	$3$	$-2$	$0$	$-12$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1+\beta _{1})q^{4}+(\beta _{4}+\cdots)q^{5}+\cdots$
182.2.h.d	$182$	$2$	182.h	91.g	$3$	$10$	$5$	$1.453$	10.0.$\cdots$.1	None		✓	✓		182.2.e.d	$2$	$0$	$-5$	$2$	$-2$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(-\beta _{4}+\beta _{5})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
182.2.i.a	$182$	$2$	182.i	91.i	$4$	$24$	$12$	$1.453$		None		✓	✓	✓	182.2.i.a	$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{4}]$
182.2.m.a	$182$	$2$	182.m	13.e	$6$	$4$	$2$	$1.453$	$\Q(\zeta_{12})$	None		✓			182.2.m.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(1-\zeta_{12}-\zeta_{12}^{2}+2\zeta_{12}^{3})q^{3}+\cdots$
182.2.m.b	$182$	$2$	182.m	13.e	$6$	$12$	$6$	$1.453$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓		182.2.m.b	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{5}q^{2}+(\beta _{2}+\beta _{10})q^{3}+(1-\beta _{7})q^{4}+\cdots$
182.2.n.a	$182$	$2$	182.n	91.r	$6$	$4$	$2$	$1.453$	$\Q(\zeta_{12})$	None		✓			182.2.n.a	$4$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}-2\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
182.2.n.b	$182$	$2$	182.n	91.r	$6$	$12$	$6$	$1.453$	12.0.$\cdots$.1	None		✓	✓		182.2.n.b	$4$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{10}q^{2}+(1-\beta _{7}+\beta _{9})q^{3}+(1-\beta _{7}+\cdots)q^{4}+\cdots$
182.2.o.a	$182$	$2$	182.o	91.k	$6$	$20$	$10$	$1.453$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓	✓	✓	182.2.o.a	$2$	$0$	$0$	$2$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{5}+\beta _{6})q^{2}-\beta _{19}q^{3}-q^{4}+(\beta _{8}+\cdots)q^{5}+\cdots$
182.2.v.a	$182$	$2$	182.v	91.u	$6$	$20$	$10$	$1.453$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓	✓	✓	182.2.o.a	$2$	$0$	$0$	$-4$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{6}q^{2}-\beta _{3}q^{3}+\beta _{4}q^{4}+(-\beta _{8}+\beta _{16}+\cdots)q^{5}+\cdots$
182.2.w.a	$182$	$2$	182.w	91.w	$12$	$40$	$10$	$1.453$		None		✓	✓	✓	182.2.w.a	$2$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{12}]$
182.2.ba.a	$182$	$2$	182.ba	91.ac	$12$	$32$	$8$	$1.453$		None		✓	✓	✓	182.2.ba.a	$4$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{12}]$
182.2.bb.a	$182$	$2$	182.bb	91.ab	$12$	$32$	$8$	$1.453$		None		✓	✓	✓	182.2.bb.a	$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{12}]$
182.2.bc.a	$182$	$2$	182.bc	91.aa	$12$	$40$	$10$	$1.453$		None		✓	✓	✓	182.2.w.a	$2$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{12}]$
182.3.b.a	$182$	$3$	182.b	7.b	$2$	$16$	$16$	$4.959$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓	✓	182.3.b.a	$2$	$0$	$0$	$0$	$0$	$4$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-\beta _{1}q^{3}+2q^{4}-\beta _{10}q^{5}+\cdots$
182.3.c.a	$182$	$3$	182.c	91.b	$2$	$16$	$16$	$4.959$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓	✓	182.3.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{9}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{2}+\beta _{1}q^{3}-2q^{4}-\beta _{12}q^{5}+\cdots$
182.3.j.a	$182$	$3$	182.j	13.d	$4$	$12$	$6$	$4.959$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓			182.3.j.a	$2$	$0$	$12$	$0$	$12$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{2})q^{2}-\beta _{5}q^{3}+2\beta _{2}q^{4}+(1+\cdots)q^{5}+\cdots$
182.3.j.b	$182$	$3$	182.j	13.d	$4$	$16$	$8$	$4.959$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓		182.3.j.b	$2$	$0$	$-16$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{7})q^{2}+\beta _{2}q^{3}+2\beta _{7}q^{4}+\cdots$
182.3.k.a	$182$	$3$	182.k	91.p	$6$	$36$	$18$	$4.959$		None		✓	✓	✓	182.3.k.a	$2$	$0$	$0$	$0$	$0$	$10$			$\mathrm{SU}(2)[C_{6}]$
182.3.l.a	$182$	$3$	182.l	91.m	$6$	$36$	$18$	$4.959$		None		✓	✓	✓	182.3.l.a	$2$	$0$	$0$	$0$	$0$	$-14$			$\mathrm{SU}(2)[C_{6}]$
182.3.p.a	$182$	$3$	182.p	91.n	$6$	$40$	$20$	$4.959$		None		✓	✓	✓	182.3.p.a	$4$	$0$	$0$	$0$	$0$	$-6$			$\mathrm{SU}(2)[C_{6}]$
182.3.q.a	$182$	$3$	182.q	91.s	$6$	$40$	$20$	$4.959$		None		✓	✓	✓	182.3.q.a	$4$	$0$	$0$	$12$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
182.3.r.a	$182$	$3$	182.r	91.l	$6$	$36$	$18$	$4.959$		None		✓	✓	✓	182.3.k.a	$2$	$0$	$0$	$6$	$0$	$8$			$\mathrm{SU}(2)[C_{6}]$
182.3.s.a	$182$	$3$	182.s	91.v	$6$	$36$	$18$	$4.959$		None		✓	✓	✓	182.3.l.a	$2$	$0$	$0$	$-6$	$0$	$4$			$\mathrm{SU}(2)[C_{6}]$
182.3.t.a	$182$	$3$	182.t	7.d	$6$	$32$	$16$	$4.959$		None		✓	✓	✓	182.3.t.a	$2$	$0$	$0$	$0$	$12$	$-4$			$\mathrm{SU}(2)[C_{6}]$
182.3.u.a	$182$	$3$	182.u	91.t	$6$	$40$	$20$	$4.959$		None		✓	✓	✓	182.3.u.a	$4$	$0$	$0$	$0$	$0$	$-18$			$\mathrm{SU}(2)[C_{6}]$
182.3.x.a	$182$	$3$	182.x	91.x	$12$	$36$	$9$	$4.959$		None		✓			182.3.x.a	$2$	$0$	$-36$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{12}]$
182.3.x.b	$182$	$3$	182.x	91.x	$12$	$36$	$9$	$4.959$		None		✓			182.3.x.b	$2$	$0$	$36$	$0$	$0$	$16$			$\mathrm{SU}(2)[C_{12}]$
182.3.y.a	$182$	$3$	182.y	13.f	$12$	$24$	$6$	$4.959$		None		✓			182.3.y.a	$2$	$0$	$-12$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{12}]$
182.3.y.b	$182$	$3$	182.y	13.f	$12$	$32$	$8$	$4.959$		None		✓	✓		182.3.y.b	$2$	$0$	$16$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$

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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.