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 102 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
456.1.l.a	$456$	$1$	456.l	456.l	$2$	$1$	$1$	$0.228$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-114}) $	$\Q(\sqrt{57}) $	✓	✓			456.1.l.a	$4$	$0$	$-1$	$1$	$0$	$0$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
456.1.l.b	$456$	$1$	456.l	456.l	$2$	$1$	$1$	$0.228$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-114}) $	$\Q(\sqrt{57}) $	✓	✓			456.1.l.a	$4$	$0$	$1$	$-1$	$0$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
456.1.s.a	$456$	$1$	456.s	456.s	$6$	$2$	$1$	$0.228$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		✓			456.1.s.a	$4$	$0$	$-1$	$-2$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{6}+\cdots$
456.1.s.b	$456$	$1$	456.s	456.s	$6$	$2$	$1$	$0.228$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		✓			456.1.s.a	$4$	$0$	$1$	$-1$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}-q^{8}+\cdots$
456.1.bt.a	$456$	$1$	456.bt	456.at	$18$	$6$	$1$	$0.228$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-2}) $	None		✓			456.1.bt.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{5}q^{2}-\zeta_{18}^{7}q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{3}q^{6}+\cdots$
456.1.bt.b	$456$	$1$	456.bt	456.at	$18$	$6$	$1$	$0.228$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-2}) $	None		✓			456.1.bt.a	$4$	$0$	$0$	$3$	$0$	$0$		$1$		$q-\zeta_{18}^{5}q^{2}-\zeta_{18}^{6}q^{3}-\zeta_{18}q^{4}-\zeta_{18}^{2}q^{6}+\cdots$
456.2.a.a	$456$	$2$	456.a	1.a	$1$	$1$	$1$	$3.641$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	456.2.a.a	$1$	$1$	$0$	$-1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-3q^{7}+q^{9}-5q^{11}-2q^{13}+\cdots$
456.2.a.b	$456$	$2$	456.a	1.a	$1$	$1$	$1$	$3.641$	$\Q$	$_{}$	None	None	✓	✓			456.2.a.b	$1$	$0$	$0$	$-1$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots$
456.2.a.c	$456$	$2$	456.a	1.a	$1$	$1$	$1$	$3.641$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	456.2.a.c	$1$	$1$	$0$	$1$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}-3q^{7}+q^{9}-q^{11}-2q^{13}+\cdots$
456.2.a.d	$456$	$2$	456.a	1.a	$1$	$1$	$1$	$3.641$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	456.2.a.d	$1$	$0$	$0$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots$
456.2.a.e	$456$	$2$	456.a	1.a	$1$	$2$	$2$	$3.641$	$\Q(\sqrt{41}) $	$_{}$	None	None	✓	✓	✓		456.2.a.e	$1$	$0$	$0$	$-2$	$-1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta q^{5}+(-2+\beta )q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots$
456.2.a.f	$456$	$2$	456.a	1.a	$1$	$2$	$2$	$3.641$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓	✓	456.2.a.f	$1$	$0$	$0$	$2$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots$
456.2.e.a	$456$	$2$	456.e	152.b	$2$	$40$	$40$	$3.641$		$_{}$	None	None		✓	✓	✓	456.2.e.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
456.2.f.a	$456$	$2$	456.f	57.d	$2$	$10$	$10$	$3.641$	10.0.$\cdots$.1	$_{}$	None	None		✓			456.2.f.a	$2$	$0$	$0$	$-1$	$0$	$-2$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}+\beta _{6}q^{5}-\beta _{4}q^{7}-\beta _{3}q^{9}+\cdots$
456.2.f.b	$456$	$2$	456.f	57.d	$2$	$10$	$10$	$3.641$	10.0.$\cdots$.1	$_{}$	None	None		✓			456.2.f.a	$2$	$0$	$0$	$1$	$0$	$-2$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}+\beta _{6}q^{5}-\beta _{4}q^{7}-\beta _{3}q^{9}+\cdots$
456.2.g.a	$456$	$2$	456.g	8.b	$2$	$18$	$18$	$3.641$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓			456.2.g.a	$2$	$0$	$2$	$0$	$0$	$-12$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{14}q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+\beta _{13}q^{5}+\cdots$
456.2.g.b	$456$	$2$	456.g	8.b	$2$	$18$	$18$	$3.641$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓			456.2.g.b	$2$	$0$	$2$	$0$	$0$	$20$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{2}+\beta _{4}q^{3}+\beta _{2}q^{4}-\beta _{5}q^{5}+\cdots$
456.2.j.a	$456$	$2$	456.j	24.f	$2$	$4$	$4$	$3.641$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		✓			456.2.j.a	$4$	$0$	$0$	$-4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(1+\beta _{3})q^{4}+\cdots$
456.2.j.b	$456$	$2$	456.j	24.f	$2$	$8$	$8$	$3.641$	8.0.170772624.1	$_{}$	None	None		✓			456.2.j.b	$4$	$0$	$0$	$-2$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(-\beta _{1}-\beta _{5}-\beta _{6}-\beta _{7})q^{3}+\cdots$
456.2.j.c	$456$	$2$	456.j	24.f	$2$	$12$	$12$	$3.641$	12.0.$\cdots$.1	$_{}$	None	None		✓			456.2.j.c	$4$	$0$	$0$	$-2$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-\beta _{8}q^{3}+(-\beta _{4}+\beta _{5})q^{4}+\cdots$
456.2.j.d	$456$	$2$	456.j	24.f	$2$	$24$	$24$	$3.641$		$_{}$	None	None		✓			456.2.j.d	$4$	$0$	$0$	$2$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
456.2.j.e	$456$	$2$	456.j	24.f	$2$	$24$	$24$	$3.641$		$_{}$	None	None		✓			456.2.j.e	$4$	$0$	$0$	$6$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
456.2.p.a	$456$	$2$	456.p	456.p	$2$	$12$	$12$	$3.641$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	$\Q(\sqrt{-38}) $	None		✓			456.2.p.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{3}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{3}q^{2}+\beta _{8}q^{3}-2q^{4}-\beta _{2}q^{6}+(\beta _{10}+\cdots)q^{7}+\cdots$
456.2.p.b	$456$	$2$	456.p	456.p	$2$	$64$	$64$	$3.641$		$_{}$	None	None		✓	✓		456.2.p.b	$8$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$
456.2.q.a	$456$	$2$	456.q	19.c	$3$	$2$	$1$	$3.641$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			456.2.q.a	$2$	$1$	$0$	$-1$	$-2$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{5}-3q^{7}+\cdots$
456.2.q.b	$456$	$2$	456.q	19.c	$3$	$2$	$1$	$3.641$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			456.2.q.b	$2$	$0$	$0$	$-1$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+3q^{7}-\zeta_{6}q^{9}+2q^{11}+\cdots$
456.2.q.c	$456$	$2$	456.q	19.c	$3$	$2$	$1$	$3.641$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			456.2.q.c	$2$	$0$	$0$	$1$	$2$	$-10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{5}-5q^{7}+\cdots$
456.2.q.d	$456$	$2$	456.q	19.c	$3$	$4$	$2$	$3.641$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			456.2.q.d	$2$	$0$	$0$	$-2$	$2$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{1})q^{3}+(1+\beta _{1}+\beta _{2})q^{5}+\cdots$
456.2.q.e	$456$	$2$	456.q	19.c	$3$	$4$	$2$	$3.641$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			456.2.q.e	$2$	$0$	$0$	$2$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1})q^{3}+(-1-\beta _{1}-\beta _{2})q^{5}+\cdots$
456.2.q.f	$456$	$2$	456.q	19.c	$3$	$6$	$3$	$3.641$	$\Q(\zeta_{18})$	$_{}$	None	None		✓	✓		456.2.q.f	$2$	$0$	$0$	$3$	$0$	$6$		$2^{6}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta_1 q^{3}+\beta_{2} q^{5}+(\beta_{5}+1)q^{7}+\cdots$
456.2.u.a	$456$	$2$	456.u	456.u	$6$	$4$	$2$	$3.641$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-2}) $	None		✓			456.2.u.a	$4$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots$
456.2.u.b	$456$	$2$	456.u	456.u	$6$	$4$	$2$	$3.641$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-2}) $	None		✓			456.2.u.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots$
456.2.u.c	$456$	$2$	456.u	456.u	$6$	$8$	$4$	$3.641$	$\Q(\sqrt{2}, \sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		✓			456.2.u.c	$8$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}-\beta _{7})q^{2}-\beta _{3}q^{3}+(-2+2\beta _{6}+\cdots)q^{4}+\cdots$
456.2.u.d	$456$	$2$	456.u	456.u	$6$	$136$	$68$	$3.641$		$_{}$	None	None		✓	✓		456.2.u.d	$8$	$0$	$0$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
456.2.v.a	$456$	$2$	456.v	456.v	$6$	$152$	$76$	$3.641$		$_{}$	None	None		✓	✓	✓	456.2.v.a	$8$	$0$	$0$	$0$	$0$	$-16$			$\mathrm{SU}(2)[C_{6}]$
456.2.y.a	$456$	$2$	456.y	152.o	$6$	$80$	$40$	$3.641$		$_{}$	None	None		✓	✓	✓	456.2.y.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
456.2.be.a	$456$	$2$	456.be	152.p	$6$	$80$	$40$	$3.641$		$_{}$	None	None		✓	✓	✓	456.2.be.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
456.2.bf.a	$456$	$2$	456.bf	57.f	$6$	$4$	$2$	$3.641$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		✓			456.2.bf.a	$2$	$0$	$0$	$1$	$-3$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
456.2.bf.b	$456$	$2$	456.bf	57.f	$6$	$4$	$2$	$3.641$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		✓			456.2.bf.a	$2$	$0$	$0$	$2$	$3$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{1})q^{5}+(1+\cdots)q^{7}+\cdots$
456.2.bf.c	$456$	$2$	456.bf	57.f	$6$	$16$	$8$	$3.641$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			456.2.bf.c	$2$	$0$	$0$	$-1$	$-3$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{1}q^{3}-\beta _{14}q^{5}+(\beta _{5}-\beta _{13})q^{7}+\cdots$
456.2.bf.d	$456$	$2$	456.bf	57.f	$6$	$16$	$8$	$3.641$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			456.2.bf.c	$2$	$0$	$0$	$1$	$3$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{4}q^{3}+(-\beta _{11}+\beta _{14})q^{5}+(\beta _{5}-\beta _{13}+\cdots)q^{7}+\cdots$
456.2.bg.a	$456$	$2$	456.bg	19.e	$9$	$12$	$2$	$3.641$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			456.2.bg.a	$2$	$0$	$0$	$0$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\beta _{2}-\beta _{11})q^{3}-\beta _{1}q^{5}+(-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
456.2.bg.b	$456$	$2$	456.bg	19.e	$9$	$12$	$2$	$3.641$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			456.2.bg.b	$2$	$0$	$0$	$0$	$3$	$-6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{4}q^{3}+(1+\beta _{6}+\beta _{9}+\beta _{11})q^{5}+\cdots$
456.2.bg.c	$456$	$2$	456.bg	19.e	$9$	$18$	$3$	$3.641$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓			456.2.bg.c	$2$	$0$	$0$	$0$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{7}q^{3}+(\beta _{2}-\beta _{4})q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
456.2.bg.d	$456$	$2$	456.bg	19.e	$9$	$18$	$3$	$3.641$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		✓			456.2.bg.d	$2$	$0$	$0$	$0$	$3$	$6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+\beta _{9}q^{3}+(1+\beta _{5}-\beta _{6}+\beta _{12}+\beta _{16}+\cdots)q^{5}+\cdots$
456.2.bj.a	$456$	$2$	456.bj	456.aj	$18$	$456$	$76$	$3.641$		$_{}$	None	None		✓	✓	✓	456.2.bj.a	$8$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{18}]$
456.2.bk.a	$456$	$2$	456.bk	152.t	$18$	$240$	$40$	$3.641$		$_{}$	None	None		✓	✓	✓	456.2.bk.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
456.2.bm.a	$456$	$2$	456.bm	57.j	$18$	$60$	$10$	$3.641$		$_{}$	None	None		✓			456.2.bm.a	$2$	$0$	$0$	$-3$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
456.2.bm.b	$456$	$2$	456.bm	57.j	$18$	$60$	$10$	$3.641$		$_{}$	None	None		✓			456.2.bm.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
456.2.bp.a	$456$	$2$	456.bp	152.v	$18$	$240$	$40$	$3.641$		$_{}$	None	None		✓	✓	✓	456.2.bp.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$

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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.