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 140 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
133.1.m.a	$133$	$1$	133.m	133.m	$6$	$4$	$2$	$0.066$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓	✓	133.1.m.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{5}q^{5}+\cdots$
133.1.r.a	$133$	$1$	133.r	133.r	$6$	$2$	$1$	$0.066$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-19}) $	None		✓	✓	✓	133.1.r.a	$4$	$0$	$0$	$0$	$1$	$-1$		$1$		$q-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
133.2.a.a	$133$	$2$	133.a	1.a	$1$	$2$	$2$	$1.062$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓	✓	133.2.a.a	$1$	$1$	$-3$	$-3$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots$
133.2.a.b	$133$	$2$	133.a	1.a	$1$	$2$	$2$	$1.062$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓	✓	✓	133.2.a.b	$1$	$1$	$-1$	$-3$	$-6$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-2+\beta )q^{3}+(1+\beta )q^{4}-3q^{5}+\cdots$
133.2.a.c	$133$	$2$	133.a	1.a	$1$	$2$	$2$	$1.062$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓	✓	133.2.a.c	$1$	$0$	$1$	$3$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2-\beta )q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots$
133.2.a.d	$133$	$2$	133.a	1.a	$1$	$3$	$3$	$1.062$	3.3.229.1	$_{}$	None	None	✓	✓	✓	✓	133.2.a.d	$1$	$0$	$2$	$3$	$-2$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+(1-\beta _{1})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots$
133.2.c.a	$133$	$2$	133.c	133.c	$2$	$2$	$2$	$1.062$	$\Q(\sqrt{-19}) $	$_{}$	$\Q(\sqrt{-19}) $	None		✓			133.2.c.a	$4$	$0$	$0$	$0$	$0$	$-3$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{4}+(-1+2\beta )q^{5}+(-1-\beta )q^{7}+\cdots$
133.2.c.b	$133$	$2$	133.c	133.c	$2$	$4$	$4$	$1.062$	$\Q(i, \sqrt{13})$	$_{}$	None	None		✓			133.2.c.b	$2$	$0$	$0$	$-2$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+(-2+\beta _{3})q^{4}+\cdots$
133.2.c.c	$133$	$2$	133.c	133.c	$2$	$4$	$4$	$1.062$	$\Q(i, \sqrt{13})$	$_{}$	None	None		✓			133.2.c.b	$2$	$0$	$0$	$2$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(-2+\beta _{3})q^{4}+\cdots$
133.2.e.a	$133$	$2$	133.e	19.c	$3$	$4$	$2$	$1.062$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			133.2.e.a	$2$	$0$	$-1$	$0$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(1-2\beta _{1}+\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
133.2.e.b	$133$	$2$	133.e	19.c	$3$	$6$	$3$	$1.062$	6.0.309123.1	$_{}$	None	None		✓			133.2.e.b	$2$	$0$	$-2$	$-1$	$3$	$6$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{4}+\beta _{5})q^{2}+(\beta _{1}-\beta _{5})q^{3}+\cdots$
133.2.e.c	$133$	$2$	133.e	19.c	$3$	$10$	$5$	$1.062$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		✓	✓		133.2.e.c	$2$	$0$	$1$	$3$	$-1$	$-10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{6}+\beta _{7})q^{3}+(-1+\beta _{6}+\cdots)q^{4}+\cdots$
133.2.f.a	$133$	$2$	133.f	7.c	$3$	$2$	$1$	$1.062$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			133.2.f.a	$2$	$1$	$-2$	$-2$	$-3$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
133.2.f.b	$133$	$2$	133.f	7.c	$3$	$4$	$2$	$1.062$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			133.2.f.b	$2$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}-2\beta _{1}q^{5}+\cdots$
133.2.f.c	$133$	$2$	133.f	7.c	$3$	$4$	$2$	$1.062$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			133.2.f.c	$2$	$0$	$2$	$0$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots$
133.2.f.d	$133$	$2$	133.f	7.c	$3$	$14$	$7$	$1.062$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓	✓		133.2.f.d	$2$	$0$	$-2$	$2$	$2$	$-1$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{10}q^{2}+\beta _{8}q^{3}+(-2-\beta _{5}-\beta _{6}+\cdots)q^{4}+\cdots$
133.2.g.a	$133$	$2$	133.g	133.g	$3$	$24$	$12$	$1.062$		$_{}$	None	None		✓	✓	✓	133.2.g.a	$2$	$0$	$1$	$-6$	$0$	$-2$			$\mathrm{SU}(2)[C_{3}]$
133.2.h.a	$133$	$2$	133.h	133.h	$3$	$24$	$12$	$1.062$		$_{}$	None	None		✓	✓	✓	133.2.g.a	$2$	$0$	$-2$	$3$	$0$	$-2$			$\mathrm{SU}(2)[C_{3}]$
133.2.i.a	$133$	$2$	133.i	133.i	$6$	$2$	$1$	$1.062$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			133.2.i.a	$2$	$0$	$0$	$-1$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-2\zeta_{6})q^{2}-\zeta_{6}q^{3}-q^{4}+(-2+\cdots)q^{6}+\cdots$
133.2.i.b	$133$	$2$	133.i	133.i	$6$	$2$	$1$	$1.062$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			133.2.i.b	$2$	$0$	$0$	$1$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(-2+\cdots)q^{6}+\cdots$
133.2.i.c	$133$	$2$	133.i	133.i	$6$	$4$	$2$	$1.062$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None		✓			133.2.i.c	$2$	$0$	$0$	$1$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{3})q^{2}+(1-2\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots$
133.2.i.d	$133$	$2$	133.i	133.i	$6$	$16$	$8$	$1.062$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓		133.2.i.d	$2$	$0$	$0$	$-4$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{1}q^{2}+(1+\beta _{4}-\beta _{6}+\beta _{9})q^{3}+(-2+\cdots)q^{4}+\cdots$
133.2.o.a	$133$	$2$	133.o	133.o	$6$	$4$	$2$	$1.062$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			133.2.o.a	$2$	$0$	$-6$	$-2$	$0$	$-10$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots$
133.2.o.b	$133$	$2$	133.o	133.o	$6$	$4$	$2$	$1.062$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	$\Q(\sqrt{-19}) $	None		✓			133.2.o.b	$4$	$0$	$0$	$0$	$-3$	$3$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-2+2\beta _{2})q^{4}+(-1+\beta _{2}+\beta _{3})q^{5}+\cdots$
133.2.o.c	$133$	$2$	133.o	133.o	$6$	$4$	$2$	$1.062$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			133.2.o.a	$2$	$0$	$6$	$2$	$0$	$-10$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(1+\cdots)q^{3}+\cdots$
133.2.o.d	$133$	$2$	133.o	133.o	$6$	$6$	$3$	$1.062$	6.0.6967728.1	$_{}$	None	None		✓			133.2.o.d	$2$	$0$	$-9$	$2$	$-3$	$5$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots$
133.2.o.e	$133$	$2$	133.o	133.o	$6$	$6$	$3$	$1.062$	6.0.6967728.1	$_{}$	None	None		✓			133.2.o.d	$2$	$0$	$9$	$-2$	$-3$	$5$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{3})q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots$
133.2.p.a	$133$	$2$	133.p	133.p	$6$	$4$	$2$	$1.062$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None		✓			133.2.p.a	$2$	$0$	$-3$	$-2$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\beta _{3})q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
133.2.p.b	$133$	$2$	133.p	133.p	$6$	$4$	$2$	$1.062$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None		✓			133.2.p.a	$2$	$0$	$-3$	$2$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\beta _{3})q^{2}+\beta _{2}q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
133.2.p.c	$133$	$2$	133.p	133.p	$6$	$12$	$6$	$1.062$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓		133.2.p.c	$4$	$0$	$0$	$0$	$0$	$-12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{2}+\beta _{6}+\beta _{11})q^{2}+(-\beta _{7}-\beta _{8}+\cdots)q^{3}+\cdots$
133.2.s.a	$133$	$2$	133.s	133.s	$6$	$2$	$1$	$1.062$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			133.2.i.a	$2$	$1$	$-3$	$-2$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2+\zeta_{6})q^{2}-q^{3}+(1-\zeta_{6})q^{4}+\cdots$
133.2.s.b	$133$	$2$	133.s	133.s	$6$	$2$	$1$	$1.062$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			133.2.i.b	$2$	$0$	$3$	$2$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-\zeta_{6})q^{2}+q^{3}+(1-\zeta_{6})q^{4}+(2+\cdots)q^{6}+\cdots$
133.2.s.c	$133$	$2$	133.s	133.s	$6$	$4$	$2$	$1.062$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None		✓			133.2.i.c	$2$	$0$	$-3$	$2$	$-9$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\beta _{3})q^{2}+(1-\beta _{1}-\beta _{3})q^{3}+\cdots$
133.2.s.d	$133$	$2$	133.s	133.s	$6$	$16$	$8$	$1.062$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓		133.2.i.d	$2$	$0$	$0$	$-8$	$9$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}+\beta _{2})q^{2}+\beta _{4}q^{3}+(4-\beta _{2}-3\beta _{6}+\cdots)q^{4}+\cdots$
133.2.u.a	$133$	$2$	133.u	133.u	$9$	$66$	$11$	$1.062$		$_{}$	None	None		✓	✓	✓	133.2.u.a	$2$	$0$	$-3$	$-3$	$-3$	$0$			$\mathrm{SU}(2)[C_{9}]$
133.2.v.a	$133$	$2$	133.v	19.e	$9$	$30$	$5$	$1.062$		$_{}$	None	None		✓			133.2.v.a	$2$	$0$	$0$	$-3$	$-3$	$-15$			$\mathrm{SU}(2)[C_{9}]$
133.2.v.b	$133$	$2$	133.v	19.e	$9$	$30$	$5$	$1.062$		$_{}$	None	None		✓			133.2.v.b	$2$	$0$	$0$	$-3$	$3$	$15$			$\mathrm{SU}(2)[C_{9}]$
133.2.w.a	$133$	$2$	133.w	133.w	$9$	$66$	$11$	$1.062$		$_{}$	None	None		✓	✓	✓	133.2.u.a	$2$	$0$	$-3$	$-3$	$-3$	$-9$			$\mathrm{SU}(2)[C_{9}]$
133.2.ba.a	$133$	$2$	133.ba	133.aa	$18$	$72$	$12$	$1.062$		$_{}$	None	None		✓	✓	✓	133.2.ba.a	$4$	$0$	$-12$	$0$	$0$	$-6$			$\mathrm{SU}(2)[C_{18}]$
133.2.bb.a	$133$	$2$	133.bb	133.ab	$18$	$66$	$11$	$1.062$		$_{}$	None	None		✓	✓	✓	133.2.bb.a	$2$	$0$	$-3$	$-9$	$-9$	$-6$			$\mathrm{SU}(2)[C_{18}]$
133.2.bf.a	$133$	$2$	133.bf	133.af	$18$	$66$	$11$	$1.062$		$_{}$	None	None		✓	✓	✓	133.2.bb.a	$2$	$0$	$-3$	$-9$	$-9$	$3$			$\mathrm{SU}(2)[C_{18}]$
133.3.b.a	$133$	$3$	133.b	19.b	$2$	$20$	$20$	$3.624$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓	✓	✓	133.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{9}q^{3}+(-2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots$
133.3.d.a	$133$	$3$	133.d	7.b	$2$	$4$	$4$	$3.624$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	None	None		✓			133.3.d.a	$2$	$0$	$4$	$0$	$0$	$3$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(\beta _{1}-\beta _{3})q^{3}-3q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots$
133.3.d.b	$133$	$3$	133.d	7.b	$2$	$20$	$20$	$3.624$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓	✓		133.3.d.b	$2$	$0$	$-2$	$0$	$0$	$2$		$2^{8}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-\beta _{9}q^{3}+(3+\beta _{1})q^{4}+\beta _{15}q^{5}+\cdots$
133.3.j.a	$133$	$3$	133.j	133.j	$6$	$48$	$24$	$3.624$		$_{}$	None	None		✓	✓	✓	133.3.j.a	$2$	$0$	$0$	$-3$	$-4$	$-2$			$\mathrm{SU}(2)[C_{6}]$
133.3.k.a	$133$	$3$	133.k	133.k	$6$	$48$	$24$	$3.624$		$_{}$	None	None		✓	✓	✓	133.3.k.a	$2$	$0$	$1$	$0$	$-6$	$-8$			$\mathrm{SU}(2)[C_{6}]$
133.3.l.a	$133$	$3$	133.l	7.d	$6$	$48$	$24$	$3.624$		$_{}$	None	None		✓	✓	✓	133.3.l.a	$2$	$0$	$-2$	$0$	$-3$	$-5$			$\mathrm{SU}(2)[C_{6}]$
133.3.m.a	$133$	$3$	133.m	133.m	$6$	$52$	$26$	$3.624$		$_{}$	None	None		✓	✓	✓	133.3.m.a	$4$	$0$	$-2$	$0$	$0$	$12$			$\mathrm{SU}(2)[C_{6}]$
133.3.n.a	$133$	$3$	133.n	133.n	$6$	$48$	$24$	$3.624$		$_{}$	None	None		✓	✓	✓	133.3.j.a	$2$	$0$	$-3$	$0$	$2$	$-2$			$\mathrm{SU}(2)[C_{6}]$
133.3.q.a	$133$	$3$	133.q	19.d	$6$	$40$	$20$	$3.624$		$_{}$	None	None		✓	✓	✓	133.3.q.a	$2$	$0$	$0$	$12$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$

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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.