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 111 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
152.1.g.a	$152$	$1$	152.g	152.g	$2$	$1$	$1$	$0.076$	$\Q$	$D_{3}$	$\Q(\sqrt{-38}) $	None	✓	✓			152.1.g.a	$2$	$0$	$-1$	$1$	$0$	$-1$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
152.1.g.b	$152$	$1$	152.g	152.g	$2$	$1$	$1$	$0.076$	$\Q$	$D_{3}$	$\Q(\sqrt{-38}) $	None	✓	✓			152.1.g.a	$2$	$0$	$1$	$-1$	$0$	$-1$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$
152.1.k.a	$152$	$1$	152.k	152.k	$6$	$2$	$1$	$0.076$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		✓	✓	✓	152.1.k.a	$4$	$0$	$-1$	$1$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots$
152.1.u.a	$152$	$1$	152.u	152.u	$18$	$6$	$1$	$0.076$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		✓	✓	✓	152.1.u.a	$4$	$0$	$0$	$-3$	$0$	$0$		$1$		$q-\zeta_{18}^{5}q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7})q^{3}-\zeta_{18}q^{4}+\cdots$
152.2.a.a	$152$	$2$	152.a	1.a	$1$	$1$	$1$	$1.214$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	152.2.a.a	$1$	$1$	$0$	$-2$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots$
152.2.a.b	$152$	$2$	152.a	1.a	$1$	$1$	$1$	$1.214$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	152.2.a.b	$1$	$0$	$0$	$1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{7}-2q^{9}+2q^{11}+q^{13}+\cdots$
152.2.a.c	$152$	$2$	152.a	1.a	$1$	$3$	$3$	$1.214$	3.3.961.1	$_{}$	None	None	✓	✓	✓	✓	152.2.a.c	$1$	$0$	$0$	$1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots$
152.2.b.a	$152$	$2$	152.b	152.b	$2$	$2$	$2$	$1.214$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-2}) $	None		✓			152.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}+2\beta q^{3}-2q^{4}-4q^{6}-2\beta q^{8}+\cdots$
152.2.b.b	$152$	$2$	152.b	152.b	$2$	$4$	$4$	$1.214$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			152.2.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}+\beta _{3}q^{4}+(-2+\cdots)q^{6}+\cdots$
152.2.b.c	$152$	$2$	152.b	152.b	$2$	$12$	$12$	$1.214$	12.0.$\cdots$.1	$_{}$	None	None		✓	✓		152.2.b.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}+(-\beta _{5}+\beta _{8}+\cdots)q^{5}+\cdots$
152.2.c.a	$152$	$2$	152.c	8.b	$2$	$2$	$2$	$1.214$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			152.2.c.a	$2$	$0$	$-2$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(i-1)q^{2}-2 i q^{4}+2 q^{7}+(2 i+2)q^{8}+\cdots$
152.2.c.b	$152$	$2$	152.c	8.b	$2$	$16$	$16$	$1.214$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		152.2.c.b	$2$	$0$	$0$	$0$	$0$	$-8$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{2}+\beta _{4}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots$
152.2.i.a	$152$	$2$	152.i	19.c	$3$	$2$	$1$	$1.214$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			152.2.i.a	$2$	$0$	$0$	$-1$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots$
152.2.i.b	$152$	$2$	152.i	19.c	$3$	$2$	$1$	$1.214$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			152.2.i.b	$2$	$0$	$0$	$-1$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots$
152.2.i.c	$152$	$2$	152.i	19.c	$3$	$6$	$3$	$1.214$	6.0.2696112.1	$_{}$	None	None		✓	✓		152.2.i.c	$2$	$0$	$0$	$-1$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{5})q^{3}-\beta _{1}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
152.2.o.a	$152$	$2$	152.o	152.o	$6$	$4$	$2$	$1.214$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			152.2.o.a	$4$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$
152.2.o.b	$152$	$2$	152.o	152.o	$6$	$4$	$2$	$1.214$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-2}) $	None		✓			152.2.o.b	$4$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$
152.2.o.c	$152$	$2$	152.o	152.o	$6$	$28$	$14$	$1.214$		$_{}$	None	None		✓	✓		152.2.o.c	$4$	$0$	$-3$	$-6$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
152.2.p.a	$152$	$2$	152.p	152.p	$6$	$36$	$18$	$1.214$		$_{}$	None	None		✓	✓	✓	152.2.p.a	$4$	$0$	$-1$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{6}]$
152.2.q.a	$152$	$2$	152.q	19.e	$9$	$6$	$1$	$1.214$	$\Q(\zeta_{18})$	$_{}$	None	None		✓			152.2.q.a	$2$	$0$	$0$	$-6$	$6$	$3$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-1+\zeta_{18}^{2}-\zeta_{18}^{5})q^{3}+(1-\zeta_{18}^{5})q^{5}+\cdots$
152.2.q.b	$152$	$2$	152.q	19.e	$9$	$6$	$1$	$1.214$	$\Q(\zeta_{18})$	$_{}$	None	None		✓			152.2.q.b	$2$	$0$	$0$	$9$	$-6$	$6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(1-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}+2\zeta_{18}^{5})q^{3}+\cdots$
152.2.q.c	$152$	$2$	152.q	19.e	$9$	$18$	$3$	$1.214$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓	✓		152.2.q.c	$2$	$0$	$0$	$0$	$0$	$-9$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\beta _{2}-\beta _{4})q^{3}+(-\beta _{6}+\beta _{7}-\beta _{10}+\cdots)q^{5}+\cdots$
152.2.t.a	$152$	$2$	152.t	152.t	$18$	$108$	$18$	$1.214$		$_{}$	None	None		✓	✓	✓	152.2.t.a	$4$	$0$	$-6$	$0$	$0$	$-6$			$\mathrm{SU}(2)[C_{18}]$
152.2.v.a	$152$	$2$	152.v	152.v	$18$	$12$	$2$	$1.214$	12.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-2}) $	None		✓			152.2.v.a	$4$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{18}]$	$q-\beta _{11}q^{2}+(\beta _{1}+\beta _{3}-\beta _{6}-\beta _{9}+\beta _{10}+\cdots)q^{3}+\cdots$
152.2.v.b	$152$	$2$	152.v	152.v	$18$	$96$	$16$	$1.214$		$_{}$	None	None		✓	✓		152.2.v.b	$4$	$0$	$-6$	$-6$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
152.3.e.a	$152$	$3$	152.e	19.b	$2$	$2$	$2$	$4.142$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			152.3.e.a	$2$	$0$	$0$	$0$	$14$	$22$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+7q^{5}+11q^{7}-23q^{9}+3q^{11}+\cdots$
152.3.e.b	$152$	$3$	152.e	19.b	$2$	$8$	$8$	$4.142$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		✓	✓		152.3.e.b	$2$	$0$	$0$	$0$	$-14$	$-6$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-2-\beta _{4})q^{5}+(-1+\beta _{3}+\cdots)q^{7}+\cdots$
152.3.f.a	$152$	$3$	152.f	8.d	$2$	$36$	$36$	$4.142$		$_{}$	None	None		✓	✓	✓	152.3.f.a	$2$	$0$	$2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
152.3.g.a	$152$	$3$	152.g	152.g	$2$	$3$	$3$	$4.142$	3.3.4104.1	$_{}$	$\Q(\sqrt{-38}) $	None	✓	✓			152.3.g.a	$2$	$0$	$-6$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots$
152.3.g.b	$152$	$3$	152.g	152.g	$2$	$3$	$3$	$4.142$	3.3.4104.1	$_{}$	$\Q(\sqrt{-38}) $	None	✓	✓			152.3.g.a	$2$	$0$	$6$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots$
152.3.g.c	$152$	$3$	152.g	152.g	$2$	$32$	$32$	$4.142$		$_{}$	None	None		✓	✓		152.3.g.c	$4$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{2}]$
152.3.k.a	$152$	$3$	152.k	152.k	$6$	$4$	$2$	$4.142$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-2}) $	None		✓			152.3.k.a	$4$	$0$	$4$	$-2$	$0$	$0$		$2^{2}\cdot 3$	$\mathrm{U}(1)[D_{6}]$	$q+2\beta _{1}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(-4+4\beta _{1}+\cdots)q^{4}+\cdots$
152.3.k.b	$152$	$3$	152.k	152.k	$6$	$72$	$36$	$4.142$		$_{}$	None	None		✓	✓		152.3.k.b	$4$	$0$	$-5$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
152.3.l.a	$152$	$3$	152.l	152.l	$6$	$76$	$38$	$4.142$		$_{}$	None	None		✓	✓	✓	152.3.l.a	$4$	$0$	$-3$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{6}]$
152.3.n.a	$152$	$3$	152.n	19.d	$6$	$20$	$10$	$4.142$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓	✓	✓	152.3.n.a	$2$	$0$	$0$	$-6$	$0$	$-16$		$2^{14}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{2}q^{3}+\beta _{19}q^{5}+(-1-\beta _{3})q^{7}+\cdots$
152.3.r.a	$152$	$3$	152.r	19.f	$18$	$60$	$10$	$4.142$		$_{}$	None	None		✓	✓	✓	152.3.r.a	$2$	$0$	$0$	$6$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
152.3.s.a	$152$	$3$	152.s	152.s	$18$	$228$	$38$	$4.142$		$_{}$	None	None		✓	✓	✓	152.3.s.a	$4$	$0$	$-6$	$0$	$0$	$-6$			$\mathrm{SU}(2)[C_{18}]$
152.3.u.a	$152$	$3$	152.u	152.u	$18$	$12$	$2$	$4.142$	12.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-2}) $	None		✓			152.3.u.a	$4$	$0$	$0$	$6$	$0$	$0$		$2^{6}\cdot 3$	$\mathrm{U}(1)[D_{18}]$	$q+(-2\beta _{1}+2\beta _{5})q^{2}+(\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots$
152.3.u.b	$152$	$3$	152.u	152.u	$18$	$216$	$36$	$4.142$		$_{}$	None	None		✓	✓		152.3.u.b	$4$	$0$	$-6$	$-18$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
152.4.a.a	$152$	$4$	152.a	1.a	$1$	$2$	$2$	$8.968$	$\Q(\sqrt{57}) $	$_{}$	None	None	✓	✓	✓	✓	152.4.a.a	$1$	$1$	$0$	$-1$	$-5$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-3+\beta )q^{5}+(-5+4\beta )q^{7}+\cdots$
152.4.a.b	$152$	$4$	152.a	1.a	$1$	$3$	$3$	$8.968$	3.3.3221.1	$_{}$	None	None	✓	✓	✓	✓	152.4.a.b	$1$	$1$	$0$	$-5$	$2$	$-35$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-2-\beta _{2})q^{3}+(1-\beta _{1}+2\beta _{2})q^{5}+\cdots$
152.4.a.c	$152$	$4$	152.a	1.a	$1$	$3$	$3$	$8.968$	3.3.7057.1	$_{}$	None	None	✓	✓	✓	✓	152.4.a.c	$1$	$0$	$0$	$4$	$7$	$7$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(2+2\beta _{1}+\beta _{2})q^{5}+(2+\cdots)q^{7}+\cdots$
152.4.a.d	$152$	$4$	152.a	1.a	$1$	$5$	$5$	$8.968$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	152.4.a.d	$1$	$0$	$0$	$2$	$0$	$22$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(4+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
152.4.b.a	$152$	$4$	152.b	152.b	$2$	$2$	$2$	$8.968$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-2}) $	None		✓			152.4.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2\beta q^{2}-2\beta q^{3}-8q^{4}+8q^{6}-2^{4}\beta q^{8}+\cdots$
152.4.b.b	$152$	$4$	152.b	152.b	$2$	$56$	$56$	$8.968$		$_{}$	None	None		✓	✓		152.4.b.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
152.4.c.a	$152$	$4$	152.c	8.b	$2$	$54$	$54$	$8.968$		$_{}$	None	None		✓	✓	✓	152.4.c.a	$2$	$0$	$2$	$0$	$0$	$28$			$\mathrm{SU}(2)[C_{2}]$
152.4.i.a	$152$	$4$	152.i	19.c	$3$	$14$	$7$	$8.968$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓			152.4.i.a	$2$	$0$	$0$	$5$	$5$	$-28$		$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{7})q^{3}+(\beta _{7}+\beta _{8})q^{5}+(-2+\cdots)q^{7}+\cdots$
152.4.i.b	$152$	$4$	152.i	19.c	$3$	$16$	$8$	$8.968$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓		152.4.i.b	$2$	$0$	$0$	$0$	$-5$	$-8$		$2^{12}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{5}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
152.4.o.a	$152$	$4$	152.o	152.o	$6$	$4$	$2$	$8.968$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-2}) $	None		✓			152.4.o.a	$4$	$0$	$0$	$-30$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+2\beta _{1}q^{2}+(-5+\beta _{1}-5\beta _{2})q^{3}+8\beta _{2}q^{4}+\cdots$
152.4.o.b	$152$	$4$	152.o	152.o	$6$	$112$	$56$	$8.968$		$_{}$	None	None		✓	✓		152.4.o.b	$4$	$0$	$-3$	$24$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$

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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.