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 215 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
156.1.o.a	$156$	$1$	156.o	39.i	$6$	$2$	$1$	$0.078$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	156.1.o.a	$4$	$0$	$0$	$-1$	$0$	$1$		$1$		$q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{13}+\cdots$
156.1.s.a	$156$	$1$	156.s	39.h	$6$	$2$	$1$	$0.078$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	156.1.s.a	$4$	$0$	$0$	$1$	$0$	$-3$		$1$		$q+\zeta_{6}q^{3}+(-1-\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
156.2.a.a	$156$	$2$	156.a	1.a	$1$	$1$	$1$	$1.246$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	156.2.a.a	$1$	$1$	$0$	$-1$	$-4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots$
156.2.a.b	$156$	$2$	156.a	1.a	$1$	$1$	$1$	$1.246$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	156.2.a.b	$1$	$0$	$0$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}+q^{9}+q^{13}-6q^{17}+\cdots$
156.2.b.a	$156$	$2$	156.b	13.b	$2$	$2$	$2$	$1.246$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			156.2.b.a	$2$	$0$	$0$	$-2$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\beta q^{5}+q^{9}-\beta q^{11}+(-\beta-1)q^{13}+\cdots$
156.2.b.b	$156$	$2$	156.b	13.b	$2$	$2$	$2$	$1.246$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			156.2.b.b	$2$	$0$	$0$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta q^{5}+2\beta q^{7}+q^{9}-3\beta q^{11}+\cdots$
156.2.c.a	$156$	$2$	156.c	12.b	$2$	$2$	$2$	$1.246$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			156.2.c.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(-1-\beta )q^{3}-2q^{4}-\beta q^{5}+\cdots$
156.2.c.b	$156$	$2$	156.c	12.b	$2$	$2$	$2$	$1.246$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			156.2.c.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(1+\beta )q^{3}-2q^{4}-\beta q^{5}+(-2+\cdots)q^{6}+\cdots$
156.2.c.c	$156$	$2$	156.c	12.b	$2$	$8$	$8$	$1.246$	8.0.121550625.1	$_{}$	None	None		✓			156.2.c.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(1+\beta _{1}-\beta _{6})q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots$
156.2.c.d	$156$	$2$	156.c	12.b	$2$	$12$	$12$	$1.246$	12.0.$\cdots$.1	$_{}$	None	None		✓	✓		156.2.c.d	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{11}q^{2}-\beta _{6}q^{3}-\beta _{8}q^{4}+(-\beta _{9}+\cdots)q^{5}+\cdots$
156.2.h.a	$156$	$2$	156.h	156.h	$2$	$8$	$8$	$1.246$	8.0.592240896.6	$_{}$	$\Q(\sqrt{-39}) $	None		✓			156.2.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}-\beta _{3}q^{3}-\beta _{4}q^{4}+(-\beta _{6}-\beta _{7})q^{5}+\cdots$
156.2.h.b	$156$	$2$	156.h	156.h	$2$	$16$	$16$	$1.246$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓		156.2.h.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{2}+\beta _{6}q^{3}-\beta _{12}q^{4}-\beta _{4}q^{5}+\cdots$
156.2.i.a	$156$	$2$	156.i	13.c	$3$	$2$	$1$	$1.246$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓	✓	✓	156.2.i.a	$2$	$0$	$0$	$1$	$4$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+2q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
156.2.k.a	$156$	$2$	156.k	52.f	$4$	$2$	$1$	$1.246$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			156.2.k.a	$2$	$0$	$-2$	$0$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{2}-i q^{3}+2 i q^{4}+(-i-1)q^{5}+\cdots$
156.2.k.b	$156$	$2$	156.k	52.f	$4$	$2$	$1$	$1.246$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			156.2.k.a	$2$	$0$	$-2$	$0$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{2}+i q^{3}+2 i q^{4}+(-i-1)q^{5}+\cdots$
156.2.k.c	$156$	$2$	156.k	52.f	$4$	$2$	$1$	$1.246$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			156.2.k.c	$2$	$0$	$-2$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i-1)q^{2}+i q^{3}-2 i q^{4}+(2 i+2)q^{5}+\cdots$
156.2.k.d	$156$	$2$	156.k	52.f	$4$	$2$	$1$	$1.246$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			156.2.k.c	$2$	$0$	$2$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i+1)q^{2}-i q^{3}-2 i q^{4}+(2 i+2)q^{5}+\cdots$
156.2.k.e	$156$	$2$	156.k	52.f	$4$	$10$	$5$	$1.246$	10.0.$\cdots$.1	$_{}$	None	None		✓			156.2.k.e	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{2}+\beta _{8}q^{3}+(\beta _{5}+\beta _{7})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$
156.2.k.f	$156$	$2$	156.k	52.f	$4$	$10$	$5$	$1.246$	10.0.$\cdots$.1	$_{}$	None	None		✓			156.2.k.e	$2$	$0$	$4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{2}+\beta _{6}q^{3}+(-\beta _{7}-\beta _{8})q^{4}+\cdots$
156.2.m.a	$156$	$2$	156.m	39.f	$4$	$4$	$2$	$1.246$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			156.2.m.a	$4$	$0$	$0$	$0$	$0$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta_{2} q^{3}+(\beta_{3}-\beta_{2})q^{5}+(\beta_1-1)q^{7}+\cdots$
156.2.m.b	$156$	$2$	156.m	39.f	$4$	$4$	$2$	$1.246$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			156.2.m.b	$4$	$0$	$0$	$0$	$0$	$8$		$2^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+\beta_{3} q^{3}+(-\beta_{3}+\beta_{2}-2\beta_1+2)q^{7}+\cdots$
156.2.p.a	$156$	$2$	156.p	156.p	$6$	$8$	$4$	$1.246$	8.0.3317760000.3	$_{}$	None	None		✓			156.2.p.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{5}q^{2}-\beta _{6}q^{3}-2\beta _{4}q^{4}+(\beta _{2}-\beta _{7})q^{5}+\cdots$
156.2.p.b	$156$	$2$	156.p	156.p	$6$	$40$	$20$	$1.246$		$_{}$	None	None		✓	✓		156.2.p.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
156.2.q.a	$156$	$2$	156.q	13.e	$6$	$2$	$1$	$1.246$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			156.2.q.a	$2$	$0$	$0$	$1$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{5}+(4-2\zeta_{6})q^{7}+\cdots$
156.2.q.b	$156$	$2$	156.q	13.e	$6$	$4$	$2$	$1.246$	$\Q(\sqrt{-3}, \sqrt{-43})$	$_{}$	None	None		✓	✓		156.2.q.b	$2$	$0$	$0$	$-2$	$0$	$-3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\beta _{2})q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots$
156.2.r.a	$156$	$2$	156.r	156.r	$6$	$4$	$2$	$1.246$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			156.2.r.a	$4$	$0$	$0$	$-6$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$
156.2.r.b	$156$	$2$	156.r	156.r	$6$	$4$	$2$	$1.246$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			156.2.r.a	$4$	$0$	$0$	$6$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{2}+(1-\beta _{2})q^{3}+2q^{4}-2\beta _{3}q^{5}+\cdots$
156.2.r.c	$156$	$2$	156.r	156.r	$6$	$40$	$20$	$1.246$		$_{}$	None	None		✓	✓		156.2.r.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
156.2.u.a	$156$	$2$	156.u	39.k	$12$	$4$	$1$	$1.246$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			156.2.u.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(2+2\zeta_{12}-3\zeta_{12}^{2}+\cdots)q^{7}+\cdots$
156.2.u.b	$156$	$2$	156.u	39.k	$12$	$16$	$4$	$1.246$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		156.2.u.b	$4$	$0$	$0$	$0$	$0$	$-4$		$3^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\beta _{9}-\beta _{13}-\beta _{15})q^{3}+(-\beta _{3}-\beta _{9}+\cdots)q^{5}+\cdots$
156.2.w.a	$156$	$2$	156.w	52.l	$12$	$4$	$1$	$1.246$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			156.2.w.a	$2$	$0$	$2$	$0$	$-4$	$-6$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots$
156.2.w.b	$156$	$2$	156.w	52.l	$12$	$4$	$1$	$1.246$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			156.2.w.a	$2$	$0$	$4$	$0$	$-4$	$6$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(1+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots$
156.2.w.c	$156$	$2$	156.w	52.l	$12$	$24$	$6$	$1.246$		$_{}$	None	None		✓			156.2.w.c	$2$	$0$	$-4$	$0$	$2$	$-2$			$\mathrm{SU}(2)[C_{12}]$
156.2.w.d	$156$	$2$	156.w	52.l	$12$	$24$	$6$	$1.246$		$_{}$	None	None		✓			156.2.w.c	$2$	$0$	$-2$	$0$	$2$	$2$			$\mathrm{SU}(2)[C_{12}]$
156.3.d.a	$156$	$3$	156.d	3.b	$2$	$8$	$8$	$4.251$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		✓	✓	✓	156.3.d.a	$2$	$0$	$0$	$6$	$0$	$-8$		$2^{5}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{1})q^{3}+\beta _{3}q^{5}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
156.3.e.a	$156$	$3$	156.e	52.b	$2$	$2$	$2$	$4.251$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			156.3.e.a	$2$	$0$	$-2$	$0$	$0$	$-12$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta-1)q^{2}+\beta q^{3}+(2\beta-2)q^{4}+\cdots$
156.3.e.b	$156$	$3$	156.e	52.b	$2$	$2$	$2$	$4.251$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			156.3.e.a	$2$	$0$	$2$	$0$	$0$	$12$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta+1)q^{2}+\beta q^{3}+(2\beta-2)q^{4}+\cdots$
156.3.e.c	$156$	$3$	156.e	52.b	$2$	$24$	$24$	$4.251$		$_{}$	None	None		✓	✓		156.3.e.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
156.3.f.a	$156$	$3$	156.f	4.b	$2$	$24$	$24$	$4.251$		$_{}$	None	None		✓	✓	✓	156.3.f.a	$2$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
156.3.g.a	$156$	$3$	156.g	39.d	$2$	$2$	$2$	$4.251$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			156.3.g.a	$4$	$0$	$0$	$6$	$0$	$0$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+3 q^{3}+2\beta q^{7}+9 q^{9}+(-\beta+11)q^{13}+\cdots$
156.3.g.b	$156$	$3$	156.g	39.d	$2$	$4$	$4$	$4.251$	$\Q(i, \sqrt{11})$	$_{}$	None	None		✓			156.3.g.b	$4$	$0$	$0$	$-10$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+\beta _{3})q^{3}+(-2\beta _{1}+\beta _{2})q^{5}+\cdots$
156.3.g.c	$156$	$3$	156.g	39.d	$2$	$4$	$4$	$4.251$	$\Q(\sqrt{-2}, \sqrt{15})$	$_{}$	None	None		✓			156.3.g.c	$4$	$0$	$0$	$4$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{1})q^{3}-\beta _{3}q^{5}+(-7-2\beta _{1}+\cdots)q^{9}+\cdots$
156.3.j.a	$156$	$3$	156.j	13.d	$4$	$8$	$4$	$4.251$	8.0.$\cdots$.10	$_{}$	None	None		✓	✓	✓	156.3.j.a	$2$	$0$	$0$	$0$	$12$	$-8$		$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{4}+\beta _{5})q^{5}+(-2+\cdots)q^{7}+\cdots$
156.3.l.a	$156$	$3$	156.l	156.l	$4$	$4$	$2$	$4.251$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			156.3.l.a	$4$	$0$	$0$	$0$	$0$	$-12$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta_1 q^{2}+(-\beta_{3}+\beta_{2}+\beta_1)q^{3}+\cdots$
156.3.l.b	$156$	$3$	156.l	156.l	$4$	$4$	$2$	$4.251$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			156.3.l.a	$4$	$0$	$0$	$0$	$0$	$12$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta_1 q^{2}+(-\beta_{3}-\beta_{2}+\beta_1)q^{3}+\cdots$
156.3.l.c	$156$	$3$	156.l	156.l	$4$	$96$	$48$	$4.251$		$_{}$	None	None		✓	✓		156.3.l.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
156.3.n.a	$156$	$3$	156.n	52.i	$6$	$2$	$1$	$4.251$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			156.3.n.a	$2$	$0$	$-2$	$3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2+2\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots$
156.3.n.b	$156$	$3$	156.n	52.i	$6$	$2$	$1$	$4.251$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			156.3.n.a	$2$	$0$	$2$	$-3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-2\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots$
156.3.n.c	$156$	$3$	156.n	52.i	$6$	$4$	$2$	$4.251$	$\Q(\sqrt{-3}, \sqrt{142})$	$_{}$	None	None		✓			156.3.n.c	$2$	$0$	$-8$	$6$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-2q^{2}+(2+\beta _{2})q^{3}+4q^{4}+(-1-2\beta _{2}+\cdots)q^{5}+\cdots$
156.3.n.d	$156$	$3$	156.n	52.i	$6$	$4$	$2$	$4.251$	$\Q(\sqrt{-3}, \sqrt{142})$	$_{}$	None	None		✓			156.3.n.c	$2$	$0$	$-4$	$-6$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2-2\beta _{2})q^{2}+(-2-\beta _{2})q^{3}+4\beta _{2}q^{4}+\cdots$

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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.