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 222 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
342.2.a.a	$342$	$2$	342.a	1.a	$1$	$1$	$1$	$2.731$	$\Q$	None	✓	✓	✓	✓	342.2.a.a	$1$	$1$	$-1$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-2q^{11}+\cdots$
342.2.a.b	$342$	$2$	342.a	1.a	$1$	$1$	$1$	$2.731$	$\Q$	None	✓				114.2.a.b	$1$	$0$	$-1$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+4q^{11}+\cdots$
342.2.a.c	$342$	$2$	342.a	1.a	$1$	$1$	$1$	$2.731$	$\Q$	None	✓		✓	✓	114.2.a.c	$1$	$1$	$-1$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{7}-q^{8}-4q^{13}+4q^{14}+\cdots$
342.2.a.d	$342$	$2$	342.a	1.a	$1$	$1$	$1$	$2.731$	$\Q$	None	✓				38.2.a.b	$1$	$0$	$-1$	$0$	$4$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}+3q^{7}-q^{8}-4q^{10}+\cdots$
342.2.a.e	$342$	$2$	342.a	1.a	$1$	$1$	$1$	$2.731$	$\Q$	None	✓				38.2.a.a	$1$	$0$	$1$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}+6q^{11}+5q^{13}+\cdots$
342.2.a.f	$342$	$2$	342.a	1.a	$1$	$1$	$1$	$2.731$	$\Q$	None	✓				114.2.a.a	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{7}+q^{8}-4q^{11}+4q^{14}+\cdots$
342.2.a.g	$342$	$2$	342.a	1.a	$1$	$1$	$1$	$2.731$	$\Q$	None	✓	✓	✓	✓	342.2.a.a	$1$	$0$	$1$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+q^{8}+2q^{10}+2q^{11}+\cdots$
342.2.b.a	$342$	$2$	342.b	57.d	$2$	$2$	$2$	$2.731$	$\Q(\sqrt{-2}) $	None		✓			342.2.b.a	$2$	$0$	$-2$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+\beta q^{5}+2q^{7}-q^{8}-\beta q^{10}+\cdots$
342.2.b.b	$342$	$2$	342.b	57.d	$2$	$2$	$2$	$2.731$	$\Q(\sqrt{-2}) $	None		✓			342.2.b.a	$2$	$0$	$2$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+\beta q^{5}+2q^{7}+q^{8}+\beta q^{10}+\cdots$
342.2.e.a	$342$	$2$	342.e	9.c	$3$	$6$	$3$	$2.731$	6.0.309123.1	None		✓			342.2.e.a	$2$	$0$	$-3$	$2$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{4})q^{2}+(\beta _{1}+\beta _{2}-\beta _{5})q^{3}+\cdots$
342.2.e.b	$342$	$2$	342.e	9.c	$3$	$6$	$3$	$2.731$	$\Q(\zeta_{18})$	None		✓			342.2.e.b	$2$	$0$	$3$	$0$	$0$	$6$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta_1+1)q^{2}+(\beta_{5}+\beta_{2})q^{3}+\cdots$
342.2.e.c	$342$	$2$	342.e	9.c	$3$	$12$	$6$	$2.731$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓			342.2.e.c	$2$	$0$	$-6$	$2$	$0$	$-6$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{6})q^{2}+\beta _{10}q^{3}-\beta _{6}q^{4}+\cdots$
342.2.e.d	$342$	$2$	342.e	9.c	$3$	$12$	$6$	$2.731$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			342.2.e.d	$2$	$0$	$6$	$0$	$0$	$-4$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{7})q^{2}+(\beta _{1}-\beta _{9})q^{3}-\beta _{7}q^{4}+\cdots$
342.2.f.a	$342$	$2$	342.f	171.h	$3$	$2$	$1$	$2.731$	$\Q(\sqrt{-3}) $	None		✓			342.2.f.a	$2$	$0$	$2$	$-3$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(-1-\zeta_{6})q^{6}+\cdots$
342.2.f.b	$342$	$2$	342.f	171.h	$3$	$2$	$1$	$2.731$	$\Q(\sqrt{-3}) $	None		✓			342.2.f.b	$2$	$0$	$2$	$0$	$-3$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(1-2\zeta_{6})q^{3}+q^{4}-3\zeta_{6}q^{5}+\cdots$
342.2.f.c	$342$	$2$	342.f	171.h	$3$	$2$	$1$	$2.731$	$\Q(\sqrt{-3}) $	None		✓			342.2.f.c	$2$	$0$	$2$	$0$	$1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-1+2\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+\cdots$
342.2.f.d	$342$	$2$	342.f	171.h	$3$	$2$	$1$	$2.731$	$\Q(\sqrt{-3}) $	None		✓			342.2.f.d	$2$	$0$	$2$	$3$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(2-\zeta_{6})q^{3}+q^{4}-2\zeta_{6}q^{5}+\cdots$
342.2.f.e	$342$	$2$	342.f	171.h	$3$	$4$	$2$	$2.731$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		✓			342.2.f.e	$2$	$0$	$4$	$-4$	$6$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-1+\beta _{3})q^{3}+q^{4}+3\beta _{2}q^{5}+\cdots$
342.2.f.f	$342$	$2$	342.f	171.h	$3$	$10$	$5$	$2.731$	10.0.$\cdots$.1	None		✓			342.2.f.f	$2$	$0$	$10$	$2$	$-2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(\beta _{1}+\beta _{8})q^{3}+q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
342.2.f.g	$342$	$2$	342.f	171.h	$3$	$18$	$9$	$2.731$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		✓	✓		342.2.f.g	$2$	$0$	$-18$	$0$	$0$	$5$		$2^{4}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}-\beta _{9}q^{3}+q^{4}+(\beta _{4}-\beta _{16})q^{5}+\cdots$
342.2.g.a	$342$	$2$	342.g	19.c	$3$	$2$	$1$	$2.731$	$\Q(\sqrt{-3}) $	None		✓			342.2.g.a	$2$	$0$	$-1$	$0$	$-2$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{5}+\cdots$
342.2.g.b	$342$	$2$	342.g	19.c	$3$	$2$	$1$	$2.731$	$\Q(\sqrt{-3}) $	None					38.2.c.a	$2$	$1$	$-1$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-4q^{7}+q^{8}+\cdots$
342.2.g.c	$342$	$2$	342.g	19.c	$3$	$2$	$1$	$2.731$	$\Q(\sqrt{-3}) $	None					114.2.e.b	$2$	$0$	$-1$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{7}+q^{8}+\cdots$
342.2.g.d	$342$	$2$	342.g	19.c	$3$	$2$	$1$	$2.731$	$\Q(\sqrt{-3}) $	None					114.2.e.a	$2$	$0$	$1$	$0$	$-4$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-4+4\zeta_{6})q^{5}+\cdots$
342.2.g.e	$342$	$2$	342.g	19.c	$3$	$2$	$1$	$2.731$	$\Q(\sqrt{-3}) $	None		✓			342.2.g.a	$2$	$0$	$1$	$0$	$2$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(2-2\zeta_{6})q^{5}+\cdots$
342.2.g.f	$342$	$2$	342.g	19.c	$3$	$4$	$2$	$2.731$	$\Q(\sqrt{-3}, \sqrt{7})$	None			✓		38.2.c.b	$2$	$0$	$2$	$0$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+(1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
342.2.h.a	$342$	$2$	342.h	171.g	$3$	$2$	$1$	$2.731$	$\Q(\sqrt{-3}) $	None		✓			342.2.f.c	$2$	$0$	$-1$	$-3$	$-2$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
342.2.h.b	$342$	$2$	342.h	171.g	$3$	$2$	$1$	$2.731$	$\Q(\sqrt{-3}) $	None		✓			342.2.f.d	$2$	$0$	$-1$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(1-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
342.2.h.c	$342$	$2$	342.h	171.g	$3$	$2$	$1$	$2.731$	$\Q(\sqrt{-3}) $	None		✓			342.2.f.a	$2$	$0$	$-1$	$3$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
342.2.h.d	$342$	$2$	342.h	171.g	$3$	$2$	$1$	$2.731$	$\Q(\sqrt{-3}) $	None		✓			342.2.f.b	$2$	$0$	$-1$	$3$	$6$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(2-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
342.2.h.e	$342$	$2$	342.h	171.g	$3$	$4$	$2$	$2.731$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		✓			342.2.f.e	$2$	$0$	$-2$	$2$	$-12$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots$
342.2.h.f	$342$	$2$	342.h	171.g	$3$	$10$	$5$	$2.731$	10.0.$\cdots$.1	None		✓			342.2.f.f	$2$	$0$	$-5$	$-4$	$4$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}-\beta _{3}q^{3}+(-1-\beta _{4})q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots$
342.2.h.g	$342$	$2$	342.h	171.g	$3$	$18$	$9$	$2.731$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		✓	✓		342.2.f.g	$2$	$0$	$9$	$0$	$0$	$5$		$2^{4}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{8}q^{2}+(\beta _{1}+\beta _{9})q^{3}+(-1+\beta _{8}+\cdots)q^{4}+\cdots$
342.2.j.a	$342$	$2$	342.j	171.k	$6$	$2$	$1$	$2.731$	$\Q(\sqrt{-3}) $	None		✓			342.2.j.a	$2$	$1$	$-1$	$-3$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
342.2.j.b	$342$	$2$	342.j	171.k	$6$	$2$	$1$	$2.731$	$\Q(\sqrt{-3}) $	None		✓			342.2.j.b	$2$	$0$	$1$	$-3$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
342.2.j.c	$342$	$2$	342.j	171.k	$6$	$2$	$1$	$2.731$	$\Q(\sqrt{-3}) $	None		✓			342.2.j.c	$2$	$0$	$1$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{6}q^{2}+(1-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
342.2.j.d	$342$	$2$	342.j	171.k	$6$	$8$	$4$	$2.731$	8.0.764411904.5	None		✓			342.2.j.d	$2$	$0$	$4$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{3}q^{2}+(-\beta _{1}-\beta _{6})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots$
342.2.j.e	$342$	$2$	342.j	171.k	$6$	$8$	$4$	$2.731$	8.0.152695449.1	None		✓			342.2.j.e	$2$	$0$	$4$	$5$	$0$	$6$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\beta _{6})q^{2}+(1-\beta _{1}+\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{3}+\cdots$
342.2.j.f	$342$	$2$	342.j	171.k	$6$	$18$	$9$	$2.731$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		✓	✓		342.2.j.f	$2$	$0$	$-9$	$4$	$0$	$0$		$3^{3}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{9}q^{2}+(\beta _{1}+\beta _{14})q^{3}+(-1-\beta _{9}+\cdots)q^{4}+\cdots$
342.2.n.a	$342$	$2$	342.n	171.t	$6$	$2$	$1$	$2.731$	$\Q(\sqrt{-3}) $	None		✓			342.2.j.a	$2$	$1$	$-2$	$0$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+(-2+\zeta_{6})q^{5}+\cdots$
342.2.n.b	$342$	$2$	342.n	171.t	$6$	$2$	$1$	$2.731$	$\Q(\sqrt{-3}) $	None		✓			342.2.j.c	$2$	$1$	$2$	$-3$	$-6$	$-4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(-4+2\zeta_{6})q^{5}+\cdots$
342.2.n.c	$342$	$2$	342.n	171.t	$6$	$2$	$1$	$2.731$	$\Q(\sqrt{-3}) $	None		✓			342.2.j.b	$2$	$0$	$2$	$0$	$3$	$5$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+(2-\zeta_{6})q^{5}+\cdots$
342.2.n.d	$342$	$2$	342.n	171.t	$6$	$8$	$4$	$2.731$	8.0.764411904.5	None		✓			342.2.j.d	$2$	$0$	$8$	$0$	$12$	$-8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+q^{2}+(-\beta _{1}+\beta _{4})q^{3}+q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
342.2.n.e	$342$	$2$	342.n	171.t	$6$	$8$	$4$	$2.731$	8.0.152695449.1	None		✓			342.2.j.e	$2$	$0$	$8$	$4$	$-9$	$6$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q+q^{2}+(\beta _{3}-\beta _{6})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
342.2.n.f	$342$	$2$	342.n	171.t	$6$	$18$	$9$	$2.731$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		✓	✓		342.2.j.f	$2$	$0$	$-18$	$-1$	$3$	$0$		$3^{3}$	$\mathrm{SU}(2)[C_{6}]$	$q-q^{2}+\beta _{14}q^{3}+q^{4}-\beta _{10}q^{5}-\beta _{14}q^{6}+\cdots$
342.2.p.a	$342$	$2$	342.p	171.l	$6$	$20$	$10$	$2.731$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓			342.2.p.a	$2$	$0$	$-10$	$1$	$0$	$2$		$3^{5}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{5}q^{2}+(-\beta _{1}+\beta _{9})q^{3}+(-1-\beta _{5}+\cdots)q^{4}+\cdots$
342.2.p.b	$342$	$2$	342.p	171.l	$6$	$20$	$10$	$2.731$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓			342.2.p.a	$2$	$0$	$10$	$-1$	$0$	$2$		$3^{5}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{5}q^{2}+(\beta _{1}-\beta _{9})q^{3}+(-1-\beta _{5}+\cdots)q^{4}+\cdots$
342.2.s.a	$342$	$2$	342.s	57.f	$6$	$4$	$2$	$2.731$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		✓			342.2.s.a	$2$	$0$	$-2$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$
342.2.s.b	$342$	$2$	342.s	57.f	$6$	$4$	$2$	$2.731$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		✓			342.2.s.a	$2$	$0$	$2$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$
342.2.u.a	$342$	$2$	342.u	19.e	$9$	$6$	$1$	$2.731$	$\Q(\zeta_{18})$	None					114.2.i.d	$2$	$0$	$0$	$0$	$-9$	$3$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q-\zeta_{18}q^{2}+\zeta_{18}^{2}q^{4}+(-1+\zeta_{18}^{2}+\cdots)q^{5}+\cdots$

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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.