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 162 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
570.2.a.a	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	$\Q$	None	✓	✓	✓	✓	570.2.a.a	$1$	$0$	$-1$	$-1$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots$
570.2.a.b	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	$\Q$	None	✓	✓	✓	✓	570.2.a.b	$1$	$1$	$-1$	$-1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots$
570.2.a.c	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	$\Q$	None	✓	✓	✓	✓	570.2.a.c	$1$	$1$	$-1$	$-1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
570.2.a.d	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	$\Q$	None	✓	✓	✓	✓	570.2.a.d	$1$	$0$	$-1$	$1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots$
570.2.a.e	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	$\Q$	None	✓	✓	✓	✓	570.2.a.e	$1$	$1$	$-1$	$1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots$
570.2.a.f	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	$\Q$	None	✓	✓	✓	✓	570.2.a.f	$1$	$0$	$-1$	$1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots$
570.2.a.g	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	$\Q$	None	✓	✓	✓	✓	570.2.a.g	$1$	$0$	$1$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
570.2.a.h	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	$\Q$	None	✓	✓			570.2.a.h	$1$	$0$	$1$	$-1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots$
570.2.a.i	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	$\Q$	None	✓	✓			570.2.a.i	$1$	$0$	$1$	$-1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots$
570.2.a.j	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	$\Q$	None	✓	✓			570.2.a.j	$1$	$0$	$1$	$1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots$
570.2.a.k	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	$\Q$	None	✓	✓			570.2.a.k	$1$	$0$	$1$	$1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots$
570.2.a.l	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	$\Q$	None	✓	✓			570.2.a.l	$1$	$0$	$1$	$1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
570.2.a.m	$570$	$2$	570.a	1.a	$1$	$1$	$1$	$4.551$	$\Q$	None	✓	✓			570.2.a.m	$1$	$0$	$1$	$1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots$
570.2.c.a	$570$	$2$	570.c	285.b	$2$	$4$	$4$	$4.551$	$\Q(\zeta_{8})$	None		✓			570.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots$
570.2.c.b	$570$	$2$	570.c	285.b	$2$	$4$	$4$	$4.551$	$\Q(\zeta_{8})$	None		✓			570.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots$
570.2.c.c	$570$	$2$	570.c	285.b	$2$	$8$	$8$	$4.551$	8.0.1499238400.2	None		✓			570.2.c.c	$4$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+(-1-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots$
570.2.c.d	$570$	$2$	570.c	285.b	$2$	$8$	$8$	$4.551$	$\Q(\zeta_{24})$	None		✓			570.2.c.d	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{2}-\beta_{4} q^{3}-q^{4}+(-\beta_{6}-\beta_{2})q^{5}+\cdots$
570.2.c.e	$570$	$2$	570.c	285.b	$2$	$8$	$8$	$4.551$	$\Q(\zeta_{24})$	None		✓			570.2.c.e	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{2}+(-\beta_{6}-\beta_1)q^{3}-q^{4}+\cdots$
570.2.c.f	$570$	$2$	570.c	285.b	$2$	$8$	$8$	$4.551$	8.0.1499238400.2	None		✓			570.2.c.c	$4$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+(-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots$
570.2.d.a	$570$	$2$	570.d	5.b	$2$	$2$	$2$	$4.551$	$\Q(\sqrt{-1}) $	None		✓			570.2.d.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+i q^{3}-q^{4}+(-2 i-1)q^{5}+\cdots$
570.2.d.b	$570$	$2$	570.d	5.b	$2$	$2$	$2$	$4.551$	$\Q(\sqrt{-1}) $	None		✓			570.2.d.b	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+i q^{3}-q^{4}+(i+2)q^{5}+\cdots$
570.2.d.c	$570$	$2$	570.d	5.b	$2$	$6$	$6$	$4.551$	6.0.350464.1	None		✓			570.2.d.c	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{3}q^{5}-q^{6}+\cdots$
570.2.d.d	$570$	$2$	570.d	5.b	$2$	$6$	$6$	$4.551$	6.0.350464.1	None		✓			570.2.d.d	$2$	$0$	$0$	$0$	$2$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}-\beta _{5}q^{5}+q^{6}+\cdots$
570.2.f.a	$570$	$2$	570.f	57.d	$2$	$4$	$4$	$4.551$	$\Q(\zeta_{8})$	None		✓			570.2.f.a	$2$	$0$	$-4$	$-4$	$0$	$8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+(-\beta_{2}-1)q^{3}+q^{4}+\beta_1 q^{5}+\cdots$
570.2.f.b	$570$	$2$	570.f	57.d	$2$	$4$	$4$	$4.551$	$\Q(\zeta_{8})$	None		✓			570.2.f.a	$2$	$0$	$4$	$4$	$0$	$8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(\beta_{2}+1)q^{3}+q^{4}+\beta_1 q^{5}+\cdots$
570.2.f.c	$570$	$2$	570.f	57.d	$2$	$8$	$8$	$4.551$	8.0.7278137344.1	None		✓			570.2.f.c	$2$	$0$	$-8$	$2$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots$
570.2.f.d	$570$	$2$	570.f	57.d	$2$	$8$	$8$	$4.551$	8.0.7278137344.1	None		✓			570.2.f.c	$2$	$0$	$8$	$-2$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots$
570.2.i.a	$570$	$2$	570.i	19.c	$3$	$2$	$1$	$4.551$	$\Q(\sqrt{-3}) $	None		✓			570.2.i.a	$2$	$0$	$-1$	$-1$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
570.2.i.b	$570$	$2$	570.i	19.c	$3$	$2$	$1$	$4.551$	$\Q(\sqrt{-3}) $	None		✓			570.2.i.b	$2$	$0$	$-1$	$-1$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
570.2.i.c	$570$	$2$	570.i	19.c	$3$	$2$	$1$	$4.551$	$\Q(\sqrt{-3}) $	None		✓			570.2.i.c	$2$	$0$	$-1$	$1$	$1$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
570.2.i.d	$570$	$2$	570.i	19.c	$3$	$2$	$1$	$4.551$	$\Q(\sqrt{-3}) $	None		✓			570.2.i.d	$2$	$0$	$1$	$-1$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
570.2.i.e	$570$	$2$	570.i	19.c	$3$	$2$	$1$	$4.551$	$\Q(\sqrt{-3}) $	None		✓			570.2.i.e	$2$	$0$	$1$	$1$	$-1$	$-10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
570.2.i.f	$570$	$2$	570.i	19.c	$3$	$4$	$2$	$4.551$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		✓			570.2.i.f	$2$	$0$	$-2$	$2$	$-2$	$4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1})q^{2}+(1-\beta _{1})q^{3}-\beta _{1}q^{4}+\cdots$
570.2.i.g	$570$	$2$	570.i	19.c	$3$	$4$	$2$	$4.551$	$\Q(\sqrt{-3}, \sqrt{73})$	None		✓			570.2.i.g	$2$	$0$	$2$	$-2$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{2})q^{2}+(-1+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots$
570.2.i.h	$570$	$2$	570.i	19.c	$3$	$4$	$2$	$4.551$	$\Q(\sqrt{-3}, \sqrt{19})$	None		✓			570.2.i.h	$2$	$0$	$2$	$-2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{2})q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots$
570.2.i.i	$570$	$2$	570.i	19.c	$3$	$4$	$2$	$4.551$	$\Q(\sqrt{-3}, \sqrt{7})$	None		✓			570.2.i.i	$2$	$0$	$2$	$2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{2})q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots$
570.2.i.j	$570$	$2$	570.i	19.c	$3$	$6$	$3$	$4.551$	6.0.29654208.1	None		✓	✓		570.2.i.j	$2$	$0$	$-3$	$-3$	$-3$	$2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1})q^{2}+(-1+\beta _{1})q^{3}-\beta _{1}q^{4}+\cdots$
570.2.k.a	$570$	$2$	570.k	15.e	$4$	$36$	$18$	$4.551$		None		✓			570.2.k.a	$4$	$0$	$0$	$4$	$0$	$-12$			$\mathrm{SU}(2)[C_{4}]$
570.2.k.b	$570$	$2$	570.k	15.e	$4$	$36$	$18$	$4.551$		None		✓			570.2.k.b	$4$	$0$	$0$	$4$	$0$	$20$			$\mathrm{SU}(2)[C_{4}]$
570.2.m.a	$570$	$2$	570.m	95.g	$4$	$20$	$10$	$4.551$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓			570.2.m.a	$4$	$0$	$0$	$0$	$-4$	$-4$		$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}+\beta _{11}q^{3}+\beta _{4}q^{4}+\beta _{6}q^{5}+\cdots$
570.2.m.b	$570$	$2$	570.m	95.g	$4$	$20$	$10$	$4.551$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓			570.2.m.b	$4$	$0$	$0$	$0$	$12$	$-4$		$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{7}q^{2}-\beta _{10}q^{3}+\beta _{2}q^{4}+(1+\beta _{6}+\cdots)q^{5}+\cdots$
570.2.n.a	$570$	$2$	570.n	285.q	$6$	$80$	$40$	$4.551$		None		✓	✓	✓	570.2.n.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
570.2.q.a	$570$	$2$	570.q	95.i	$6$	$8$	$4$	$4.551$	$\Q(\zeta_{24})$	None		✓			570.2.q.a	$4$	$0$	$0$	$0$	$4$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta_{4}+\beta_1)q^{2}+(-\beta_{4}+\beta_1)q^{3}+\cdots$
570.2.q.b	$570$	$2$	570.q	95.i	$6$	$12$	$6$	$4.551$	12.0.$\cdots$.1	None		✓			570.2.q.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{3}-\beta _{4})q^{2}+(-\beta _{3}-\beta _{4})q^{3}+\cdots$
570.2.q.c	$570$	$2$	570.q	95.i	$6$	$20$	$10$	$4.551$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓		570.2.q.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{11}q^{2}+\beta _{11}q^{3}+(1-\beta _{12})q^{4}+\cdots$
570.2.s.a	$570$	$2$	570.s	57.f	$6$	$24$	$12$	$4.551$		None		✓			570.2.s.a	$2$	$0$	$-12$	$4$	$0$	$-12$			$\mathrm{SU}(2)[C_{6}]$
570.2.s.b	$570$	$2$	570.s	57.f	$6$	$24$	$12$	$4.551$		None		✓			570.2.s.a	$2$	$0$	$12$	$2$	$0$	$-12$			$\mathrm{SU}(2)[C_{6}]$
570.2.u.a	$570$	$2$	570.u	19.e	$9$	$6$	$1$	$4.551$	$\Q(\zeta_{18})$	None		✓			570.2.u.a	$2$	$0$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
570.2.u.b	$570$	$2$	570.u	19.e	$9$	$6$	$1$	$4.551$	$\Q(\zeta_{18})$	None		✓			570.2.u.b	$2$	$0$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
570.2.u.c	$570$	$2$	570.u	19.e	$9$	$6$	$1$	$4.551$	$\Q(\zeta_{18})$	None		✓			570.2.u.c	$2$	$0$	$0$	$0$	$0$	$-3$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$

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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.