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 138 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
82.2.a.a	$82$	$2$	82.a	1.a	$1$	$1$	$1$	$0.655$	$\Q$	None	✓	✓	✓	✓	82.2.a.a	$1$	$1$	$-1$	$-2$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}-4q^{7}+\cdots$
82.2.a.b	$82$	$2$	82.a	1.a	$1$	$2$	$2$	$0.655$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	82.2.a.b	$1$	$0$	$2$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}-2\beta q^{5}+\beta q^{6}+\cdots$
82.2.b.a	$82$	$2$	82.b	41.b	$2$	$2$	$2$	$0.655$	$\Q(\sqrt{-2}) $	None		✓			82.2.b.a	$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+3\beta q^{7}+\cdots$
82.2.b.b	$82$	$2$	82.b	41.b	$2$	$2$	$2$	$0.655$	$\Q(\sqrt{-1}) $	None		✓			82.2.b.b	$2$	$0$	$2$	$0$	$-4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta q^{3}+q^{4}-2 q^{5}+\beta q^{6}+\cdots$
82.2.c.a	$82$	$2$	82.c	41.c	$4$	$2$	$1$	$0.655$	$\Q(\sqrt{-1}) $	None		✓			82.2.c.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+i q^{2}+(i-1)q^{3}-q^{4}+2 i q^{5}+\cdots$
82.2.c.b	$82$	$2$	82.c	41.c	$4$	$2$	$1$	$0.655$	$\Q(\sqrt{-1}) $	None		✓			82.2.c.b	$2$	$0$	$0$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-i q^{2}-q^{4}-2 i q^{5}+(-3 i+3)q^{7}+\cdots$
82.2.c.c	$82$	$2$	82.c	41.c	$4$	$2$	$1$	$0.655$	$\Q(\sqrt{-1}) $	None		✓			82.2.c.c	$2$	$0$	$0$	$4$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-i q^{2}+(-2 i+2)q^{3}-q^{4}+2 i q^{5}+\cdots$
82.2.d.a	$82$	$2$	82.d	41.d	$5$	$4$	$1$	$0.655$	$\Q(\zeta_{10})$	None		✓			82.2.d.a	$2$	$0$	$-1$	$6$	$4$	$-8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
82.2.d.b	$82$	$2$	82.d	41.d	$5$	$4$	$1$	$0.655$	$\Q(\zeta_{10})$	None		✓			82.2.d.b	$2$	$0$	$1$	$2$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
82.2.d.c	$82$	$2$	82.d	41.d	$5$	$8$	$2$	$0.655$	8.0.123765625.1	None		✓	✓		82.2.d.c	$2$	$0$	$-2$	$-10$	$-10$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{2}q^{2}+(-2-\beta _{3}+\beta _{4}-\beta _{7})q^{3}+\cdots$
82.2.f.a	$82$	$2$	82.f	41.f	$10$	$8$	$2$	$0.655$	8.0.1816890625.4	None		✓			82.2.f.a	$2$	$0$	$-2$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{5}q^{2}+(\beta _{2}+\beta _{7})q^{3}-\beta _{3}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
82.2.f.b	$82$	$2$	82.f	41.f	$10$	$8$	$2$	$0.655$	8.0.346890625.1	None		✓			82.2.f.b	$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(1-\beta _{2}+\beta _{3}+\beta _{4})q^{2}+(-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots$
82.2.g.a	$82$	$2$	82.g	41.g	$20$	$8$	$1$	$0.655$	$\Q(\zeta_{20})$	None		✓			82.2.g.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{20}]$	$q-\zeta_{20}^{3}q^{2}+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5}+\cdots)q^{3}+\cdots$
82.2.g.b	$82$	$2$	82.g	41.g	$20$	$16$	$2$	$0.655$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓		82.2.g.b	$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{20}]$	$q-\beta _{12}q^{2}+(-2+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{7}+\cdots)q^{3}+\cdots$
82.3.e.a	$82$	$3$	82.e	41.e	$8$	$4$	$1$	$2.234$	$\Q(\zeta_{8})$	None		✓			82.3.e.a	$2$	$0$	$4$	$0$	$16$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(1+\zeta_{8}^{2})q^{2}+(2\zeta_{8}-2\zeta_{8}^{2})q^{3}+2\zeta_{8}^{2}q^{4}+\cdots$
82.3.e.b	$82$	$3$	82.e	41.e	$8$	$12$	$3$	$2.234$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			82.3.e.b	$2$	$0$	$-12$	$-12$	$0$	$20$		$7^{2}$	$\mathrm{SU}(2)[C_{8}]$	$q+(-1-\beta _{3})q^{2}+(-1+\beta _{1}-\beta _{3}+\beta _{5}+\cdots)q^{3}+\cdots$
82.3.e.c	$82$	$3$	82.e	41.e	$8$	$12$	$3$	$2.234$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			82.3.e.c	$2$	$0$	$12$	$4$	$-16$	$-20$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(1+\beta _{7})q^{2}+(-\beta _{3}-\beta _{4}+\beta _{7})q^{3}+\cdots$
82.3.h.a	$82$	$3$	82.h	41.h	$40$	$48$	$3$	$2.234$		None		✓			82.3.h.a	$2$	$0$	$12$	$12$	$0$	$-20$			$\mathrm{SU}(2)[C_{40}]$
82.3.h.b	$82$	$3$	82.h	41.h	$40$	$64$	$4$	$2.234$		None		✓	✓		82.3.h.b	$2$	$0$	$-16$	$-4$	$0$	$20$			$\mathrm{SU}(2)[C_{40}]$
82.4.a.a	$82$	$4$	82.a	1.a	$1$	$1$	$1$	$4.838$	$\Q$	None	✓	✓	✓	✓	82.4.a.a	$1$	$1$	$2$	$-4$	$-18$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-4q^{3}+4q^{4}-18q^{5}-8q^{6}+\cdots$
82.4.a.b	$82$	$4$	82.a	1.a	$1$	$1$	$1$	$4.838$	$\Q$	None	✓	✓			82.4.a.b	$1$	$0$	$2$	$10$	$-6$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+10q^{3}+4q^{4}-6q^{5}+20q^{6}+\cdots$
82.4.a.c	$82$	$4$	82.a	1.a	$1$	$2$	$2$	$4.838$	$\Q(\sqrt{3}) $	None	✓	✓	✓	✓	82.4.a.c	$1$	$0$	$-4$	$2$	$8$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(1+3\beta )q^{3}+4q^{4}+(4+4\beta )q^{5}+\cdots$
82.4.a.d	$82$	$4$	82.a	1.a	$1$	$3$	$3$	$4.838$	3.3.6452.1	None	✓	✓	✓	✓	82.4.a.d	$1$	$1$	$-6$	$-4$	$-2$	$-26$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1-\beta _{2})q^{3}+4q^{4}+(-2+\cdots)q^{5}+\cdots$
82.4.a.e	$82$	$4$	82.a	1.a	$1$	$3$	$3$	$4.838$	3.3.564.1	None	✓	✓	✓		82.4.a.e	$1$	$0$	$6$	$-2$	$18$	$36$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-2+3\beta _{1}-\beta _{2})q^{3}+4q^{4}+\cdots$
82.4.b.a	$82$	$4$	82.b	41.b	$2$	$4$	$4$	$4.838$	$\Q(\sqrt{-10}, \sqrt{-66})$	None		✓			82.4.b.a	$2$	$0$	$-8$	$0$	$4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(1-\beta _{3})q^{5}+\cdots$
82.4.b.b	$82$	$4$	82.b	41.b	$2$	$6$	$6$	$4.838$	6.0.$\cdots$.1	None		✓	✓		82.4.b.b	$2$	$0$	$12$	$0$	$-4$	$0$		$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{2}-\beta _{3}q^{3}+4q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots$
82.4.c.a	$82$	$4$	82.c	41.c	$4$	$10$	$5$	$4.838$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		✓			82.4.c.a	$2$	$0$	$0$	$4$	$0$	$20$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+2\beta _{4}q^{2}+\beta _{1}q^{3}-4q^{4}+(\beta _{4}-\beta _{9})q^{5}+\cdots$
82.4.c.b	$82$	$4$	82.c	41.c	$4$	$12$	$6$	$4.838$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓		82.4.c.b	$2$	$0$	$0$	$-2$	$0$	$-20$		$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	$q+2\beta _{3}q^{2}-\beta _{1}q^{3}-4q^{4}+(-3\beta _{3}+\cdots)q^{5}+\cdots$
82.4.d.a	$82$	$4$	82.d	41.d	$5$	$20$	$5$	$4.838$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓			82.4.d.a	$2$	$0$	$-10$	$-4$	$6$	$-24$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+2\beta _{8}q^{2}+(-\beta _{4}+\beta _{5}+\beta _{8})q^{3}+4\beta _{2}q^{4}+\cdots$
82.4.d.b	$82$	$4$	82.d	41.d	$5$	$20$	$5$	$4.838$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓			82.4.d.b	$2$	$0$	$10$	$2$	$-6$	$24$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-2\beta _{6}q^{2}+(1+\beta _{2}-\beta _{3}+\beta _{5})q^{3}+\cdots$
82.4.f.a	$82$	$4$	82.f	41.f	$10$	$16$	$4$	$4.838$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			82.4.f.a	$2$	$0$	$8$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q-2\beta _{8}q^{2}+(-\beta _{1}+\beta _{7}+\beta _{8})q^{3}+(-4+\cdots)q^{4}+\cdots$
82.4.f.b	$82$	$4$	82.f	41.f	$10$	$24$	$6$	$4.838$		None		✓	✓		82.4.f.b	$2$	$0$	$-12$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{10}]$
82.4.g.a	$82$	$4$	82.g	41.g	$20$	$40$	$5$	$4.838$		None		✓			82.4.g.a	$2$	$0$	$0$	$-4$	$0$	$-20$			$\mathrm{SU}(2)[C_{20}]$
82.4.g.b	$82$	$4$	82.g	41.g	$20$	$48$	$6$	$4.838$		None		✓	✓		82.4.g.b	$2$	$0$	$0$	$2$	$0$	$20$			$\mathrm{SU}(2)[C_{20}]$
82.5.e.a	$82$	$5$	82.e	41.e	$8$	$28$	$7$	$8.476$		None		✓			82.5.e.a	$2$	$0$	$-56$	$16$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
82.5.e.b	$82$	$5$	82.e	41.e	$8$	$28$	$7$	$8.476$		None		✓			82.5.e.b	$2$	$0$	$56$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
82.5.h.a	$82$	$5$	82.h	41.h	$40$	$112$	$7$	$8.476$		None		✓			82.5.h.a	$2$	$0$	$-56$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{40}]$
82.5.h.b	$82$	$5$	82.h	41.h	$40$	$112$	$7$	$8.476$		None		✓			82.5.h.b	$2$	$0$	$56$	$-16$	$0$	$0$			$\mathrm{SU}(2)[C_{40}]$
82.6.a.a	$82$	$6$	82.a	1.a	$1$	$3$	$3$	$13.151$	3.3.73428.1	None	✓	✓	✓	✓	82.6.a.a	$1$	$1$	$12$	$-28$	$-26$	$-158$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}+(-10+\beta _{1}+\beta _{2})q^{3}+2^{4}q^{4}+\cdots$
82.6.a.b	$82$	$6$	82.a	1.a	$1$	$4$	$4$	$13.151$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	✓	✓	✓	82.6.a.b	$1$	$0$	$-16$	$8$	$12$	$158$	$-$	$2$	$\mathrm{SU}(2)$	$q-4q^{2}+(2-\beta _{1}-\beta _{3})q^{3}+2^{4}q^{4}+\cdots$
82.6.a.c	$82$	$6$	82.a	1.a	$1$	$5$	$5$	$13.151$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	✓	✓	✓	82.6.a.c	$1$	$1$	$-20$	$-10$	$-38$	$-38$	$+$	$2$	$\mathrm{SU}(2)$	$q-4q^{2}+(-2-\beta _{1})q^{3}+2^{4}q^{4}+(-8+\cdots)q^{5}+\cdots$
82.6.a.d	$82$	$6$	82.a	1.a	$1$	$6$	$6$	$13.151$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓	✓	✓	82.6.a.d	$1$	$0$	$24$	$8$	$124$	$38$	$-$	$2^{2}\cdot 5$	$\mathrm{SU}(2)$	$q+4q^{2}+(1+\beta _{1})q^{3}+2^{4}q^{4}+(21-\beta _{5})q^{5}+\cdots$
82.6.b.a	$82$	$6$	82.b	41.b	$2$	$8$	$8$	$13.151$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓			82.6.b.a	$2$	$0$	$32$	$0$	$-48$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+4q^{2}+\beta _{1}q^{3}+2^{4}q^{4}+(-6-\beta _{2}+\cdots)q^{5}+\cdots$
82.6.b.b	$82$	$6$	82.b	41.b	$2$	$10$	$10$	$13.151$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		✓	✓		82.6.b.b	$2$	$0$	$-40$	$0$	$-24$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-4q^{2}+\beta _{1}q^{3}+2^{4}q^{4}+(-2-\beta _{3}+\cdots)q^{5}+\cdots$
82.6.c.a	$82$	$6$	82.c	41.c	$4$	$16$	$8$	$13.151$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			82.6.c.a	$2$	$0$	$0$	$-2$	$0$	$-100$		$2^{8}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-4\beta _{2}q^{2}+\beta _{6}q^{3}-2^{4}q^{4}+(-3\beta _{2}+\cdots)q^{5}+\cdots$
82.6.c.b	$82$	$6$	82.c	41.c	$4$	$18$	$9$	$13.151$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		✓	✓		82.6.c.b	$2$	$0$	$0$	$-20$	$0$	$100$		$2^{11}$	$\mathrm{SU}(2)[C_{4}]$	$q+4\beta _{2}q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}-2^{4}q^{4}+\cdots$
82.6.d.a	$82$	$6$	82.d	41.d	$5$	$36$	$9$	$13.151$		None		✓			82.6.d.a	$2$	$0$	$-36$	$20$	$-98$	$120$			$\mathrm{SU}(2)[C_{5}]$
82.6.d.b	$82$	$6$	82.d	41.d	$5$	$36$	$9$	$13.151$		None		✓			82.6.d.b	$2$	$0$	$36$	$2$	$26$	$-120$			$\mathrm{SU}(2)[C_{5}]$
82.6.f.a	$82$	$6$	82.f	41.f	$10$	$32$	$8$	$13.151$		None		✓			82.6.f.a	$2$	$0$	$-32$	$0$	$48$	$0$			$\mathrm{SU}(2)[C_{10}]$
82.6.f.b	$82$	$6$	82.f	41.f	$10$	$40$	$10$	$13.151$		None		✓	✓		82.6.f.b	$2$	$0$	$40$	$0$	$24$	$0$			$\mathrm{SU}(2)[C_{10}]$

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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.