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 247 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
78.2.a.a	$78$	$2$	78.a	1.a	$1$	$1$	$1$	$0.623$	$\Q$	None	✓	✓	✓	✓	78.2.a.a	$1$	$0$	$-1$	$-1$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots$
78.2.b.a	$78$	$2$	78.b	13.b	$2$	$2$	$2$	$0.623$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	78.2.b.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{3}-q^{4}+2 i q^{5}+i q^{6}+\cdots$
78.2.e.a	$78$	$2$	78.e	13.c	$3$	$2$	$1$	$0.623$	$\Q(\sqrt{-3}) $	None		✓			78.2.e.a	$2$	$0$	$1$	$-1$	$6$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
78.2.e.b	$78$	$2$	78.e	13.c	$3$	$2$	$1$	$0.623$	$\Q(\sqrt{-3}) $	None		✓			78.2.e.b	$2$	$0$	$1$	$1$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
78.2.g.a	$78$	$2$	78.g	39.f	$4$	$12$	$6$	$0.623$	12.0.$\cdots$.52	None		✓	✓	✓	78.2.g.a	$4$	$0$	$0$	$0$	$0$	$-12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}-\beta _{4}q^{3}+\beta _{8}q^{4}+(-\beta _{1}-\beta _{11})q^{5}+\cdots$
78.2.i.a	$78$	$2$	78.i	13.e	$6$	$4$	$2$	$0.623$	$\Q(\zeta_{12})$	None		✓			78.2.i.a	$2$	$0$	$0$	$-2$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
78.2.i.b	$78$	$2$	78.i	13.e	$6$	$4$	$2$	$0.623$	$\Q(\zeta_{12})$	None		✓			78.2.i.b	$2$	$0$	$0$	$2$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
78.2.k.a	$78$	$2$	78.k	39.k	$12$	$16$	$4$	$0.623$	16.0.$\cdots$.9	None		✓	✓	✓	78.2.k.a	$4$	$0$	$0$	$0$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\beta _{7}-\beta _{15})q^{2}+(-\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots$
78.3.c.a	$78$	$3$	78.c	3.b	$2$	$8$	$8$	$2.125$	8.0.$\cdots$.2	None		✓	✓	✓	78.3.c.a	$2$	$0$	$0$	$0$	$0$	$-8$		$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+\beta _{4}q^{3}-2q^{4}+(\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots$
78.3.d.a	$78$	$3$	78.d	39.d	$2$	$4$	$4$	$2.125$	$\Q(\sqrt{2}, \sqrt{-5})$	None		✓			78.3.d.a	$4$	$0$	$0$	$-8$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2-\beta _{3})q^{3}+2q^{4}+3\beta _{1}q^{5}+\cdots$
78.3.d.b	$78$	$3$	78.d	39.d	$2$	$4$	$4$	$2.125$	$\Q(\sqrt{2}, \sqrt{-5})$	None		✓			78.3.d.b	$4$	$0$	$0$	$8$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(2+\beta _{3})q^{3}+2q^{4}-\beta _{1}q^{5}+\cdots$
78.3.f.a	$78$	$3$	78.f	13.d	$4$	$4$	$2$	$2.125$	$\Q(\zeta_{12})$	None		✓			78.3.f.a	$2$	$0$	$4$	$0$	$12$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta_1+1)q^{2}+\beta_{3} q^{3}+2\beta_1 q^{4}+\cdots$
78.3.f.b	$78$	$3$	78.f	13.d	$4$	$8$	$4$	$2.125$	8.0.$\cdots$.1	None		✓	✓		78.3.f.b	$2$	$0$	$-8$	$0$	$0$	$4$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{6})q^{2}+\beta _{1}q^{3}+2\beta _{6}q^{4}+\cdots$
78.3.h.a	$78$	$3$	78.h	39.i	$6$	$8$	$4$	$2.125$	8.0.4857532416.2	None		✓			78.3.h.a	$4$	$0$	$0$	$-2$	$0$	$-12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{2}q^{2}+(-1-\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$
78.3.h.b	$78$	$3$	78.h	39.i	$6$	$12$	$6$	$2.125$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓		78.3.h.b	$4$	$0$	$0$	$2$	$0$	$22$		$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{7}q^{2}+(-\beta _{4}+\beta _{9})q^{3}+2\beta _{1}q^{4}+\cdots$
78.3.j.a	$78$	$3$	78.j	39.h	$6$	$20$	$10$	$2.125$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓	✓	✓	78.3.j.a	$4$	$0$	$0$	$0$	$0$	$18$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{5}q^{2}-\beta _{1}q^{3}+(-2-2\beta _{6})q^{4}+\cdots$
78.3.l.a	$78$	$3$	78.l	13.f	$12$	$4$	$1$	$2.125$	$\Q(\zeta_{12})$	None		✓			78.3.l.a	$2$	$0$	$-2$	$0$	$-12$	$-10$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\cdots)q^{3}+\cdots$
78.3.l.b	$78$	$3$	78.l	13.f	$12$	$4$	$1$	$2.125$	$\Q(\zeta_{12})$	None		✓			78.3.l.b	$2$	$0$	$2$	$0$	$6$	$20$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots$
78.3.l.c	$78$	$3$	78.l	13.f	$12$	$8$	$2$	$2.125$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓	✓		78.3.l.c	$2$	$0$	$4$	$0$	$-6$	$10$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\beta _{4}-\beta _{5})q^{2}+(2\beta _{2}-\beta _{5})q^{3}+(2\beta _{2}+\cdots)q^{4}+\cdots$
78.4.a.a	$78$	$4$	78.a	1.a	$1$	$1$	$1$	$4.602$	$\Q$	None	✓	✓	✓	✓	78.4.a.a	$1$	$0$	$-2$	$-3$	$-16$	$28$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}-2^{4}q^{5}+6q^{6}+\cdots$
78.4.a.b	$78$	$4$	78.a	1.a	$1$	$1$	$1$	$4.602$	$\Q$	None	✓	✓	✓	✓	78.4.a.b	$1$	$1$	$-2$	$3$	$-16$	$-8$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}-2^{4}q^{5}-6q^{6}+\cdots$
78.4.a.c	$78$	$4$	78.a	1.a	$1$	$1$	$1$	$4.602$	$\Q$	None	✓	✓	✓	✓	78.4.a.c	$1$	$0$	$-2$	$3$	$10$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}+10q^{5}-6q^{6}+\cdots$
78.4.a.d	$78$	$4$	78.a	1.a	$1$	$1$	$1$	$4.602$	$\Q$	None	✓	✓	✓	✓	78.4.a.d	$1$	$1$	$2$	$-3$	$-20$	$-32$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}-20q^{5}-6q^{6}+\cdots$
78.4.a.e	$78$	$4$	78.a	1.a	$1$	$1$	$1$	$4.602$	$\Q$	None	✓	✓	✓	✓	78.4.a.e	$1$	$0$	$2$	$-3$	$6$	$20$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}+6q^{5}-6q^{6}+\cdots$
78.4.a.f	$78$	$4$	78.a	1.a	$1$	$1$	$1$	$4.602$	$\Q$	None	✓	✓	✓	✓	78.4.a.f	$1$	$0$	$2$	$3$	$4$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+4q^{5}+6q^{6}+\cdots$
78.4.b.a	$78$	$4$	78.b	13.b	$2$	$2$	$2$	$4.602$	$\Q(\sqrt{-1}) $	None		✓			78.4.b.a	$2$	$0$	$0$	$-6$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-3 q^{3}-4 q^{4}-4\beta q^{5}-3\beta q^{6}+\cdots$
78.4.b.b	$78$	$4$	78.b	13.b	$2$	$4$	$4$	$4.602$	$\Q(i, \sqrt{17})$	None		✓	✓		78.4.b.b	$2$	$0$	$0$	$12$	$0$	$0$		$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+3q^{3}-4q^{4}+(4\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
78.4.e.a	$78$	$4$	78.e	13.c	$3$	$2$	$1$	$4.602$	$\Q(\sqrt{-3}) $	None		✓			78.4.e.a	$2$	$0$	$-2$	$3$	$14$	$-16$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots$
78.4.e.b	$78$	$4$	78.e	13.c	$3$	$4$	$2$	$4.602$	$\Q(\sqrt{-3}, \sqrt{673})$	None		✓			78.4.e.b	$2$	$0$	$-4$	$-6$	$26$	$-9$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\beta _{2})q^{2}+(-3+3\beta _{2})q^{3}+\cdots$
78.4.e.c	$78$	$4$	78.e	13.c	$3$	$4$	$2$	$4.602$	$\Q(\sqrt{-3}, \sqrt{61})$	None		✓			78.4.e.c	$2$	$0$	$4$	$6$	$4$	$-18$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\beta _{1})q^{2}+(3-3\beta _{1})q^{3}-4\beta _{1}q^{4}+\cdots$
78.4.e.d	$78$	$4$	78.e	13.c	$3$	$6$	$3$	$4.602$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		✓	✓		78.4.e.d	$2$	$0$	$6$	$-9$	$-24$	$17$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(2+2\beta _{2})q^{2}+(-3-3\beta _{2})q^{3}+4\beta _{2}q^{4}+\cdots$
78.4.g.a	$78$	$4$	78.g	39.f	$4$	$28$	$14$	$4.602$		None		✓	✓	✓	78.4.g.a	$4$	$0$	$0$	$0$	$0$	$20$			$\mathrm{SU}(2)[C_{4}]$
78.4.i.a	$78$	$4$	78.i	13.e	$6$	$4$	$2$	$4.602$	$\Q(\zeta_{12})$	None		✓			78.4.i.a	$2$	$0$	$0$	$-6$	$0$	$-42$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+2\zeta_{12}q^{2}+(-3+3\zeta_{12}^{2})q^{3}+4\zeta_{12}^{2}q^{4}+\cdots$
78.4.i.b	$78$	$4$	78.i	13.e	$6$	$8$	$4$	$4.602$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓	✓		78.4.i.b	$2$	$0$	$0$	$12$	$0$	$24$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{4}q^{2}+3\beta _{1}q^{3}+(4-4\beta _{1})q^{4}+(3+\cdots)q^{5}+\cdots$
78.4.k.a	$78$	$4$	78.k	39.k	$12$	$56$	$14$	$4.602$		None		✓	✓	✓	78.4.k.a	$4$	$0$	$0$	$0$	$0$	$-92$			$\mathrm{SU}(2)[C_{12}]$
78.5.c.a	$78$	$5$	78.c	3.b	$2$	$16$	$16$	$8.063$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓	✓	78.5.c.a	$2$	$0$	$0$	$12$	$0$	$80$		$2^{22}\cdot 3^{9}\cdot 13^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(1+\beta _{3}-\beta _{4})q^{3}-8q^{4}+\cdots$
78.5.d.a	$78$	$5$	78.d	39.d	$2$	$20$	$20$	$8.063$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓	✓	78.5.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{30}\cdot 3^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-\beta _{1}q^{3}+8q^{4}+(-2\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots$
78.5.f.a	$78$	$5$	78.f	13.d	$4$	$8$	$4$	$8.063$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓			78.5.f.a	$2$	$0$	$-16$	$0$	$-36$	$-8$		$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2+2\beta _{2})q^{2}-3\beta _{1}q^{3}-8\beta _{2}q^{4}+\cdots$
78.5.f.b	$78$	$5$	78.f	13.d	$4$	$8$	$4$	$8.063$	8.0.$\cdots$.2	None		✓			78.5.f.b	$2$	$0$	$16$	$0$	$60$	$88$		$2^{5}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(2+2\beta _{2})q^{2}+\beta _{3}q^{3}+8\beta _{2}q^{4}+(7+\cdots)q^{5}+\cdots$
78.5.h.a	$78$	$5$	78.h	39.i	$6$	$36$	$18$	$8.063$		None		✓	✓	✓	78.5.h.a	$4$	$0$	$0$	$0$	$0$	$-90$			$\mathrm{SU}(2)[C_{6}]$
78.5.j.a	$78$	$5$	78.j	39.h	$6$	$36$	$18$	$8.063$		None		✓	✓	✓	78.5.j.a	$4$	$0$	$0$	$0$	$0$	$126$			$\mathrm{SU}(2)[C_{6}]$
78.5.l.a	$78$	$5$	78.l	13.f	$12$	$8$	$2$	$8.063$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓			78.5.l.a	$2$	$0$	$-8$	$0$	$-72$	$118$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-2-2\beta _{1}+2\beta _{4})q^{2}+(-3\beta _{4}-6\beta _{5}+\cdots)q^{3}+\cdots$
78.5.l.b	$78$	$5$	78.l	13.f	$12$	$8$	$2$	$8.063$	8.0.$\cdots$.10	None		✓			78.5.l.b	$2$	$0$	$8$	$0$	$-24$	$22$		$3^{2}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+(2-2\beta _{1}+2\beta _{2})q^{2}+(3\beta _{2}+6\beta _{3}+\cdots)q^{3}+\cdots$
78.5.l.c	$78$	$5$	78.l	13.f	$12$	$12$	$3$	$8.063$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓			78.5.l.c	$2$	$0$	$-12$	$0$	$12$	$48$		$3^{2}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+(-2+2\beta _{1}-2\beta _{3})q^{2}+(6\beta _{2}+3\beta _{3}+\cdots)q^{3}+\cdots$
78.5.l.d	$78$	$5$	78.l	13.f	$12$	$12$	$3$	$8.063$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			78.5.l.d	$2$	$0$	$12$	$0$	$60$	$-48$		$3^{2}\cdot 13$	$\mathrm{SU}(2)[C_{12}]$	$q+(2+2\beta _{1}-2\beta _{2}-2\beta _{4})q^{2}+(-3\beta _{1}+\cdots)q^{3}+\cdots$
78.6.a.a	$78$	$6$	78.a	1.a	$1$	$1$	$1$	$12.510$	$\Q$	None	✓	✓	✓	✓	78.6.a.a	$1$	$1$	$-4$	$-9$	$4$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}-9q^{3}+2^{4}q^{4}+4q^{5}+6^{2}q^{6}+\cdots$
78.6.a.b	$78$	$6$	78.a	1.a	$1$	$1$	$1$	$12.510$	$\Q$	None	✓	✓	✓	✓	78.6.a.b	$1$	$1$	$-4$	$9$	$24$	$-238$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+9q^{3}+2^{4}q^{4}+24q^{5}-6^{2}q^{6}+\cdots$
78.6.a.c	$78$	$6$	78.a	1.a	$1$	$1$	$1$	$12.510$	$\Q$	None	✓	✓	✓	✓	78.6.a.c	$1$	$0$	$-4$	$9$	$76$	$100$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+9q^{3}+2^{4}q^{4}+76q^{5}-6^{2}q^{6}+\cdots$
78.6.a.d	$78$	$6$	78.a	1.a	$1$	$1$	$1$	$12.510$	$\Q$	None	✓	✓	✓	✓	78.6.a.d	$1$	$1$	$4$	$-9$	$4$	$-146$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}-9q^{3}+2^{4}q^{4}+4q^{5}-6^{2}q^{6}+\cdots$
78.6.a.e	$78$	$6$	78.a	1.a	$1$	$1$	$1$	$12.510$	$\Q$	None	✓	✓	✓	✓	78.6.a.e	$1$	$0$	$4$	$-9$	$56$	$-68$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}-9q^{3}+2^{4}q^{4}+56q^{5}-6^{2}q^{6}+\cdots$

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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.