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 323 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
80.1.h.a	$80$	$1$	80.h	20.d	$2$	$1$	$1$	$0.040$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	✓	✓	✓	✓	80.1.h.a	$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-q^{5}-q^{9}+q^{25}+2q^{29}-2q^{41}+\cdots$
80.2.a.a	$80$	$2$	80.a	1.a	$1$	$1$	$1$	$0.639$	$\Q$	$_{}$	None	None	✓		✓	✓	40.2.a.a	$1$	$0$	$0$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{7}-3q^{9}-4q^{11}-2q^{13}+\cdots$
80.2.a.b	$80$	$2$	80.a	1.a	$1$	$1$	$1$	$0.639$	$\Q$	$_{}$	None	None	✓		✓	✓	20.2.a.a	$1$	$0$	$0$	$2$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}-2q^{7}+q^{9}+2q^{13}+\cdots$
80.2.c.a	$80$	$2$	80.c	5.b	$2$	$2$	$2$	$0.639$	$\Q(\sqrt{-1}) $	$_{}$	None	None			✓	✓	40.2.c.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+(\beta-1)q^{5}-\beta q^{7}-q^{9}+\cdots$
80.2.j.a	$80$	$2$	80.j	80.j	$4$	$2$	$1$	$0.639$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			80.2.j.a	$2$	$0$	$2$	$0$	$2$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i+1)q^{2}+2 i q^{3}-2 i q^{4}+\cdots$
80.2.j.b	$80$	$2$	80.j	80.j	$4$	$18$	$9$	$0.639$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		✓	✓		80.2.j.b	$2$	$0$	$-4$	$0$	$-4$	$2$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{6}q^{2}-\beta _{16}q^{3}-\beta _{13}q^{4}+(-1+\cdots)q^{5}+\cdots$
80.2.l.a	$80$	$2$	80.l	16.e	$4$	$16$	$8$	$0.639$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓	✓	80.2.l.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{9}q^{2}+(\beta _{3}-\beta _{6}+\beta _{11})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
80.2.n.a	$80$	$2$	80.n	20.e	$4$	$2$	$1$	$0.639$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			80.2.n.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(i+2)q^{5}-3 i q^{9}+(5 i-5)q^{13}+\cdots$
80.2.n.b	$80$	$2$	80.n	20.e	$4$	$4$	$2$	$0.639$	$\Q(\zeta_{12})$	$_{}$	None	None		✓	✓		80.2.n.b	$4$	$0$	$0$	$0$	$-4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta_{2} q^{3}+(-2\beta_1-1)q^{5}+\beta_{3} q^{7}+\cdots$
80.2.q.a	$80$	$2$	80.q	80.q	$4$	$2$	$1$	$0.639$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			80.2.q.a	$2$	$0$	$-2$	$2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{2}+(i+1)q^{3}+2 i q^{4}+\cdots$
80.2.q.b	$80$	$2$	80.q	80.q	$4$	$2$	$1$	$0.639$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			80.2.q.a	$2$	$0$	$2$	$-2$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{2}+(-i-1)q^{3}+2 i q^{4}+\cdots$
80.2.q.c	$80$	$2$	80.q	80.q	$4$	$16$	$8$	$0.639$	16.0.$\cdots$.1	$_{}$	None	None		✓	✓		80.2.q.c	$4$	$0$	$0$	$0$	$-8$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{12}q^{2}+(-\beta _{3}-\beta _{11}-\beta _{13}+\beta _{14}+\cdots)q^{3}+\cdots$
80.2.s.a	$80$	$2$	80.s	80.s	$4$	$2$	$1$	$0.639$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			80.2.j.a	$2$	$1$	$-2$	$-4$	$-4$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i-1)q^{2}-2 q^{3}-2 i q^{4}+(i-2)q^{5}+\cdots$
80.2.s.b	$80$	$2$	80.s	80.s	$4$	$18$	$9$	$0.639$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		✓	✓		80.2.j.b	$2$	$0$	$0$	$0$	$2$	$2$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{13}q^{4}+\beta _{17}q^{5}+\cdots$
80.3.b.a	$80$	$3$	80.b	4.b	$2$	$4$	$4$	$2.180$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓	✓	✓	80.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}+(-9+6\beta _{1}+\cdots)q^{9}+\cdots$
80.3.h.a	$80$	$3$	80.h	20.d	$2$	$2$	$2$	$2.180$	$\Q(\sqrt{5}) $	$_{}$	$\Q(\sqrt{-5}) $	None	✓	✓			80.3.h.a	$4$	$0$	$0$	$0$	$10$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{3}+5q^{5}+3\beta q^{7}+11q^{9}-5\beta q^{15}+\cdots$
80.3.h.b	$80$	$3$	80.h	20.d	$2$	$4$	$4$	$2.180$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓	✓		80.3.h.b	$4$	$0$	$0$	$0$	$-4$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+3\beta _{1}q^{7}+\cdots$
80.3.i.a	$80$	$3$	80.i	80.i	$4$	$44$	$22$	$2.180$		$_{}$	None	None		✓	✓	✓	80.3.i.a	$2$	$0$	$-2$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{4}]$
80.3.k.a	$80$	$3$	80.k	80.k	$4$	$44$	$22$	$2.180$		$_{}$	None	None		✓	✓	✓	80.3.k.a	$4$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{4}]$
80.3.p.a	$80$	$3$	80.p	5.c	$4$	$2$	$1$	$2.180$	$\Q(\sqrt{-1}) $	$_{}$	None	None					20.3.f.a	$2$	$0$	$0$	$-2$	$-6$	$14$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i-1)q^{3}+(4 i-3)q^{5}+(7 i+7)q^{7}+\cdots$
80.3.p.b	$80$	$3$	80.p	5.c	$4$	$2$	$1$	$2.180$	$\Q(\sqrt{-1}) $	$_{}$	None	None					40.3.l.a	$2$	$0$	$0$	$-2$	$10$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i-1)q^{3}+5 q^{5}+(3 i+3)q^{7}+\cdots$
80.3.p.c	$80$	$3$	80.p	5.c	$4$	$2$	$1$	$2.180$	$\Q(\sqrt{-1}) $	$_{}$	None	None					10.3.c.a	$2$	$0$	$0$	$4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2 i+2)q^{3}-5 i q^{5}+(-2 i-2)q^{7}+\cdots$
80.3.p.d	$80$	$3$	80.p	5.c	$4$	$4$	$2$	$2.180$	$\Q(i, \sqrt{41})$	$_{}$	None	None			✓		40.3.l.b	$2$	$0$	$0$	$2$	$-6$	$-14$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
80.3.r.a	$80$	$3$	80.r	16.f	$4$	$32$	$16$	$2.180$		$_{}$	None	None		✓	✓	✓	80.3.r.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
80.3.t.a	$80$	$3$	80.t	80.t	$4$	$44$	$22$	$2.180$		$_{}$	None	None		✓	✓	✓	80.3.i.a	$2$	$0$	$-2$	$-4$	$-2$	$0$			$\mathrm{SU}(2)[C_{4}]$
80.4.a.a	$80$	$4$	80.a	1.a	$1$	$1$	$1$	$4.720$	$\Q$	$_{}$	None	None	✓				40.4.a.c	$1$	$0$	$0$	$-10$	$-5$	$18$	$+$	$1$	$\mathrm{SU}(2)$	$q-10q^{3}-5q^{5}+18q^{7}+73q^{9}+2^{4}q^{11}+\cdots$
80.4.a.b	$80$	$4$	80.a	1.a	$1$	$1$	$1$	$4.720$	$\Q$	$_{}$	None	None	✓		✓	✓	40.4.a.b	$1$	$1$	$0$	$-4$	$5$	$-16$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{3}+5q^{5}-2^{4}q^{7}-11q^{9}-6^{2}q^{11}+\cdots$
80.4.a.c	$80$	$4$	80.a	1.a	$1$	$1$	$1$	$4.720$	$\Q$	$_{}$	None	None	✓				20.4.a.a	$1$	$0$	$0$	$-4$	$5$	$16$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{3}+5q^{5}+2^{4}q^{7}-11q^{9}+60q^{11}+\cdots$
80.4.a.d	$80$	$4$	80.a	1.a	$1$	$1$	$1$	$4.720$	$\Q$	$_{}$	None	None	✓		✓	✓	5.4.a.a	$1$	$1$	$0$	$-2$	$-5$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-5q^{5}-6q^{7}-23q^{9}-2^{5}q^{11}+\cdots$
80.4.a.e	$80$	$4$	80.a	1.a	$1$	$1$	$1$	$4.720$	$\Q$	$_{}$	None	None	✓				40.4.a.a	$1$	$0$	$0$	$6$	$-5$	$34$	$+$	$1$	$\mathrm{SU}(2)$	$q+6q^{3}-5q^{5}+34q^{7}+9q^{9}-2^{4}q^{11}+\cdots$
80.4.a.f	$80$	$4$	80.a	1.a	$1$	$1$	$1$	$4.720$	$\Q$	$_{}$	None	None	✓				10.4.a.a	$1$	$0$	$0$	$8$	$5$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+8q^{3}+5q^{5}+4q^{7}+37q^{9}-12q^{11}+\cdots$
80.4.c.a	$80$	$4$	80.c	5.b	$2$	$2$	$2$	$4.720$	$\Q(\sqrt{-1}) $	$_{}$	None	None					10.4.b.a	$2$	$0$	$0$	$0$	$-10$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+(-5\beta-5)q^{5}-13\beta q^{7}+\cdots$
80.4.c.b	$80$	$4$	80.c	5.b	$2$	$2$	$2$	$4.720$	$\Q(\sqrt{-19}) $	$_{}$	None	None					20.4.c.a	$2$	$0$	$0$	$0$	$14$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}+(7-\beta )q^{5}+\beta q^{7}-7^{2}q^{9}+\cdots$
80.4.c.c	$80$	$4$	80.c	5.b	$2$	$4$	$4$	$4.720$	$\Q(i, \sqrt{6})$	$_{}$	None	None			✓		40.4.c.a	$2$	$0$	$0$	$0$	$-4$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots$
80.4.j.a	$80$	$4$	80.j	80.j	$4$	$68$	$34$	$4.720$		$_{}$	None	None		✓	✓	✓	80.4.j.a	$2$	$0$	$-2$	$0$	$-2$	$-4$			$\mathrm{SU}(2)[C_{4}]$
80.4.l.a	$80$	$4$	80.l	16.e	$4$	$48$	$24$	$4.720$		$_{}$	None	None		✓	✓	✓	80.4.l.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
80.4.n.a	$80$	$4$	80.n	20.e	$4$	$2$	$1$	$4.720$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			80.4.n.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-11 i+2)q^{5}-27 i q^{9}+(-55 i+55)q^{13}+\cdots$
80.4.n.b	$80$	$4$	80.n	20.e	$4$	$4$	$2$	$4.720$	$\Q(i, \sqrt{35})$	$_{}$	None	None		✓			80.4.n.b	$4$	$0$	$0$	$0$	$-20$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{3}+(-5+10\beta _{1})q^{5}+\beta _{3}q^{7}+\cdots$
80.4.n.c	$80$	$4$	80.n	20.e	$4$	$12$	$6$	$4.720$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓		80.4.n.c	$4$	$0$	$0$	$0$	$16$	$0$		$2^{24}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{4})q^{5}+(-2\beta _{2}+\cdots)q^{7}+\cdots$
80.4.q.a	$80$	$4$	80.q	80.q	$4$	$68$	$34$	$4.720$		$_{}$	None	None		✓	✓	✓	80.4.q.a	$4$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{4}]$
80.4.s.a	$80$	$4$	80.s	80.s	$4$	$68$	$34$	$4.720$		$_{}$	None	None		✓	✓	✓	80.4.j.a	$2$	$0$	$-2$	$-4$	$-2$	$-4$			$\mathrm{SU}(2)[C_{4}]$
80.5.b.a	$80$	$5$	80.b	4.b	$2$	$4$	$4$	$8.270$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			80.5.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{3}q^{7}+(-9-6\beta _{2}+\cdots)q^{9}+\cdots$
80.5.b.b	$80$	$5$	80.b	4.b	$2$	$4$	$4$	$8.270$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			80.5.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}-5\beta _{1}q^{5}+(2\beta _{2}+7\beta _{3})q^{7}+\cdots$
80.5.h.a	$80$	$5$	80.h	20.d	$2$	$2$	$2$	$8.270$	$\Q(\sqrt{5}) $	$_{}$	$\Q(\sqrt{-5}) $	None	✓	✓			80.5.h.a	$4$	$0$	$0$	$0$	$-50$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{3}-5^{2}q^{5}-3\beta q^{7}+239q^{9}+\cdots$
80.5.h.b	$80$	$5$	80.h	20.d	$2$	$2$	$2$	$8.270$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			80.5.h.b	$4$	$0$	$0$	$0$	$14$	$0$		$2^{3}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta+7)q^{5}-81 q^{9}+10\beta q^{13}+\cdots$
80.5.h.c	$80$	$5$	80.h	20.d	$2$	$8$	$8$	$8.270$	8.0.$\cdots$.10	$_{}$	None	None		✓	✓		80.5.h.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{28}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+\beta _{4}q^{5}+(2\beta _{3}-\beta _{7})q^{7}+(1+\cdots)q^{9}+\cdots$
80.5.i.a	$80$	$5$	80.i	80.i	$4$	$92$	$46$	$8.270$		$_{}$	None	None		✓	✓	✓	80.5.i.a	$2$	$0$	$-2$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{4}]$
80.5.k.a	$80$	$5$	80.k	80.k	$4$	$92$	$46$	$8.270$		$_{}$	None	None		✓	✓	✓	80.5.k.a	$4$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{4}]$
80.5.p.a	$80$	$5$	80.p	5.c	$4$	$2$	$1$	$8.270$	$\Q(\sqrt{-1}) $	$_{}$	None	None					40.5.l.a	$2$	$0$	$0$	$-20$	$40$	$84$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(10 i-10)q^{3}+(15 i+20)q^{5}+\cdots$
80.5.p.b	$80$	$5$	80.p	5.c	$4$	$2$	$1$	$8.270$	$\Q(\sqrt{-1}) $	$_{}$	None	None					10.5.c.a	$2$	$0$	$0$	$-18$	$-30$	$-58$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(9 i-9)q^{3}+(20 i-15)q^{5}+(-29 i-29)q^{7}+\cdots$

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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.