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 51 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
1480.1.h.a	$1480$	$1$	1480.h	1480.h	$2$	$1$	$1$	$0.739$	$\Q$	$D_{3}$	$\Q(\sqrt{-370}) $	None	✓	✓			1480.1.h.a	$2$	$0$	$-1$	$0$	$-1$	$-1$		$1$		$q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{9}+\cdots$
1480.1.h.b	$1480$	$1$	1480.h	1480.h	$2$	$1$	$1$	$0.739$	$\Q$	$D_{3}$	$\Q(\sqrt{-370}) $	None	✓	✓			1480.1.h.a	$2$	$0$	$-1$	$0$	$1$	$1$		$1$		$q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}+q^{9}+\cdots$
1480.1.h.c	$1480$	$1$	1480.h	1480.h	$2$	$1$	$1$	$0.739$	$\Q$	$D_{3}$	$\Q(\sqrt{-370}) $	None	✓	✓			1480.1.h.a	$2$	$0$	$1$	$0$	$-1$	$1$		$1$		$q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}+q^{9}+\cdots$
1480.1.h.d	$1480$	$1$	1480.h	1480.h	$2$	$1$	$1$	$0.739$	$\Q$	$D_{3}$	$\Q(\sqrt{-370}) $	None	✓	✓			1480.1.h.a	$2$	$0$	$1$	$0$	$1$	$-1$		$1$		$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{9}+\cdots$
1480.1.h.e	$1480$	$1$	1480.h	1480.h	$2$	$2$	$2$	$0.739$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-10}) $, $\Q(\sqrt{-74}) $	$\Q(\sqrt{185}) $		✓			1480.1.h.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-q^{4}-i q^{5}+i q^{8}+q^{9}+\cdots$
1480.1.h.f	$1480$	$1$	1480.h	1480.h	$2$	$8$	$8$	$0.739$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-74}) $	None		✓	✓		1480.1.h.f	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{20}^{5}q^{2}+(\zeta_{20}^{2}+\zeta_{20}^{8})q^{3}-q^{4}+\cdots$
1480.1.v.a	$1480$	$1$	1480.v	1480.v	$4$	$4$	$2$	$0.739$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓	✓	✓	1480.1.v.a	$4$	$0$	$4$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}-\zeta_{8}q^{5}+\zeta_{8}q^{7}+q^{8}+\cdots$
1480.1.bc.a	$1480$	$1$	1480.bc	1480.ac	$4$	$4$	$2$	$0.739$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓	✓	✓	1480.1.v.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}q^{5}+\zeta_{8}^{3}q^{7}+\cdots$
1480.1.by.a	$1480$	$1$	1480.by	1480.ay	$6$	$2$	$1$	$0.739$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-10}) $	None		✓			1480.1.by.a	$4$	$0$	$-1$	$0$	$-1$	$-2$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\cdots$
1480.1.by.b	$1480$	$1$	1480.by	1480.ay	$6$	$2$	$1$	$0.739$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-10}) $	None		✓			1480.1.by.a	$4$	$0$	$1$	$0$	$1$	$2$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}^{2}q^{7}+\cdots$
1480.1.bz.a	$1480$	$1$	1480.bz	1480.az	$6$	$4$	$2$	$0.739$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-10}) $	None		✓	✓	✓	1480.1.bz.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
1480.1.cm.a	$1480$	$1$	1480.cm	1480.bm	$12$	$8$	$2$	$0.739$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	1480.1.cm.a	$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{24}q^{2}-\zeta_{24}^{11}q^{3}+\zeta_{24}^{2}q^{4}+\cdots$
1480.1.de.a	$1480$	$1$	1480.de	1480.ce	$18$	$6$	$1$	$0.739$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-10}) $	None		✓			1480.1.de.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{2}q^{5}+\cdots$
1480.1.de.b	$1480$	$1$	1480.de	1480.ce	$18$	$6$	$1$	$0.739$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-10}) $	None		✓			1480.1.de.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}-\zeta_{18}^{2}q^{5}+\cdots$
1480.1.dj.a	$1480$	$1$	1480.dj	1480.cj	$18$	$12$	$2$	$0.739$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-10}) $	None		✓	✓	✓	1480.1.dj.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{36}^{7}q^{2}+\zeta_{36}^{14}q^{4}+\zeta_{36}^{17}q^{5}+\cdots$
1480.2.a.a	$1480$	$2$	1480.a	1.a	$1$	$1$	$1$	$11.818$	$\Q$	$_{}$	None	None	✓	✓			1480.2.a.a	$1$	$2$	$0$	$-3$	$-1$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}-5q^{7}+6q^{9}-3q^{11}+\cdots$
1480.2.a.b	$1480$	$2$	1480.a	1.a	$1$	$1$	$1$	$11.818$	$\Q$	$_{}$	None	None	✓	✓			1480.2.a.b	$1$	$1$	$0$	$-2$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+2q^{7}+q^{9}-6q^{13}+\cdots$
1480.2.a.c	$1480$	$2$	1480.a	1.a	$1$	$1$	$1$	$11.818$	$\Q$	$_{}$	None	None	✓	✓			1480.2.a.c	$1$	$1$	$0$	$1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}-2q^{9}-3q^{11}+q^{15}+\cdots$
1480.2.a.d	$1480$	$2$	1480.a	1.a	$1$	$1$	$1$	$11.818$	$\Q$	$_{}$	None	None	✓	✓			1480.2.a.d	$1$	$0$	$0$	$2$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots$
1480.2.a.e	$1480$	$2$	1480.a	1.a	$1$	$3$	$3$	$11.818$	3.3.316.1	$_{}$	None	None	✓	✓	✓	✓	1480.2.a.e	$1$	$1$	$0$	$1$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}-\beta _{1}q^{7}+\beta _{2}q^{9}+(-1+\cdots)q^{11}+\cdots$
1480.2.a.f	$1480$	$2$	1480.a	1.a	$1$	$3$	$3$	$11.818$	3.3.568.1	$_{}$	None	None	✓	✓	✓		1480.2.a.f	$1$	$0$	$0$	$1$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}-\beta _{1}q^{7}+(1+2\beta _{1}+\beta _{2})q^{9}+\cdots$
1480.2.a.g	$1480$	$2$	1480.a	1.a	$1$	$5$	$5$	$11.818$	5.5.583504.1	$_{}$	None	None	✓	✓	✓	✓	1480.2.a.g	$1$	$1$	$0$	$-5$	$5$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+q^{5}+(-1-\beta _{2}+\beta _{4})q^{7}+\cdots$
1480.2.a.h	$1480$	$2$	1480.a	1.a	$1$	$5$	$5$	$11.818$	5.5.935504.1	$_{}$	None	None	✓	✓	✓	✓	1480.2.a.h	$1$	$1$	$0$	$-1$	$-5$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+\beta _{3}q^{7}+(\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots$
1480.2.a.i	$1480$	$2$	1480.a	1.a	$1$	$5$	$5$	$11.818$	5.5.6397264.1	$_{}$	None	None	✓	✓	✓		1480.2.a.i	$1$	$0$	$0$	$0$	$-5$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(1+\beta _{1}-\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots$
1480.2.a.j	$1480$	$2$	1480.a	1.a	$1$	$5$	$5$	$11.818$	5.5.998068.1	$_{}$	None	None	✓	✓	✓	✓	1480.2.a.j	$1$	$0$	$0$	$1$	$-5$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{3}-q^{5}-\beta _{2}q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$
1480.2.a.k	$1480$	$2$	1480.a	1.a	$1$	$6$	$6$	$11.818$	6.6.693982032.1	$_{}$	None	None	✓	✓	✓	✓	1480.2.a.k	$1$	$0$	$0$	$1$	$6$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+(1+\beta _{2})q^{7}+(2+\beta _{3}+\cdots)q^{9}+\cdots$
1480.2.d.a	$1480$	$2$	1480.d	5.b	$2$	$2$	$2$	$11.818$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1480.2.d.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{3}+(-i-2)q^{5}+4 i q^{7}+\cdots$
1480.2.d.b	$1480$	$2$	1480.d	5.b	$2$	$20$	$20$	$11.818$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			1480.2.d.b	$2$	$0$	$0$	$0$	$4$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{15}q^{5}+(-\beta _{7}+\beta _{8})q^{7}+\cdots$
1480.2.d.c	$1480$	$2$	1480.d	5.b	$2$	$32$	$32$	$11.818$		$_{}$	None	None		✓	✓		1480.2.d.c	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1480.2.e.a	$1480$	$2$	1480.e	185.d	$2$	$4$	$4$	$11.818$	$\Q(\sqrt{-2}, \sqrt{5})$	$_{}$	None	None		✓			1480.2.e.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{3}q^{7}+\beta _{2}q^{9}+\cdots$
1480.2.e.b	$1480$	$2$	1480.e	185.d	$2$	$4$	$4$	$11.818$	$\Q(\sqrt{-2}, \sqrt{5})$	$_{}$	None	None		✓			1480.2.e.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}+\beta _{3}q^{7}+\beta _{2}q^{9}+\cdots$
1480.2.e.c	$1480$	$2$	1480.e	185.d	$2$	$24$	$24$	$11.818$		$_{}$	None	None		✓			1480.2.e.c	$2$	$0$	$0$	$0$	$-3$	$0$			$\mathrm{SU}(2)[C_{2}]$
1480.2.e.d	$1480$	$2$	1480.e	185.d	$2$	$24$	$24$	$11.818$		$_{}$	None	None		✓			1480.2.e.c	$2$	$0$	$0$	$0$	$3$	$0$			$\mathrm{SU}(2)[C_{2}]$
1480.2.p.a	$1480$	$2$	1480.p	37.b	$2$	$2$	$2$	$11.818$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1480.2.p.a	$2$	$0$	$0$	$4$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 q^{3}-i q^{5}+4 q^{7}+q^{9}+4 q^{11}+\cdots$
1480.2.p.b	$1480$	$2$	1480.p	37.b	$2$	$4$	$4$	$11.818$	$\Q(i, \sqrt{33})$	$_{}$	None	None		✓			1480.2.p.b	$2$	$0$	$0$	$2$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{3})q^{3}-\beta _{2}q^{5}+q^{7}+(6-\beta _{3})q^{9}+\cdots$
1480.2.p.c	$1480$	$2$	1480.p	37.b	$2$	$12$	$12$	$11.818$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			1480.2.p.c	$2$	$0$	$0$	$-6$	$0$	$-10$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{3})q^{3}+\beta _{7}q^{5}+(-2-\beta _{3}+\cdots)q^{7}+\cdots$
1480.2.p.d	$1480$	$2$	1480.p	37.b	$2$	$20$	$20$	$11.818$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓	✓		1480.2.p.d	$2$	$0$	$0$	$-4$	$0$	$6$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{16}q^{3}+\beta _{11}q^{5}-\beta _{8}q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots$
1480.2.q.a	$1480$	$2$	1480.q	37.c	$3$	$18$	$9$	$11.818$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓			1480.2.q.a	$2$	$0$	$0$	$2$	$-9$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{3})q^{3}+(-1+\beta _{13})q^{5}+\cdots$
1480.2.q.b	$1480$	$2$	1480.q	37.c	$3$	$18$	$9$	$11.818$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓			1480.2.q.b	$2$	$0$	$0$	$2$	$9$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+(1+\beta _{5})q^{5}-\beta _{8}q^{7}+(-\beta _{4}+\cdots)q^{9}+\cdots$
1480.2.q.c	$1480$	$2$	1480.q	37.c	$3$	$20$	$10$	$11.818$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			1480.2.q.c	$2$	$0$	$0$	$0$	$-10$	$-4$		$3^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{3})q^{3}+(-1-\beta _{5})q^{5}+\beta _{4}q^{7}+\cdots$
1480.2.q.d	$1480$	$2$	1480.q	37.c	$3$	$20$	$10$	$11.818$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			1480.2.q.d	$2$	$0$	$0$	$0$	$10$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{6}q^{3}-\beta _{3}q^{5}+\beta _{15}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots$
1480.2.br.a	$1480$	$2$	1480.br	37.e	$6$	$36$	$18$	$11.818$		$_{}$	None	None		✓			1480.2.br.a	$2$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{6}]$
1480.2.br.b	$1480$	$2$	1480.br	37.e	$6$	$40$	$20$	$11.818$		$_{}$	None	None		✓	✓		1480.2.br.b	$2$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
1480.4.a.a	$1480$	$4$	1480.a	1.a	$1$	$12$	$12$	$87.323$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1480.4.a.a	$1$	$1$	$0$	$-3$	$60$	$-30$	$-$	$2^{10}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+5q^{5}+(-3+\beta _{1}-\beta _{5})q^{7}+\cdots$
1480.4.a.b	$1480$	$4$	1480.a	1.a	$1$	$12$	$12$	$87.323$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1480.4.a.b	$1$	$1$	$0$	$-1$	$-60$	$10$	$-$	$2^{10}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-5q^{5}+(1+\beta _{5})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
1480.4.a.c	$1480$	$4$	1480.a	1.a	$1$	$13$	$13$	$87.323$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1480.4.a.c	$1$	$1$	$0$	$3$	$-65$	$18$	$-$	$2^{15}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-5q^{5}+(1-\beta _{6})q^{7}+(7-\beta _{1}+\cdots)q^{9}+\cdots$
1480.4.a.d	$1480$	$4$	1480.a	1.a	$1$	$13$	$13$	$87.323$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1480.4.a.d	$1$	$0$	$0$	$9$	$-65$	$11$	$+$	$2^{11}\cdot 3$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-5q^{5}+(1+\beta _{5})q^{7}+(10+\cdots)q^{9}+\cdots$
1480.4.a.e	$1480$	$4$	1480.a	1.a	$1$	$13$	$13$	$87.323$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1480.4.a.e	$1$	$0$	$0$	$11$	$65$	$9$	$+$	$2^{11}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+5q^{5}+(1+\beta _{7})q^{7}+(12+\cdots)q^{9}+\cdots$
1480.4.a.f	$1480$	$4$	1480.a	1.a	$1$	$14$	$14$	$87.323$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1480.4.a.f	$1$	$1$	$0$	$-13$	$70$	$-40$	$-$	$2^{14}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+5q^{5}+(-3-\beta _{4}+\cdots)q^{7}+\cdots$
1480.4.a.g	$1480$	$4$	1480.a	1.a	$1$	$15$	$15$	$87.323$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1480.4.a.g	$1$	$0$	$0$	$-13$	$-75$	$3$	$+$	$2^{18}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-5q^{5}-\beta _{3}q^{7}+(8+\cdots)q^{9}+\cdots$

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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.