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 193 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
2240.1.c.a	$2240$	$1$	2240.c	280.c	$2$	$2$	$2$	$1.118$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{14}) $		✓			2240.1.c.a	$8$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-i q^{5}-q^{7}+q^{9}+2 i q^{11}+2 i q^{13}+\cdots$
2240.1.c.b	$2240$	$1$	2240.c	280.c	$2$	$2$	$2$	$1.118$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{14}) $		✓			2240.1.c.a	$8$	$0$	$0$	$0$	$0$	$2$		$1$		$q-i q^{5}+q^{7}+q^{9}-2 i q^{11}+2 i q^{13}+\cdots$
2240.1.c.c	$2240$	$1$	2240.c	280.c	$2$	$4$	$4$	$1.118$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-35}) $	None		✓			2240.1.c.c	$8$	$0$	$0$	$0$	$0$	$-4$		$2^{2}$		$q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{3}-\zeta_{12}^{3}q^{5}+\cdots$
2240.1.c.d	$2240$	$1$	2240.c	280.c	$2$	$4$	$4$	$1.118$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-35}) $	None		✓			2240.1.c.c	$8$	$0$	$0$	$0$	$0$	$4$		$2^{2}$		$q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{3}-\zeta_{12}^{3}q^{5}+\cdots$
2240.1.p.a	$2240$	$1$	2240.p	35.c	$2$	$1$	$1$	$1.118$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓				140.1.h.a	$2$	$0$	$0$	$-1$	$-1$	$-1$		$1$		$q-q^{3}-q^{5}-q^{7}-q^{11}+q^{13}+q^{15}+\cdots$
2240.1.p.b	$2240$	$1$	2240.p	35.c	$2$	$1$	$1$	$1.118$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓				140.1.h.a	$2$	$0$	$0$	$-1$	$1$	$-1$		$1$		$q-q^{3}+q^{5}-q^{7}+q^{11}-q^{13}-q^{15}+\cdots$
2240.1.p.c	$2240$	$1$	2240.p	35.c	$2$	$1$	$1$	$1.118$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓				140.1.h.a	$2$	$0$	$0$	$1$	$-1$	$1$		$1$		$q+q^{3}-q^{5}+q^{7}+q^{11}+q^{13}-q^{15}+\cdots$
2240.1.p.d	$2240$	$1$	2240.p	35.c	$2$	$1$	$1$	$1.118$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓				140.1.h.a	$2$	$0$	$0$	$1$	$1$	$1$		$1$		$q+q^{3}+q^{5}+q^{7}-q^{11}-q^{13}+q^{15}+\cdots$
2240.1.p.e	$2240$	$1$	2240.p	35.c	$2$	$4$	$4$	$1.118$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-5}) $	None			✓		1120.1.p.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{8}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots$
2240.1.bk.a	$2240$	$1$	2240.bk	280.y	$4$	$8$	$4$	$1.118$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-14}) $	None		✓			2240.1.bk.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{16}^{5}+\zeta_{16}^{7})q^{3}-\zeta_{16}^{3}q^{5}+\cdots$
2240.1.bk.b	$2240$	$1$	2240.bk	280.y	$4$	$8$	$4$	$1.118$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-14}) $	None		✓			2240.1.bk.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{16}^{5}-\zeta_{16}^{7})q^{3}-\zeta_{16}^{3}q^{5}+\zeta_{16}^{6}q^{7}+\cdots$
2240.1.br.a	$2240$	$1$	2240.br	35.i	$6$	$8$	$4$	$1.118$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-5}) $	None			✓	✓	1120.1.br.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{3}-\zeta_{24}^{10}q^{5}-\zeta_{24}^{11}q^{7}+\cdots$
2240.1.bt.a	$2240$	$1$	2240.bt	140.p	$6$	$2$	$1$	$1.118$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None					140.1.p.a	$4$	$0$	$0$	$-1$	$1$	$-1$		$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}-q^{15}+\cdots$
2240.1.bt.b	$2240$	$1$	2240.bt	140.p	$6$	$2$	$1$	$1.118$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None					140.1.p.a	$4$	$0$	$0$	$1$	$1$	$1$		$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+q^{15}+\cdots$
2240.1.bt.c	$2240$	$1$	2240.bt	140.p	$6$	$4$	$2$	$1.118$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None			✓		560.1.bt.a	$8$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{5}q^{7}+\cdots$
2240.1.ca.a	$2240$	$1$	2240.ca	280.ak	$6$	$4$	$2$	$1.118$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-10}) $	None		✓			2240.1.ca.a	$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{12}q^{5}-q^{7}+\zeta_{12}^{4}q^{9}-\zeta_{12}^{5}q^{11}+\cdots$
2240.1.ca.b	$2240$	$1$	2240.ca	280.ak	$6$	$4$	$2$	$1.118$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-10}) $	None		✓			2240.1.ca.a	$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{12}q^{5}+q^{7}+\zeta_{12}^{4}q^{9}+\zeta_{12}^{5}q^{11}+\cdots$
2240.1.da.a	$2240$	$1$	2240.da	35.l	$12$	$8$	$2$	$1.118$	$\Q(\zeta_{24})$	$S_{4}$	None	None			✓	✓	1120.1.da.a	$8$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{24}^{5}q^{3}+\zeta_{24}^{4}q^{5}-\zeta_{24}^{11}q^{7}+\cdots$
2240.1.dl.a	$2240$	$1$	2240.dl	280.at	$12$	$8$	$2$	$1.118$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓			2240.1.dl.a	$8$	$0$	$0$	$-4$	$0$	$0$		$1$		$q+(\zeta_{24}^{2}+\zeta_{24}^{8})q^{3}-\zeta_{24}^{7}q^{5}+\zeta_{24}^{9}q^{7}+\cdots$
2240.1.dl.b	$2240$	$1$	2240.dl	280.at	$12$	$8$	$2$	$1.118$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓			2240.1.dl.a	$8$	$0$	$0$	$4$	$0$	$0$		$1$		$q+(-\zeta_{24}^{2}-\zeta_{24}^{8})q^{3}-\zeta_{24}^{7}q^{5}+\cdots$
2240.2.a.a	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				280.2.a.a	$1$	$0$	$0$	$-3$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}-q^{7}+6q^{9}-5q^{11}+\cdots$
2240.2.a.b	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				1120.2.a.b	$1$	$1$	$0$	$-3$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}+q^{7}+6q^{9}-3q^{11}+\cdots$
2240.2.a.c	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				140.2.a.b	$1$	$0$	$0$	$-3$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}-q^{7}+6q^{9}+5q^{11}+\cdots$
2240.2.a.d	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				1120.2.a.a	$1$	$1$	$0$	$-3$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}+q^{7}+6q^{9}-q^{11}+q^{13}+\cdots$
2240.2.a.e	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				1120.2.a.e	$1$	$0$	$0$	$-1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}-2q^{9}-5q^{11}-5q^{13}+\cdots$
2240.2.a.f	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				1120.2.a.f	$1$	$1$	$0$	$-1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}-2q^{9}+3q^{11}+7q^{13}+\cdots$
2240.2.a.g	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				140.2.a.a	$1$	$0$	$0$	$-1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}-2q^{9}-3q^{11}+q^{13}+\cdots$
2240.2.a.h	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				1120.2.a.d	$1$	$0$	$0$	$-1$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-q^{7}-2q^{9}+q^{11}-3q^{13}+\cdots$
2240.2.a.i	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				1120.2.a.c	$1$	$1$	$0$	$-1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-q^{7}-2q^{9}+q^{11}+q^{13}+\cdots$
2240.2.a.j	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				280.2.a.b	$1$	$0$	$0$	$-1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}-2q^{9}-5q^{11}-q^{13}+\cdots$
2240.2.a.k	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				35.2.a.a	$1$	$1$	$0$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}-2q^{9}+3q^{11}-5q^{13}+\cdots$
2240.2.a.l	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				1120.2.a.i	$1$	$0$	$0$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}-3q^{9}+2q^{13}+2q^{17}+\cdots$
2240.2.a.m	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				1120.2.a.i	$1$	$1$	$0$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}-3q^{9}+2q^{13}+2q^{17}+\cdots$
2240.2.a.n	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				70.2.a.a	$1$	$0$	$0$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}-3q^{9}-4q^{11}+6q^{13}+\cdots$
2240.2.a.o	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				1120.2.a.g	$1$	$0$	$0$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}-3q^{9}+4q^{11}-2q^{13}+\cdots$
2240.2.a.p	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				1120.2.a.g	$1$	$1$	$0$	$0$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}-3q^{9}-4q^{11}-2q^{13}+\cdots$
2240.2.a.q	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				70.2.a.a	$1$	$0$	$0$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}-3q^{9}+4q^{11}+6q^{13}+\cdots$
2240.2.a.r	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				140.2.a.a	$1$	$0$	$0$	$1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots$
2240.2.a.s	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				1120.2.a.f	$1$	$0$	$0$	$1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}-2q^{9}-3q^{11}+7q^{13}+\cdots$
2240.2.a.t	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				1120.2.a.e	$1$	$1$	$0$	$1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}-2q^{9}+5q^{11}-5q^{13}+\cdots$
2240.2.a.u	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				35.2.a.a	$1$	$1$	$0$	$1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}-2q^{9}-3q^{11}-5q^{13}+\cdots$
2240.2.a.v	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				280.2.a.b	$1$	$0$	$0$	$1$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}-2q^{9}+5q^{11}-q^{13}+\cdots$
2240.2.a.w	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				1120.2.a.d	$1$	$1$	$0$	$1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{7}-2q^{9}-q^{11}-3q^{13}+\cdots$
2240.2.a.x	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				1120.2.a.c	$1$	$0$	$0$	$1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{7}-2q^{9}-q^{11}+q^{13}+\cdots$
2240.2.a.y	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				1120.2.a.b	$1$	$0$	$0$	$3$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-q^{5}-q^{7}+6q^{9}+3q^{11}+\cdots$
2240.2.a.z	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				280.2.a.a	$1$	$0$	$0$	$3$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-q^{5}+q^{7}+6q^{9}+5q^{11}+\cdots$
2240.2.a.ba	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				1120.2.a.a	$1$	$0$	$0$	$3$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}-q^{7}+6q^{9}+q^{11}+q^{13}+\cdots$
2240.2.a.bb	$2240$	$2$	2240.a	1.a	$1$	$1$	$1$	$17.886$	$\Q$	$_{}$	None	None	✓				140.2.a.b	$1$	$0$	$0$	$3$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}+q^{7}+6q^{9}-5q^{11}+\cdots$
2240.2.a.bc	$2240$	$2$	2240.a	1.a	$1$	$2$	$2$	$17.886$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				1120.2.a.r	$1$	$1$	$0$	$-1$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-q^{5}-q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots$
2240.2.a.bd	$2240$	$2$	2240.a	1.a	$1$	$2$	$2$	$17.886$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		✓		35.2.a.b	$1$	$1$	$0$	$-1$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-q^{5}+q^{7}+(1+\beta )q^{9}+\beta q^{11}+\cdots$

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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.