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 213 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
2160.1.c.a	$2160$	$1$	2160.c	15.d	$2$	$1$	$1$	$1.078$	$\Q$	$D_{3}$	$\Q(\sqrt{-15}) $	None	✓				135.1.d.a	$2$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-q^{5}+q^{17}+q^{19}-q^{23}+q^{25}+\cdots$
2160.1.c.b	$2160$	$1$	2160.c	15.d	$2$	$1$	$1$	$1.078$	$\Q$	$D_{3}$	$\Q(\sqrt{-15}) $	None	✓				135.1.d.a	$2$	$0$	$0$	$0$	$1$	$0$		$1$		$q+q^{5}-q^{17}+q^{19}+q^{23}+q^{25}+\cdots$
2160.1.c.c	$2160$	$1$	2160.c	15.d	$2$	$4$	$4$	$1.078$	$\Q(\zeta_{8})$	$S_{4}$	None	None			✓		1080.1.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{7}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots$
2160.1.r.a	$2160$	$1$	2160.r	80.k	$4$	$8$	$4$	$1.078$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-15}) $	None		✓	✓	✓	2160.1.r.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{3}q^{5}-\zeta_{24}^{3}q^{8}+\cdots$
2160.1.ba.a	$2160$	$1$	2160.ba	240.z	$4$	$4$	$2$	$1.078$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓	✓	✓	2160.1.ba.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}-\zeta_{8}q^{8}+\cdots$
2160.1.be.a	$2160$	$1$	2160.be	240.ad	$4$	$4$	$2$	$1.078$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓	✓	✓	2160.1.ba.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}-\zeta_{8}q^{8}+\cdots$
2160.1.bn.a	$2160$	$1$	2160.bn	240.am	$4$	$4$	$2$	$1.078$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			2160.1.bn.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}q^{5}+(-\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{7}+\cdots$
2160.1.bn.b	$2160$	$1$	2160.bn	240.am	$4$	$4$	$2$	$1.078$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			2160.1.bn.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}q^{5}+(\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots$
2160.1.bn.c	$2160$	$1$	2160.bn	240.am	$4$	$8$	$4$	$1.078$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-15}) $	None		✓	✓		2160.1.bn.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+\zeta_{24}^{3}q^{5}-\zeta_{24}^{3}q^{8}+\cdots$
2160.1.bu.a	$2160$	$1$	2160.bu	180.p	$6$	$4$	$2$	$1.078$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None			✓	✓	720.1.bu.a	$8$	$0$	$0$	$0$	$-2$	$0$		$3$		$q+\zeta_{12}^{4}q^{5}+(\zeta_{12}+\zeta_{12}^{3})q^{7}+(\zeta_{12}^{3}+\cdots)q^{23}+\cdots$
2160.1.dq.a	$2160$	$1$	2160.dq	540.af	$18$	$12$	$2$	$1.078$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-5}) $	None		✓	✓	✓	2160.1.dq.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{36}^{7}q^{3}-\zeta_{36}^{16}q^{5}+(-\zeta_{36}-\zeta_{36}^{15}+\cdots)q^{7}+\cdots$
2160.2.a.a	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				270.2.a.a	$1$	$0$	$0$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}-3q^{11}-q^{13}+3q^{17}+\cdots$
2160.2.a.b	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				270.2.a.b	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}-3q^{11}+5q^{13}-3q^{17}+\cdots$
2160.2.a.c	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				540.2.a.c	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+2q^{13}+3q^{17}-5q^{19}+\cdots$
2160.2.a.d	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				1080.2.a.f	$1$	$0$	$0$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+q^{11}+q^{13}+q^{17}+\cdots$
2160.2.a.e	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				1080.2.a.e	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+4q^{11}-2q^{13}-5q^{17}+\cdots$
2160.2.a.f	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				1080.2.a.d	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{11}-3q^{17}+q^{19}+3q^{23}+\cdots$
2160.2.a.g	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				1080.2.a.c	$1$	$1$	$0$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}-2q^{11}-5q^{13}+4q^{17}+\cdots$
2160.2.a.h	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				540.2.a.b	$1$	$0$	$0$	$0$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}+6q^{11}-q^{13}+q^{19}+\cdots$
2160.2.a.i	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				1080.2.a.b	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-6q^{13}+7q^{17}-7q^{19}+\cdots$
2160.2.a.j	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				135.2.a.a	$1$	$1$	$0$	$0$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+3q^{7}+2q^{11}-5q^{13}-8q^{17}+\cdots$
2160.2.a.k	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				540.2.a.a	$1$	$0$	$0$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}-6q^{11}-4q^{13}-3q^{17}+\cdots$
2160.2.a.l	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				1080.2.a.a	$1$	$0$	$0$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}-2q^{11}+4q^{13}+q^{17}+\cdots$
2160.2.a.m	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				1080.2.a.e	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-4q^{11}-2q^{13}+5q^{17}+\cdots$
2160.2.a.n	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				1080.2.a.f	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-q^{11}+q^{13}-q^{17}+\cdots$
2160.2.a.o	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				540.2.a.c	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}+2q^{13}-3q^{17}-5q^{19}+\cdots$
2160.2.a.p	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				270.2.a.a	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}+3q^{11}-q^{13}-3q^{17}+\cdots$
2160.2.a.q	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				270.2.a.b	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}+3q^{11}+5q^{13}+3q^{17}+\cdots$
2160.2.a.r	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				1080.2.a.d	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{11}+3q^{17}+q^{19}-3q^{23}+\cdots$
2160.2.a.s	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				540.2.a.b	$1$	$1$	$0$	$0$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}-6q^{11}-q^{13}+q^{19}+\cdots$
2160.2.a.t	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				1080.2.a.c	$1$	$0$	$0$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}+2q^{11}-5q^{13}-4q^{17}+\cdots$
2160.2.a.u	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				1080.2.a.b	$1$	$1$	$0$	$0$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-6q^{13}-7q^{17}-7q^{19}+\cdots$
2160.2.a.v	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				135.2.a.a	$1$	$0$	$0$	$0$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+3q^{7}-2q^{11}-5q^{13}+8q^{17}+\cdots$
2160.2.a.w	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				1080.2.a.a	$1$	$0$	$0$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{7}+2q^{11}+4q^{13}-q^{17}+\cdots$
2160.2.a.x	$2160$	$2$	2160.a	1.a	$1$	$1$	$1$	$17.248$	$\Q$	$_{}$	None	None	✓				540.2.a.a	$1$	$0$	$0$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{7}+6q^{11}-4q^{13}+3q^{17}+\cdots$
2160.2.a.y	$2160$	$2$	2160.a	1.a	$1$	$2$	$2$	$17.248$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓		✓		135.2.a.c	$1$	$0$	$0$	$0$	$-2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{5}+(-1-\beta )q^{7}+(1-\beta )q^{11}+(3+\cdots)q^{13}+\cdots$
2160.2.a.z	$2160$	$2$	2160.a	1.a	$1$	$2$	$2$	$17.248$	$\Q(\sqrt{73}) $	$_{}$	None	None	✓		✓		1080.2.a.m	$1$	$1$	$0$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-\beta q^{7}+(-1+\beta )q^{11}+3q^{13}+\cdots$
2160.2.a.ba	$2160$	$2$	2160.a	1.a	$1$	$2$	$2$	$17.248$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓		✓		135.2.a.c	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{5}+(-1-\beta )q^{7}+(-1+\beta )q^{11}+\cdots$
2160.2.a.bb	$2160$	$2$	2160.a	1.a	$1$	$2$	$2$	$17.248$	$\Q(\sqrt{73}) $	$_{}$	None	None	✓		✓		1080.2.a.m	$1$	$0$	$0$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-\beta q^{7}+(1-\beta )q^{11}+3q^{13}+\cdots$
2160.2.f.a	$2160$	$2$	2160.f	5.b	$2$	$2$	$2$	$17.248$	$\Q(\sqrt{-1}) $	$_{}$	None	None					540.2.d.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(i-2)q^{5}+2 i q^{7}-2 q^{11}-6 i q^{13}+\cdots$
2160.2.f.b	$2160$	$2$	2160.f	5.b	$2$	$2$	$2$	$17.248$	$\Q(\sqrt{-1}) $	$_{}$	None	None					1080.2.f.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-i-2)q^{5}+2 i q^{7}+2 q^{11}+\cdots$
2160.2.f.c	$2160$	$2$	2160.f	5.b	$2$	$2$	$2$	$17.248$	$\Q(\sqrt{-1}) $	$_{}$	None	None					1080.2.f.b	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2 i-1)q^{5}+4 i q^{7}+q^{11}-i q^{13}+\cdots$
2160.2.f.d	$2160$	$2$	2160.f	5.b	$2$	$2$	$2$	$17.248$	$\Q(\sqrt{-1}) $	$_{}$	None	None					270.2.c.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2 i-1)q^{5}+4 i q^{7}+5 q^{11}+\cdots$
2160.2.f.e	$2160$	$2$	2160.f	5.b	$2$	$2$	$2$	$17.248$	$\Q(\sqrt{-1}) $	$_{}$	None	None					270.2.c.a	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2 i+1)q^{5}+4 i q^{7}-5 q^{11}-3 i q^{13}+\cdots$
2160.2.f.f	$2160$	$2$	2160.f	5.b	$2$	$2$	$2$	$17.248$	$\Q(\sqrt{-1}) $	$_{}$	None	None					1080.2.f.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2 i+1)q^{5}+4 i q^{7}-q^{11}+\cdots$
2160.2.f.g	$2160$	$2$	2160.f	5.b	$2$	$2$	$2$	$17.248$	$\Q(\sqrt{-1}) $	$_{}$	None	None					1080.2.f.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(i+2)q^{5}+2 i q^{7}-2 q^{11}-2 i q^{13}+\cdots$
2160.2.f.h	$2160$	$2$	2160.f	5.b	$2$	$2$	$2$	$17.248$	$\Q(\sqrt{-1}) $	$_{}$	None	None					540.2.d.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-i+2)q^{5}+2 i q^{7}+2 q^{11}+\cdots$
2160.2.f.i	$2160$	$2$	2160.f	5.b	$2$	$4$	$4$	$17.248$	$\Q(i, \sqrt{6})$	$_{}$	None	None					1080.2.f.e	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+(-2+\cdots)q^{11}+\cdots$
2160.2.f.j	$2160$	$2$	2160.f	5.b	$2$	$4$	$4$	$17.248$	$\Q(i, \sqrt{5})$	$_{}$	$\Q(\sqrt{-15}) $	None					135.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{5}+(-\beta _{1}-2\beta _{2})q^{17}+(-2+\cdots)q^{19}+\cdots$
2160.2.f.k	$2160$	$2$	2160.f	5.b	$2$	$4$	$4$	$17.248$	$\Q(\zeta_{8})$	$_{}$	None	None					135.2.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{3} q^{5}+\beta_1 q^{7}+(2\beta_{3}-\beta_{2})q^{11}+\cdots$

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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.