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 215 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
3024.1.f.a	$3024$	$1$	3024.f	7.b	$2$	$2$	$2$	$1.509$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None					756.1.d.b	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(-\zeta_{6}+\cdots)q^{19}+\cdots$
3024.1.f.b	$3024$	$1$	3024.f	7.b	$2$	$2$	$2$	$1.509$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{21}) $					756.1.d.a	$4$	$0$	$0$	$0$	$0$	$2$		$2$		$q+(-\zeta_{6}-\zeta_{6}^{2})q^{5}+q^{7}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{17}+\cdots$
3024.1.o.a	$3024$	$1$	3024.o	84.h	$2$	$2$	$2$	$1.509$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-21}) $	None	✓	✓			3024.1.o.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\beta q^{5}-q^{7}-\beta q^{11}+q^{19}+\beta q^{23}+\cdots$
3024.1.o.b	$3024$	$1$	3024.o	84.h	$2$	$2$	$2$	$1.509$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3024.1.o.b	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{13}-q^{19}+\cdots$
3024.1.o.c	$3024$	$1$	3024.o	84.h	$2$	$2$	$2$	$1.509$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3024.1.o.b	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{13}+q^{19}+\cdots$
3024.1.o.d	$3024$	$1$	3024.o	84.h	$2$	$2$	$2$	$1.509$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-21}) $	None	✓	✓			3024.1.o.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\beta q^{5}+q^{7}+\beta q^{11}-q^{19}-\beta q^{23}+\cdots$
3024.1.bk.a	$3024$	$1$	3024.bk	84.j	$6$	$2$	$1$	$1.509$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3024.1.bk.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+\zeta_{6}q^{19}+\cdots$
3024.1.bk.b	$3024$	$1$	3024.bk	84.j	$6$	$2$	$1$	$1.509$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3024.1.bk.b	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{7}+\zeta_{6}q^{19}-\zeta_{6}^{2}q^{25}+\zeta_{6}^{2}q^{31}+\cdots$
3024.1.bk.c	$3024$	$1$	3024.bk	84.j	$6$	$2$	$1$	$1.509$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3024.1.bk.b	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{19}-\zeta_{6}^{2}q^{25}-\zeta_{6}^{2}q^{31}+\cdots$
3024.1.bk.d	$3024$	$1$	3024.bk	84.j	$6$	$2$	$1$	$1.509$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3024.1.bk.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}-\zeta_{6}q^{19}+\cdots$
3024.1.bw.a	$3024$	$1$	3024.bw	252.u	$6$	$4$	$2$	$1.509$	$\Q(\zeta_{12})$	$A_{4}$	None	None			✓	✓	1008.1.bw.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+\zeta_{12}q^{11}+\cdots$
3024.1.cd.a	$3024$	$1$	3024.cd	28.g	$6$	$2$	$1$	$1.509$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3024.1.cd.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-q^{7}+q^{13}+\zeta_{6}q^{25}+(1-\zeta_{6}^{2})q^{31}+\cdots$
3024.1.cd.b	$3024$	$1$	3024.cd	28.g	$6$	$2$	$1$	$1.509$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3024.1.cd.b	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q-\zeta_{6}q^{7}-q^{13}+(-1-\zeta_{6})q^{19}+\zeta_{6}q^{25}+\cdots$
3024.1.cd.c	$3024$	$1$	3024.cd	28.g	$6$	$2$	$1$	$1.509$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3024.1.cd.b	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q+\zeta_{6}q^{7}-q^{13}+(1+\zeta_{6})q^{19}+\zeta_{6}q^{25}+\cdots$
3024.1.cd.d	$3024$	$1$	3024.cd	28.g	$6$	$2$	$1$	$1.509$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			3024.1.cd.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+q^{7}+q^{13}+\zeta_{6}q^{25}+(-1+\zeta_{6}^{2}+\cdots)q^{31}+\cdots$
3024.1.cg.a	$3024$	$1$	3024.cg	7.d	$6$	$2$	$1$	$1.509$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None					756.1.z.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{7}+(-1+\zeta_{6}^{2})q^{19}+\zeta_{6}^{2}q^{25}+\cdots$
3024.1.cg.b	$3024$	$1$	3024.cg	7.d	$6$	$2$	$1$	$1.509$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None					189.1.m.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{25}+\cdots$
3024.1.dc.a	$3024$	$1$	3024.dc	21.h	$6$	$2$	$1$	$1.509$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					189.1.q.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-q^{7}-q^{13}-\zeta_{6}^{2}q^{19}-\zeta_{6}q^{25}+\cdots$
3024.1.dc.b	$3024$	$1$	3024.dc	21.h	$6$	$2$	$1$	$1.509$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None					756.1.bk.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q+\zeta_{6}q^{7}+q^{13}+\zeta_{6}^{2}q^{19}-\zeta_{6}q^{25}+\cdots$
3024.1.dc.c	$3024$	$1$	3024.dc	21.h	$6$	$4$	$2$	$1.509$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None			✓		1512.1.cu.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\beta _{1}q^{5}+\beta _{2}q^{7}+(\beta _{1}-\beta _{3})q^{17}+(1+\cdots)q^{19}+\cdots$
3024.1.dd.a	$3024$	$1$	3024.dd	252.al	$6$	$4$	$2$	$1.509$	$\Q(\zeta_{12})$	$A_{4}$	None	None			✓	✓	1008.1.bw.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$		$q+q^{5}+\zeta_{12}^{5}q^{7}-\zeta_{12}^{3}q^{11}+\zeta_{12}^{2}q^{13}+\cdots$
3024.1.eg.a	$3024$	$1$	3024.eg	336.at	$12$	$8$	$2$	$1.509$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓			3024.1.eg.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{7}q^{5}-\zeta_{24}^{6}q^{7}+\cdots$
3024.1.eg.b	$3024$	$1$	3024.eg	336.at	$12$	$8$	$2$	$1.509$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓			3024.1.eg.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{10}q^{7}+\cdots$
3024.2.a.a	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				378.2.a.a	$1$	$1$	$0$	$0$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+q^{7}-4q^{11}+3q^{13}+7q^{17}+\cdots$
3024.2.a.b	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				1512.2.a.a	$1$	$1$	$0$	$0$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+q^{7}+4q^{11}-q^{13}-3q^{17}+\cdots$
3024.2.a.c	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				378.2.a.b	$1$	$0$	$0$	$0$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-q^{7}-3q^{11}-4q^{13}-6q^{17}+\cdots$
3024.2.a.d	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				756.2.a.b	$1$	$1$	$0$	$0$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-q^{7}+2q^{13}-3q^{17}+4q^{19}+\cdots$
3024.2.a.e	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				756.2.a.a	$1$	$0$	$0$	$0$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-q^{7}+3q^{11}+2q^{13}+6q^{17}+\cdots$
3024.2.a.f	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				189.2.a.b	$1$	$0$	$0$	$0$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-q^{7}+6q^{11}-4q^{13}-3q^{17}+\cdots$
3024.2.a.g	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				1512.2.a.f	$1$	$1$	$0$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}-6q^{13}+7q^{17}+8q^{19}+\cdots$
3024.2.a.h	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				1512.2.a.e	$1$	$1$	$0$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}+3q^{11}-2q^{17}-q^{19}+\cdots$
3024.2.a.i	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				1512.2.a.d	$1$	$0$	$0$	$0$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}-2q^{11}-4q^{13}+3q^{17}+\cdots$
3024.2.a.j	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				1512.2.a.c	$1$	$1$	$0$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}+q^{11}-4q^{13}+6q^{17}+\cdots$
3024.2.a.k	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				756.2.a.c	$1$	$1$	$0$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}+2q^{11}-5q^{17}-2q^{19}+\cdots$
3024.2.a.l	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				189.2.a.a	$1$	$0$	$0$	$0$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}+4q^{11}-2q^{13}+3q^{17}+\cdots$
3024.2.a.m	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				378.2.a.c	$1$	$0$	$0$	$0$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}+5q^{11}-2q^{17}+q^{19}+\cdots$
3024.2.a.n	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				1512.2.a.b	$1$	$0$	$0$	$0$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}+6q^{11}+4q^{13}+3q^{17}+\cdots$
3024.2.a.o	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				378.2.a.d	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+5q^{13}-3q^{17}-2q^{19}-9q^{23}+\cdots$
3024.2.a.p	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				378.2.a.d	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+5q^{13}+3q^{17}-2q^{19}+9q^{23}+\cdots$
3024.2.a.q	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				1512.2.a.e	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}-3q^{11}+2q^{17}-q^{19}+\cdots$
3024.2.a.r	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				1512.2.a.f	$1$	$0$	$0$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}-6q^{13}-7q^{17}+8q^{19}+\cdots$
3024.2.a.s	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				1512.2.a.b	$1$	$1$	$0$	$0$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}-6q^{11}+4q^{13}-3q^{17}+\cdots$
3024.2.a.t	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				378.2.a.c	$1$	$0$	$0$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}-5q^{11}+2q^{17}+q^{19}+\cdots$
3024.2.a.u	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				189.2.a.a	$1$	$1$	$0$	$0$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}-4q^{11}-2q^{13}-3q^{17}+\cdots$
3024.2.a.v	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				756.2.a.c	$1$	$0$	$0$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}-2q^{11}+5q^{17}-2q^{19}+\cdots$
3024.2.a.w	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				1512.2.a.c	$1$	$1$	$0$	$0$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}-q^{11}-4q^{13}-6q^{17}+\cdots$
3024.2.a.x	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				1512.2.a.d	$1$	$1$	$0$	$0$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}+2q^{11}-4q^{13}-3q^{17}+\cdots$
3024.2.a.y	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				189.2.a.b	$1$	$1$	$0$	$0$	$3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-q^{7}-6q^{11}-4q^{13}+3q^{17}+\cdots$
3024.2.a.z	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				756.2.a.a	$1$	$0$	$0$	$0$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-q^{7}-3q^{11}+2q^{13}-6q^{17}+\cdots$
3024.2.a.ba	$3024$	$2$	3024.a	1.a	$1$	$1$	$1$	$24.147$	$\Q$	$_{}$	None	None	✓				756.2.a.b	$1$	$0$	$0$	$0$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-q^{7}+2q^{13}+3q^{17}+4q^{19}+\cdots$

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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.