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 121 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
3120.1.be.a	$3120$	$1$	3120.be	195.e	$2$	$1$	$1$	$1.557$	$\Q$	$D_{3}$	$\Q(\sqrt{-195}) $	None	✓				780.1.o.a	$2$	$0$	$0$	$-1$	$-1$	$-1$		$1$		$q-q^{3}-q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
3120.1.be.b	$3120$	$1$	3120.be	195.e	$2$	$1$	$1$	$1.557$	$\Q$	$D_{3}$	$\Q(\sqrt{-195}) $	None	✓				780.1.o.a	$2$	$0$	$0$	$-1$	$1$	$1$		$1$		$q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+q^{13}+\cdots$
3120.1.be.c	$3120$	$1$	3120.be	195.e	$2$	$1$	$1$	$1.557$	$\Q$	$D_{3}$	$\Q(\sqrt{-195}) $	None	✓				780.1.o.a	$2$	$0$	$0$	$1$	$-1$	$1$		$1$		$q+q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
3120.1.be.d	$3120$	$1$	3120.be	195.e	$2$	$1$	$1$	$1.557$	$\Q$	$D_{3}$	$\Q(\sqrt{-195}) $	None	✓				780.1.o.a	$2$	$0$	$0$	$1$	$1$	$-1$		$1$		$q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
3120.1.be.e	$3120$	$1$	3120.be	195.e	$2$	$4$	$4$	$1.557$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None			✓		195.1.e.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{3}+\zeta_{8}^{3}q^{5}-q^{9}+(-\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{11}+\cdots$
3120.1.bu.a	$3120$	$1$	3120.bu	195.j	$4$	$4$	$2$	$1.557$	$\Q(\zeta_{8})$	$S_{4}$	None	None			✓	✓	780.1.t.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{3}-\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{7}-\zeta_{8}^{2}q^{9}+\cdots$
3120.1.bx.a	$3120$	$1$	3120.bx	3120.ax	$4$	$8$	$4$	$1.557$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		✓			3120.1.bx.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{2}q^{3}+\zeta_{16}^{6}q^{4}+\cdots$
3120.1.bx.b	$3120$	$1$	3120.bx	3120.ax	$4$	$8$	$4$	$1.557$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		✓			3120.1.bx.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{3}q^{2}-\zeta_{16}^{2}q^{3}+\zeta_{16}^{6}q^{4}+\cdots$
3120.1.dl.a	$3120$	$1$	3120.dl	3120.cl	$4$	$2$	$1$	$1.557$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			3120.1.dl.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+iq^{3}+q^{4}-iq^{5}-iq^{6}-q^{8}+\cdots$
3120.1.dl.b	$3120$	$1$	3120.dl	3120.cl	$4$	$2$	$1$	$1.557$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			3120.1.dl.b	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+iq^{2}-iq^{3}-q^{4}-q^{5}+q^{6}-iq^{8}+\cdots$
3120.1.dl.c	$3120$	$1$	3120.dl	3120.cl	$4$	$2$	$1$	$1.557$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			3120.1.dl.b	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-iq^{2}-iq^{3}-q^{4}+q^{5}-q^{6}+iq^{8}+\cdots$
3120.1.dl.d	$3120$	$1$	3120.dl	3120.cl	$4$	$2$	$1$	$1.557$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			3120.1.dl.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+iq^{3}+q^{4}+iq^{5}+iq^{6}+q^{8}+\cdots$
3120.1.dl.e	$3120$	$1$	3120.dl	3120.cl	$4$	$4$	$2$	$1.557$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			3120.1.dl.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+\cdots$
3120.1.dl.f	$3120$	$1$	3120.dl	3120.cl	$4$	$4$	$2$	$1.557$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			3120.1.dl.f	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{3}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\cdots$
3120.1.dq.a	$3120$	$1$	3120.dq	3120.cq	$4$	$2$	$1$	$1.557$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			3120.1.dl.b	$4$	$0$	$-2$	$-2$	$0$	$0$		$1$		$q-q^{2}-q^{3}+q^{4}+iq^{5}+q^{6}-q^{8}+\cdots$
3120.1.dq.b	$3120$	$1$	3120.dq	3120.cq	$4$	$2$	$1$	$1.557$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			3120.1.dl.a	$4$	$0$	$0$	$2$	$-2$	$0$		$1$		$q+iq^{2}+q^{3}-q^{4}-q^{5}+iq^{6}-iq^{8}+\cdots$
3120.1.dq.c	$3120$	$1$	3120.dq	3120.cq	$4$	$2$	$1$	$1.557$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			3120.1.dl.a	$4$	$0$	$0$	$2$	$2$	$0$		$1$		$q-iq^{2}+q^{3}-q^{4}+q^{5}-iq^{6}+iq^{8}+\cdots$
3120.1.dq.d	$3120$	$1$	3120.dq	3120.cq	$4$	$2$	$1$	$1.557$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			3120.1.dl.b	$4$	$0$	$2$	$-2$	$0$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}-iq^{5}-q^{6}+q^{8}+\cdots$
3120.1.dq.e	$3120$	$1$	3120.dq	3120.cq	$4$	$4$	$2$	$1.557$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			3120.1.dl.e	$8$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}-q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}+\cdots$
3120.1.dq.f	$3120$	$1$	3120.dq	3120.cq	$4$	$4$	$2$	$1.557$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		✓			3120.1.dl.f	$8$	$0$	$0$	$4$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}+q^{3}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}+\cdots$
3120.1.ff.a	$3120$	$1$	3120.ff	195.u	$4$	$4$	$2$	$1.557$	$\Q(\zeta_{8})$	$S_{4}$	None	None			✓	✓	780.1.t.a	$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{5}-q^{7}+\zeta_{8}^{2}q^{9}+\cdots$
3120.1.iq.a	$3120$	$1$	3120.iq	3120.hq	$12$	$8$	$2$	$1.557$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	3120.1.iq.a	$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{24}q^{2}-\zeta_{24}^{10}q^{3}+\zeta_{24}^{2}q^{4}+\cdots$
3120.1.iv.a	$3120$	$1$	3120.iv	3120.hv	$12$	$8$	$2$	$1.557$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	3120.1.iq.a	$8$	$0$	$0$	$-4$	$0$	$4$		$1$		$q-\zeta_{24}q^{2}-\zeta_{24}^{4}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{9}q^{5}+\cdots$
3120.2.a.a	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				390.2.a.c	$1$	$0$	$0$	$-1$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-4q^{7}+q^{9}-q^{13}+q^{15}+\cdots$
3120.2.a.b	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				390.2.a.g	$1$	$1$	$0$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{7}+q^{9}+q^{13}+q^{15}+\cdots$
3120.2.a.c	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓		✓	✓	1560.2.a.i	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}-q^{13}+q^{15}+2q^{17}+\cdots$
3120.2.a.d	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				195.2.a.c	$1$	$0$	$0$	$-1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}+q^{9}-5q^{11}-q^{13}+\cdots$
3120.2.a.e	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				780.2.a.d	$1$	$1$	$0$	$-1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}+q^{9}-3q^{11}+q^{13}+\cdots$
3120.2.a.f	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				1560.2.a.h	$1$	$0$	$0$	$-1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}+q^{9}+5q^{11}+q^{13}+\cdots$
3120.2.a.g	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				780.2.a.c	$1$	$0$	$0$	$-1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}+q^{9}+6q^{11}-q^{13}+\cdots$
3120.2.a.h	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				1560.2.a.g	$1$	$0$	$0$	$-1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+4q^{7}+q^{9}-4q^{11}+q^{13}+\cdots$
3120.2.a.i	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				1560.2.a.l	$1$	$1$	$0$	$-1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-4q^{7}+q^{9}+q^{13}-q^{15}+\cdots$
3120.2.a.j	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				390.2.a.d	$1$	$0$	$0$	$-1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{7}+q^{9}+q^{13}-q^{15}+\cdots$
3120.2.a.k	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				195.2.a.a	$1$	$0$	$0$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-4q^{11}+q^{13}-q^{15}+\cdots$
3120.2.a.l	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				1560.2.a.k	$1$	$1$	$0$	$-1$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+2q^{7}+q^{9}+q^{13}-q^{15}+\cdots$
3120.2.a.m	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				1560.2.a.j	$1$	$0$	$0$	$-1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+3q^{7}+q^{9}+3q^{11}-q^{13}+\cdots$
3120.2.a.n	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				195.2.a.d	$1$	$0$	$0$	$-1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+3q^{7}+q^{9}+5q^{11}+q^{13}+\cdots$
3120.2.a.o	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				390.2.a.e	$1$	$1$	$0$	$1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{7}+q^{9}-4q^{11}-q^{13}+\cdots$
3120.2.a.p	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				1560.2.a.b	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}-4q^{11}+q^{13}-q^{15}+\cdots$
3120.2.a.q	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				390.2.a.a	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}-q^{13}-q^{15}-6q^{17}+\cdots$
3120.2.a.r	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				1560.2.a.a	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}+q^{13}-q^{15}-6q^{17}+\cdots$
3120.2.a.s	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				1560.2.a.f	$1$	$0$	$0$	$1$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-4q^{7}+q^{9}-4q^{11}+q^{13}+\cdots$
3120.2.a.t	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				780.2.a.b	$1$	$1$	$0$	$1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-3q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
3120.2.a.u	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				195.2.a.b	$1$	$0$	$0$	$1$	$1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-3q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
3120.2.a.v	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓		✓	✓	1560.2.a.e	$1$	$1$	$0$	$1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{7}+q^{9}-4q^{11}-q^{13}+\cdots$
3120.2.a.w	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				390.2.a.f	$1$	$1$	$0$	$1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}-4q^{11}+q^{13}+q^{15}+\cdots$
3120.2.a.x	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				1560.2.a.d	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+4q^{11}+q^{13}+q^{15}+\cdots$
3120.2.a.y	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				390.2.a.b	$1$	$0$	$0$	$1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+2q^{7}+q^{9}-4q^{11}-q^{13}+\cdots$
3120.2.a.z	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				780.2.a.a	$1$	$0$	$0$	$1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}-q^{13}+\cdots$
3120.2.a.ba	$3120$	$2$	3120.a	1.a	$1$	$1$	$1$	$24.913$	$\Q$	$_{}$	None	None	✓				1560.2.a.c	$1$	$0$	$0$	$1$	$1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+5q^{7}+q^{9}-q^{11}+q^{13}+\cdots$

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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.