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 149 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	5	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4800.2.a.a	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				600.2.a.e	$1$	$0$	$0$	$-1$	$0$	$-5$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-5q^{7}+q^{9}-6q^{11}-3q^{13}+\cdots$
4800.2.a.b	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				600.2.a.e	$1$	$0$	$0$	$-1$	$0$	$-5$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-5q^{7}+q^{9}+6q^{11}+3q^{13}+\cdots$
4800.2.a.c	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				480.2.f.c	$1$	$1$	$0$	$-1$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{7}+q^{9}-4q^{13}+8q^{19}+\cdots$
4800.2.a.d	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				30.2.a.a	$1$	$0$	$0$	$-1$	$0$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{7}+q^{9}+2q^{13}-6q^{17}+\cdots$
4800.2.a.e	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				480.2.f.c	$1$	$1$	$0$	$-1$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{7}+q^{9}+4q^{13}-8q^{19}+\cdots$
4800.2.a.f	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				96.2.a.a	$1$	$1$	$0$	$-1$	$0$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
4800.2.a.g	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				2400.2.a.k	$1$	$1$	$0$	$-1$	$0$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{7}+q^{9}-4q^{11}+7q^{13}+\cdots$
4800.2.a.h	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				2400.2.a.l	$1$	$0$	$0$	$-1$	$0$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{7}+q^{9}-5q^{13}+5q^{19}+\cdots$
4800.2.a.i	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				2400.2.a.l	$1$	$1$	$0$	$-1$	$0$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{7}+q^{9}+5q^{13}-5q^{19}+\cdots$
4800.2.a.j	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				2400.2.a.k	$1$	$0$	$0$	$-1$	$0$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{7}+q^{9}+4q^{11}-7q^{13}+\cdots$
4800.2.a.k	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				120.2.f.a	$1$	$0$	$0$	$-1$	$0$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
4800.2.a.l	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				30.2.c.a	$1$	$0$	$0$	$-1$	$0$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots$
4800.2.a.m	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				30.2.c.a	$1$	$1$	$0$	$-1$	$0$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots$
4800.2.a.n	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				120.2.f.a	$1$	$1$	$0$	$-1$	$0$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
4800.2.a.o	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				300.2.a.b	$1$	$0$	$0$	$-1$	$0$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-6q^{11}-5q^{13}+\cdots$
4800.2.a.p	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				300.2.a.b	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+6q^{11}+5q^{13}+\cdots$
4800.2.a.q	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				24.2.a.a	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}-4q^{11}-2q^{13}-2q^{17}+\cdots$
4800.2.a.r	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				120.2.a.b	$1$	$0$	$0$	$-1$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}-4q^{11}+6q^{13}+6q^{17}+\cdots$
4800.2.a.s	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				480.2.a.d	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}+2q^{13}-6q^{17}+4q^{19}+\cdots$
4800.2.a.t	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				15.2.a.a	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}+4q^{11}-2q^{13}-2q^{17}+\cdots$
4800.2.a.u	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				480.2.a.b	$1$	$0$	$0$	$-1$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}+4q^{11}+2q^{13}+2q^{17}+\cdots$
4800.2.a.v	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				2400.2.a.e	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-4q^{11}-3q^{13}+\cdots$
4800.2.a.w	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				2400.2.a.f	$1$	$1$	$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-q^{13}-3q^{19}-q^{21}+\cdots$
4800.2.a.x	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				2400.2.a.f	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+q^{13}+3q^{19}-q^{21}+\cdots$
4800.2.a.y	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				2400.2.a.e	$1$	$0$	$0$	$-1$	$0$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+4q^{11}+3q^{13}+\cdots$
4800.2.a.z	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				480.2.f.a	$1$	$1$	$0$	$-1$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots$
4800.2.a.ba	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				480.2.f.a	$1$	$1$	$0$	$-1$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}+6q^{11}+2q^{13}+\cdots$
4800.2.a.bb	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				75.2.a.a	$1$	$1$	$0$	$-1$	$0$	$3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{7}+q^{9}-2q^{11}+q^{13}+\cdots$
4800.2.a.bc	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				600.2.a.b	$1$	$0$	$0$	$-1$	$0$	$3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{7}+q^{9}-2q^{11}+3q^{13}+\cdots$
4800.2.a.bd	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				600.2.a.b	$1$	$0$	$0$	$-1$	$0$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{7}+q^{9}+2q^{11}-3q^{13}+\cdots$
4800.2.a.be	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				75.2.a.a	$1$	$1$	$0$	$-1$	$0$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{7}+q^{9}+2q^{11}-q^{13}+\cdots$
4800.2.a.bf	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				60.2.d.a	$1$	$1$	$0$	$-1$	$0$	$4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}+q^{9}-4q^{11}-4q^{17}+\cdots$
4800.2.a.bg	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				480.2.a.a	$1$	$1$	$0$	$-1$	$0$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots$
4800.2.a.bh	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				120.2.a.a	$1$	$0$	$0$	$-1$	$0$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots$
4800.2.a.bi	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				480.2.a.c	$1$	$0$	$0$	$-1$	$0$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}+q^{9}-2q^{13}+6q^{17}+\cdots$
4800.2.a.bj	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				60.2.d.a	$1$	$0$	$0$	$-1$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}+q^{9}+4q^{11}+4q^{17}+\cdots$
4800.2.a.bk	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				60.2.d.a	$1$	$0$	$0$	$1$	$0$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}+q^{9}-4q^{11}+4q^{17}+\cdots$
4800.2.a.bl	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				120.2.a.a	$1$	$0$	$0$	$1$	$0$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots$
4800.2.a.bm	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				480.2.a.c	$1$	$1$	$0$	$1$	$0$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}+q^{9}-2q^{13}+6q^{17}+\cdots$
4800.2.a.bn	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				60.2.d.a	$1$	$1$	$0$	$1$	$0$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}+q^{9}+4q^{11}-4q^{17}+\cdots$
4800.2.a.bo	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				480.2.a.a	$1$	$0$	$0$	$1$	$0$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots$
4800.2.a.bp	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				600.2.a.b	$1$	$0$	$0$	$1$	$0$	$-3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{7}+q^{9}-2q^{11}-3q^{13}+\cdots$
4800.2.a.bq	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				75.2.a.a	$1$	$1$	$0$	$1$	$0$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{7}+q^{9}-2q^{11}-q^{13}+\cdots$
4800.2.a.br	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				75.2.a.a	$1$	$1$	$0$	$1$	$0$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{7}+q^{9}+2q^{11}+q^{13}+\cdots$
4800.2.a.bs	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				600.2.a.b	$1$	$0$	$0$	$1$	$0$	$-3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{7}+q^{9}+2q^{11}+3q^{13}+\cdots$
4800.2.a.bt	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				480.2.f.a	$1$	$0$	$0$	$1$	$0$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots$
4800.2.a.bu	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				480.2.f.a	$1$	$0$	$0$	$1$	$0$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots$
4800.2.a.bv	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				2400.2.a.e	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-4q^{11}+3q^{13}+\cdots$
4800.2.a.bw	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				2400.2.a.f	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-q^{13}+3q^{19}-q^{21}+\cdots$
4800.2.a.bx	$4800$	$2$	4800.a	1.a	$1$	$1$	$1$	$38.328$	$\Q$	None	✓				2400.2.a.f	$1$	$1$	$0$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+q^{13}-3q^{19}-q^{21}+\cdots$

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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.