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 87 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$ -expansion
4080.2.a.a	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				1020.2.a.g	$1$	$1$	$0$	$-1$	$-1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-5q^{7}+q^{9}-3q^{11}+2q^{13}+\cdots$
4080.2.a.b	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				2040.2.a.l	$1$	$1$	$0$	$-1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}+2q^{13}+\cdots$
4080.2.a.c	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				510.2.a.f	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots$
4080.2.a.d	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				1020.2.a.f	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+2q^{11}+2q^{13}+\cdots$
4080.2.a.e	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				2040.2.a.k	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
4080.2.a.f	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				1020.2.a.e	$1$	$0$	$0$	$-1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}+q^{9}+3q^{11}-4q^{13}+\cdots$
4080.2.a.g	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				2040.2.a.j	$1$	$0$	$0$	$-1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}+q^{9}+5q^{11}+4q^{13}+\cdots$
4080.2.a.h	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				2040.2.a.i	$1$	$1$	$0$	$-1$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}-2q^{13}+\cdots$
4080.2.a.i	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				2040.2.a.h	$1$	$1$	$0$	$-1$	$-1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+4q^{7}+q^{9}+2q^{13}+q^{15}+\cdots$
4080.2.a.j	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				2040.2.a.q	$1$	$0$	$0$	$-1$	$1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-3q^{7}+q^{9}-5q^{11}-q^{15}+\cdots$
4080.2.a.k	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				2040.2.a.p	$1$	$1$	$0$	$-1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots$
4080.2.a.l	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				510.2.a.g	$1$	$1$	$0$	$-1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{7}+q^{9}-4q^{13}-q^{15}+\cdots$
4080.2.a.m	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				2040.2.a.o	$1$	$0$	$0$	$-1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}+q^{9}+3q^{11}-4q^{13}+\cdots$
4080.2.a.n	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				510.2.a.b	$1$	$0$	$0$	$-1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+2q^{7}+q^{9}-4q^{11}-q^{15}+\cdots$
4080.2.a.o	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				2040.2.a.n	$1$	$0$	$0$	$-1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+2q^{7}+q^{9}-q^{15}-q^{17}+\cdots$
4080.2.a.p	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				2040.2.a.m	$1$	$1$	$0$	$-1$	$1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+3q^{7}+q^{9}+q^{11}-6q^{13}+\cdots$
4080.2.a.q	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				1020.2.a.h	$1$	$0$	$0$	$-1$	$1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+5q^{7}+q^{9}+5q^{11}-q^{15}+\cdots$
4080.2.a.r	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				510.2.a.d	$1$	$1$	$0$	$1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{7}+q^{9}+4q^{13}-q^{15}+\cdots$
4080.2.a.s	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				510.2.a.a	$1$	$0$	$0$	$1$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots$
4080.2.a.t	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				2040.2.a.c	$1$	$0$	$0$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}-2q^{13}-q^{15}-q^{17}+\cdots$
4080.2.a.u	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				2040.2.a.b	$1$	$0$	$0$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots$
4080.2.a.v	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				1020.2.a.a	$1$	$1$	$0$	$1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots$
4080.2.a.w	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				2040.2.a.a	$1$	$0$	$0$	$1$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+3q^{7}+q^{9}-3q^{11}+4q^{13}+\cdots$
4080.2.a.x	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				510.2.a.c	$1$	$0$	$0$	$1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
4080.2.a.y	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				1020.2.a.d	$1$	$1$	$0$	$1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-3q^{7}+q^{9}-q^{11}-2q^{13}+\cdots$
4080.2.a.z	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				2040.2.a.g	$1$	$1$	$0$	$1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-3q^{7}+q^{9}+q^{11}-6q^{13}+\cdots$
4080.2.a.ba	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				510.2.a.e	$1$	$1$	$0$	$1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
4080.2.a.bb	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				2040.2.a.f	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}-2q^{13}+q^{15}+q^{17}+\cdots$
4080.2.a.bc	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				1020.2.a.c	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+6q^{11}+2q^{13}+\cdots$
4080.2.a.bd	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				1020.2.a.b	$1$	$0$	$0$	$1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+3q^{7}+q^{9}-3q^{11}-4q^{13}+\cdots$
4080.2.a.be	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				2040.2.a.e	$1$	$0$	$0$	$1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+3q^{7}+q^{9}+3q^{11}+4q^{13}+\cdots$
4080.2.a.bf	$4080$	$2$	4080.a	1.a	$1$	$1$	$1$	$32.579$	$\Q$	None	✓				2040.2.a.d	$1$	$0$	$0$	$1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
4080.2.a.bg	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	$\Q(\sqrt{17})$	None	✓		✓		2040.2.a.v	$1$	$0$	$0$	$-2$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+\beta q^{7}+q^{9}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
4080.2.a.bh	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	$\Q(\sqrt{33})$	None	✓		✓		1020.2.a.j	$1$	$1$	$0$	$-2$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots$
4080.2.a.bi	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	$\Q(\sqrt{33})$	None	✓		✓		2040.2.a.w	$1$	$1$	$0$	$-2$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-\beta q^{7}+q^{9}+\beta q^{11}-2q^{13}+\cdots$
4080.2.a.bj	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	$\Q(\sqrt{17})$	None	✓				2040.2.a.t	$1$	$1$	$0$	$2$	$-2$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+(-2-\beta )q^{7}+q^{9}-\beta q^{11}+\cdots$
4080.2.a.bk	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	$\Q(\sqrt{33})$	None	✓				1020.2.a.i	$1$	$0$	$0$	$2$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-\beta q^{7}+q^{9}+(2+\beta )q^{11}+\cdots$
4080.2.a.bl	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	$\Q(\sqrt{13})$	None	✓				255.2.a.a	$1$	$0$	$0$	$2$	$-2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-\beta q^{7}+q^{9}-5q^{11}+(-3+\cdots)q^{13}+\cdots$
4080.2.a.bm	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	$\Q(\sqrt{73})$	None	✓		✓		2040.2.a.s	$1$	$0$	$0$	$2$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots$
4080.2.a.bn	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	$\Q(\sqrt{17})$	None	✓				2040.2.a.r	$1$	$1$	$0$	$2$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+\beta q^{7}+q^{9}-\beta q^{11}-2q^{13}+\cdots$
4080.2.a.bo	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	$\Q(\sqrt{33})$	None	✓		✓		2040.2.a.u	$1$	$0$	$0$	$2$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots$
4080.2.a.bp	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	$\Q(\sqrt{5})$	None	✓				255.2.a.b	$1$	$0$	$0$	$2$	$2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-\beta q^{7}+q^{9}+(-1-2\beta )q^{11}+\cdots$
4080.2.a.bq	$4080$	$2$	4080.a	1.a	$1$	$2$	$2$	$32.579$	$\Q(\sqrt{6})$	None	✓				510.2.a.h	$1$	$0$	$0$	$2$	$2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+\beta q^{7}+q^{9}+(2+\beta )q^{13}+\cdots$
4080.2.a.br	$4080$	$2$	4080.a	1.a	$1$	$3$	$3$	$32.579$	3.3.229.1	None	✓		✓		255.2.a.c	$1$	$0$	$0$	$-3$	$3$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+(-1+\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
4080.2.a.bs	$4080$	$2$	4080.a	1.a	$1$	$3$	$3$	$32.579$	3.3.316.1	None	✓		✓		2040.2.a.x	$1$	$1$	$0$	$3$	$3$	$-3$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+(-1-\beta _{1})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
4080.2.a.bt	$4080$	$2$	4080.a	1.a	$1$	$4$	$4$	$32.579$	4.4.13768.1	None	✓		✓		255.2.a.d	$1$	$0$	$0$	$-4$	$-4$	$-4$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+(-1-\beta _{1})q^{7}+q^{9}-\beta _{3}q^{11}+\cdots$
4080.2.h.a	$4080$	$2$	4080.h	17.b	$2$	$2$	$2$	$32.579$	$\Q(\sqrt{-1})$	None					1020.2.e.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}-i q^{5}-q^{9}+2 i q^{11}-6 q^{13}+\cdots$
4080.2.h.b	$4080$	$2$	4080.h	17.b	$2$	$2$	$2$	$32.579$	$\Q(\sqrt{-1})$	None					2040.2.h.a	$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+i q^{5}+4 i q^{7}-q^{9}-4 i q^{11}+\cdots$
4080.2.h.c	$4080$	$2$	4080.h	17.b	$2$	$2$	$2$	$32.579$	$\Q(\sqrt{-1})$	None					2040.2.h.c	$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}-i q^{5}+4 i q^{7}-q^{9}-2 q^{13}+\cdots$
4080.2.h.d	$4080$	$2$	4080.h	17.b	$2$	$2$	$2$	$32.579$	$\Q(\sqrt{-1})$	None					2040.2.h.d	$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+i q^{5}+2 i q^{7}-q^{9}-2 q^{13}+\cdots$

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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.