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 57 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
6000.2.a.a	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				750.2.a.d	$1$	$0$	$0$	$-2$	$0$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-3-\beta )q^{7}+q^{9}+(4-3\beta )q^{11}+\cdots$
6000.2.a.b	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				750.2.a.a	$1$	$1$	$0$	$-2$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-2-2\beta )q^{7}+q^{9}+(-1+3\beta )q^{11}+\cdots$
6000.2.a.c	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				1500.2.a.a	$1$	$1$	$0$	$-2$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta )q^{7}+q^{9}-q^{11}+(1+\cdots)q^{13}+\cdots$
6000.2.a.d	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				750.2.a.c	$1$	$0$	$0$	$-2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2\beta q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots$
6000.2.a.e	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				375.2.a.b	$1$	$0$	$0$	$-2$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta q^{7}+q^{9}+(-1-2\beta )q^{11}+\cdots$
6000.2.a.f	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				750.2.a.b	$1$	$1$	$0$	$-2$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta q^{7}+q^{9}+(1-\beta )q^{11}+(3+\cdots)q^{13}+\cdots$
6000.2.a.g	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				3000.2.a.a	$1$	$1$	$0$	$-2$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta q^{7}+q^{9}+3q^{11}-3q^{13}+\cdots$
6000.2.a.h	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				3000.2.a.b	$1$	$0$	$0$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}+2\beta q^{11}+(-4+2\beta )q^{13}+\cdots$
6000.2.a.i	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				1500.2.a.c	$1$	$1$	$0$	$-2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2\beta q^{7}+q^{9}+(-2+2\beta )q^{11}+\cdots$
6000.2.a.j	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				1500.2.a.b	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2\beta q^{7}+q^{9}+4q^{11}+(-2+\cdots)q^{13}+\cdots$
6000.2.a.k	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				3000.2.a.c	$1$	$1$	$0$	$-2$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}-2q^{11}+(-4+2\beta )q^{13}+\cdots$
6000.2.a.l	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				3000.2.a.d	$1$	$0$	$0$	$-2$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(3-\beta )q^{7}+q^{9}+q^{11}+(3-2\beta )q^{13}+\cdots$
6000.2.a.m	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				375.2.a.a	$1$	$1$	$0$	$-2$	$0$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(3-\beta )q^{7}+q^{9}+(3+2\beta )q^{11}+\cdots$
6000.2.a.n	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				1500.2.a.d	$1$	$0$	$0$	$-2$	$0$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(4-\beta )q^{7}+q^{9}+(-3+4\beta )q^{11}+\cdots$
6000.2.a.o	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				1500.2.a.d	$1$	$1$	$0$	$2$	$0$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-3-\beta )q^{7}+q^{9}+(1-4\beta )q^{11}+\cdots$
6000.2.a.p	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				3000.2.a.d	$1$	$1$	$0$	$2$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2-\beta )q^{7}+q^{9}+q^{11}+(-1+\cdots)q^{13}+\cdots$
6000.2.a.q	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				375.2.a.a	$1$	$0$	$0$	$2$	$0$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2-\beta )q^{7}+q^{9}+(5-2\beta )q^{11}+\cdots$
6000.2.a.r	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				3000.2.a.c	$1$	$1$	$0$	$2$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}+q^{9}-2q^{11}+(4-2\beta )q^{13}+\cdots$
6000.2.a.s	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				1500.2.a.c	$1$	$1$	$0$	$2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2\beta q^{7}+q^{9}+(-2+2\beta )q^{11}+\cdots$
6000.2.a.t	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				1500.2.a.b	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2\beta q^{7}+q^{9}+4q^{11}+(2-4\beta )q^{13}+\cdots$
6000.2.a.u	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				3000.2.a.b	$1$	$0$	$0$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}+2\beta q^{11}+(4-2\beta )q^{13}+\cdots$
6000.2.a.v	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				375.2.a.b	$1$	$1$	$0$	$2$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{7}+q^{9}+(-1-2\beta )q^{11}+\cdots$
6000.2.a.w	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				750.2.a.b	$1$	$1$	$0$	$2$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{7}+q^{9}+(1-\beta )q^{11}+(-3+\cdots)q^{13}+\cdots$
6000.2.a.x	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				3000.2.a.a	$1$	$0$	$0$	$2$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{7}+q^{9}+3q^{11}+3q^{13}+\cdots$
6000.2.a.y	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				750.2.a.c	$1$	$1$	$0$	$2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2\beta q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots$
6000.2.a.z	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				1500.2.a.a	$1$	$0$	$0$	$2$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{7}+q^{9}-q^{11}+(-1+\cdots)q^{13}+\cdots$
6000.2.a.ba	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				750.2.a.a	$1$	$0$	$0$	$2$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(2+2\beta )q^{7}+q^{9}+(-1+3\beta )q^{11}+\cdots$
6000.2.a.bb	$6000$	$2$	6000.a	1.a	$1$	$2$	$2$	$47.910$	$\Q(\sqrt{5})$	None	✓				750.2.a.d	$1$	$0$	$0$	$2$	$0$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(4-\beta )q^{7}+q^{9}+(1+3\beta )q^{11}+\cdots$
6000.2.a.bc	$6000$	$2$	6000.a	1.a	$1$	$4$	$4$	$47.910$	4.4.47025.1	None	✓				3000.2.a.j	$1$	$1$	$0$	$-4$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{1}+\beta _{2})q^{7}+q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
6000.2.a.bd	$6000$	$2$	6000.a	1.a	$1$	$4$	$4$	$47.910$	4.4.13025.1	None	✓				3000.2.a.i	$1$	$1$	$0$	$-4$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$
6000.2.a.be	$6000$	$2$	6000.a	1.a	$1$	$4$	$4$	$47.910$	4.4.36025.1	None	✓				3000.2.a.l	$1$	$0$	$0$	$-4$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{1}q^{7}+q^{9}+(1+2\beta _{2}+\beta _{3})q^{11}+\cdots$
6000.2.a.bf	$6000$	$2$	6000.a	1.a	$1$	$4$	$4$	$47.910$	4.4.13025.1	None	✓				3000.2.a.k	$1$	$0$	$0$	$-4$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta _{1}+\beta _{3})q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$
6000.2.a.bg	$6000$	$2$	6000.a	1.a	$1$	$4$	$4$	$47.910$	4.4.2525.1	None	✓		✓		375.2.a.e	$1$	$0$	$0$	$-4$	$0$	$4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{1})q^{7}+q^{9}+(-2-\beta _{2}+\cdots)q^{11}+\cdots$
6000.2.a.bh	$6000$	$2$	6000.a	1.a	$1$	$4$	$4$	$47.910$	4.4.2525.1	None	✓		✓		375.2.a.e	$1$	$0$	$0$	$4$	$0$	$-4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta _{1})q^{7}+q^{9}+(-2-\beta _{2}+\cdots)q^{11}+\cdots$
6000.2.a.bi	$6000$	$2$	6000.a	1.a	$1$	$4$	$4$	$47.910$	4.4.13025.1	None	✓				3000.2.a.k	$1$	$1$	$0$	$4$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{3})q^{7}+q^{9}+\cdots$
6000.2.a.bj	$6000$	$2$	6000.a	1.a	$1$	$4$	$4$	$47.910$	4.4.36025.1	None	✓				3000.2.a.l	$1$	$0$	$0$	$4$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{7}+q^{9}+(1+2\beta _{2}+\beta _{3})q^{11}+\cdots$
6000.2.a.bk	$6000$	$2$	6000.a	1.a	$1$	$4$	$4$	$47.910$	4.4.13025.1	None	✓				3000.2.a.i	$1$	$1$	$0$	$4$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{1})q^{7}+q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$
6000.2.a.bl	$6000$	$2$	6000.a	1.a	$1$	$4$	$4$	$47.910$	4.4.47025.1	None	✓				3000.2.a.j	$1$	$0$	$0$	$4$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta _{1}-\beta _{2})q^{7}+q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
6000.2.f.a	$6000$	$2$	6000.f	5.b	$2$	$4$	$4$	$47.910$	$\Q(i, \sqrt{5})$	None					750.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+2\beta _{1}q^{7}-q^{9}+(-2+\beta _{2}+\cdots)q^{11}+\cdots$
6000.2.f.b	$6000$	$2$	6000.f	5.b	$2$	$4$	$4$	$47.910$	$\Q(i, \sqrt{5})$	None					375.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+\beta _{1}q^{7}-q^{9}+(-1+2\beta _{2}+\cdots)q^{11}+\cdots$
6000.2.f.c	$6000$	$2$	6000.f	5.b	$2$	$4$	$4$	$47.910$	$\Q(i, \sqrt{5})$	None					3000.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+2\beta _{3}q^{7}-q^{9}-2q^{11}+(-2\beta _{1}+\cdots)q^{13}+\cdots$
6000.2.f.d	$6000$	$2$	6000.f	5.b	$2$	$4$	$4$	$47.910$	$\Q(i, \sqrt{5})$	None					1500.2.a.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(\beta _{1}+4\beta _{3})q^{7}-q^{9}+(-3+\cdots)q^{11}+\cdots$
6000.2.f.e	$6000$	$2$	6000.f	5.b	$2$	$4$	$4$	$47.910$	$\Q(i, \sqrt{5})$	None					1500.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(\beta _{1}-\beta _{3})q^{7}-q^{9}-q^{11}+\cdots$
6000.2.f.f	$6000$	$2$	6000.f	5.b	$2$	$4$	$4$	$47.910$	$\Q(i, \sqrt{5})$	None					1500.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+2\beta _{1}q^{7}-q^{9}+(-2-2\beta _{2}+\cdots)q^{11}+\cdots$
6000.2.f.g	$6000$	$2$	6000.f	5.b	$2$	$4$	$4$	$47.910$	$\Q(i, \sqrt{5})$	None					750.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(2\beta _{1}-2\beta _{3})q^{7}-q^{9}+(-1+\cdots)q^{11}+\cdots$
6000.2.f.h	$6000$	$2$	6000.f	5.b	$2$	$4$	$4$	$47.910$	$\Q(i, \sqrt{5})$	None					750.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+\beta _{1}q^{7}-q^{9}+(1+\beta _{2})q^{11}+\cdots$
6000.2.f.i	$6000$	$2$	6000.f	5.b	$2$	$4$	$4$	$47.910$	$\Q(i, \sqrt{5})$	None					3000.2.a.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(\beta _{1}+3\beta _{3})q^{7}-q^{9}+q^{11}+\cdots$
6000.2.f.j	$6000$	$2$	6000.f	5.b	$2$	$4$	$4$	$47.910$	$\Q(i, \sqrt{5})$	None					3000.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}-q^{9}+(2+2\beta _{2})q^{11}+(-2\beta _{1}+\cdots)q^{13}+\cdots$
6000.2.f.k	$6000$	$2$	6000.f	5.b	$2$	$4$	$4$	$47.910$	$\Q(i, \sqrt{5})$	None					750.2.a.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+(\beta _{1}+4\beta _{3})q^{7}-q^{9}+(1-3\beta _{2}+\cdots)q^{11}+\cdots$
6000.2.f.l	$6000$	$2$	6000.f	5.b	$2$	$4$	$4$	$47.910$	$\Q(i, \sqrt{5})$	None					3000.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+\beta _{1}q^{7}-q^{9}+3q^{11}+3\beta _{3}q^{13}+\cdots$

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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.