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 96 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
1850.2.a.a	$1850$	$2$	1850.a	1.a	$1$	$1$	$1$	$14.772$	$\Q$	None	✓	✓			1850.2.a.a	$1$	$1$	$-1$	$-2$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}-4q^{7}-q^{8}+\cdots$
1850.2.a.b	$1850$	$2$	1850.a	1.a	$1$	$1$	$1$	$14.772$	$\Q$	None	✓	✓			1850.2.a.b	$1$	$1$	$-1$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots$
1850.2.a.c	$1850$	$2$	1850.a	1.a	$1$	$1$	$1$	$14.772$	$\Q$	None	✓	✓			1850.2.a.c	$1$	$0$	$-1$	$-1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots$
1850.2.a.d	$1850$	$2$	1850.a	1.a	$1$	$1$	$1$	$14.772$	$\Q$	None	✓				370.2.b.b	$1$	$1$	$-1$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{9}-3q^{11}+\cdots$
1850.2.a.e	$1850$	$2$	1850.a	1.a	$1$	$1$	$1$	$14.772$	$\Q$	None	✓				370.2.b.a	$1$	$1$	$-1$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{7}-q^{8}-3q^{9}-2q^{13}+\cdots$
1850.2.a.f	$1850$	$2$	1850.a	1.a	$1$	$1$	$1$	$14.772$	$\Q$	None	✓				370.2.a.d	$1$	$1$	$-1$	$2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-2q^{7}-q^{8}+\cdots$
1850.2.a.g	$1850$	$2$	1850.a	1.a	$1$	$1$	$1$	$14.772$	$\Q$	None	✓	✓			1850.2.a.g	$1$	$0$	$-1$	$3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-3q^{6}-q^{8}+6q^{9}+\cdots$
1850.2.a.h	$1850$	$2$	1850.a	1.a	$1$	$1$	$1$	$14.772$	$\Q$	None	✓	✓			1850.2.a.g	$1$	$1$	$1$	$-3$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}-3q^{6}+q^{8}+6q^{9}+\cdots$
1850.2.a.i	$1850$	$2$	1850.a	1.a	$1$	$1$	$1$	$14.772$	$\Q$	None	✓				370.2.a.c	$1$	$1$	$1$	$-2$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots$
1850.2.a.j	$1850$	$2$	1850.a	1.a	$1$	$1$	$1$	$14.772$	$\Q$	None	✓				370.2.b.a	$1$	$1$	$1$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}-3q^{9}+2q^{13}+\cdots$
1850.2.a.k	$1850$	$2$	1850.a	1.a	$1$	$1$	$1$	$14.772$	$\Q$	None	✓				370.2.a.b	$1$	$1$	$1$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-3q^{9}-4q^{11}-2q^{13}+\cdots$
1850.2.a.l	$1850$	$2$	1850.a	1.a	$1$	$1$	$1$	$14.772$	$\Q$	None	✓				370.2.b.b	$1$	$1$	$1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}-3q^{11}+\cdots$
1850.2.a.m	$1850$	$2$	1850.a	1.a	$1$	$1$	$1$	$14.772$	$\Q$	None	✓	✓			1850.2.a.c	$1$	$1$	$1$	$1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots$
1850.2.a.n	$1850$	$2$	1850.a	1.a	$1$	$1$	$1$	$14.772$	$\Q$	None	✓	✓			1850.2.a.b	$1$	$0$	$1$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{8}+q^{9}+\cdots$
1850.2.a.o	$1850$	$2$	1850.a	1.a	$1$	$1$	$1$	$14.772$	$\Q$	None	✓				370.2.a.a	$1$	$0$	$1$	$2$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{7}+q^{8}+\cdots$
1850.2.a.p	$1850$	$2$	1850.a	1.a	$1$	$1$	$1$	$14.772$	$\Q$	None	✓	✓			1850.2.a.a	$1$	$0$	$1$	$2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}+4q^{7}+q^{8}+\cdots$
1850.2.a.q	$1850$	$2$	1850.a	1.a	$1$	$2$	$2$	$14.772$	$\Q(\sqrt{33}) $	None	✓				370.2.a.f	$1$	$1$	$-2$	$-4$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}+(1+\beta )q^{7}+\cdots$
1850.2.a.r	$1850$	$2$	1850.a	1.a	$1$	$2$	$2$	$14.772$	$\Q(\sqrt{6}) $	None	✓	✓	✓		1850.2.a.r	$1$	$1$	$-2$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta )q^{3}+q^{4}+(1-\beta )q^{6}+\cdots$
1850.2.a.s	$1850$	$2$	1850.a	1.a	$1$	$2$	$2$	$14.772$	$\Q(\sqrt{6}) $	None	✓				370.2.b.c	$1$	$0$	$-2$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+(-2-\beta )q^{7}+\cdots$
1850.2.a.t	$1850$	$2$	1850.a	1.a	$1$	$2$	$2$	$14.772$	$\Q(\sqrt{5}) $	None	✓				74.2.a.b	$1$	$0$	$-2$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+2\beta q^{7}+\cdots$
1850.2.a.u	$1850$	$2$	1850.a	1.a	$1$	$2$	$2$	$14.772$	$\Q(\sqrt{13}) $	None	✓				74.2.a.a	$1$	$0$	$2$	$-3$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots$
1850.2.a.v	$1850$	$2$	1850.a	1.a	$1$	$2$	$2$	$14.772$	$\Q(\sqrt{6}) $	None	✓				370.2.b.c	$1$	$0$	$2$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+(2-\beta )q^{7}+\cdots$
1850.2.a.w	$1850$	$2$	1850.a	1.a	$1$	$2$	$2$	$14.772$	$\Q(\sqrt{6}) $	None	✓	✓			1850.2.a.r	$1$	$0$	$2$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
1850.2.a.x	$1850$	$2$	1850.a	1.a	$1$	$2$	$2$	$14.772$	$\Q(\sqrt{3}) $	None	✓				370.2.a.e	$1$	$0$	$2$	$2$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
1850.2.a.y	$1850$	$2$	1850.a	1.a	$1$	$3$	$3$	$14.772$	3.3.1524.1	None	✓	✓	✓		1850.2.a.y	$1$	$1$	$-3$	$-1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots$
1850.2.a.z	$1850$	$2$	1850.a	1.a	$1$	$3$	$3$	$14.772$	3.3.892.1	None	✓				370.2.a.g	$1$	$0$	$-3$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{2}q^{6}+\beta _{1}q^{7}+\cdots$
1850.2.a.ba	$1850$	$2$	1850.a	1.a	$1$	$3$	$3$	$14.772$	3.3.148.1	None	✓	✓			1850.2.a.ba	$1$	$0$	$-3$	$3$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta _{2})q^{3}+q^{4}+(-1-\beta _{2})q^{6}+\cdots$
1850.2.a.bb	$1850$	$2$	1850.a	1.a	$1$	$3$	$3$	$14.772$	3.3.148.1	None	✓	✓	✓		1850.2.a.ba	$1$	$1$	$3$	$-3$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(-1-\beta _{2})q^{6}+\cdots$
1850.2.a.bc	$1850$	$2$	1850.a	1.a	$1$	$3$	$3$	$14.772$	3.3.1524.1	None	✓	✓			1850.2.a.y	$1$	$0$	$3$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
1850.2.a.bd	$1850$	$2$	1850.a	1.a	$1$	$5$	$5$	$14.772$	5.5.1791440.1	None	✓		✓		370.2.b.d	$1$	$0$	$-5$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
1850.2.a.be	$1850$	$2$	1850.a	1.a	$1$	$5$	$5$	$14.772$	5.5.1791440.1	None	✓		✓		370.2.b.d	$1$	$0$	$5$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots$
1850.2.b.a	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	$\Q(\sqrt{-1}) $	None		✓			1850.2.a.g	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+3 i q^{3}-q^{4}-3 q^{6}-i q^{8}+\cdots$
1850.2.b.b	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	$\Q(\sqrt{-1}) $	None					370.2.a.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+2 i q^{3}-q^{4}-2 q^{6}+2 i q^{7}+\cdots$
1850.2.b.c	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	$\Q(\sqrt{-1}) $	None					370.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+2 i q^{3}-q^{4}-2 q^{6}-i q^{7}+\cdots$
1850.2.b.d	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	$\Q(\sqrt{-1}) $	None					370.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+i q^{8}+3 q^{9}-4 q^{11}+\cdots$
1850.2.b.e	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	$\Q(\sqrt{-1}) $	None		✓			1850.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+i q^{3}-q^{4}+q^{6}+4 i q^{7}+\cdots$
1850.2.b.f	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	$\Q(\sqrt{-1}) $	None		✓			1850.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+2 i q^{3}-q^{4}+2 q^{6}-4 i q^{7}+\cdots$
1850.2.b.g	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	$\Q(\sqrt{-1}) $	None					370.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+2 i q^{3}-q^{4}+2 q^{6}-i q^{7}+\cdots$
1850.2.b.h	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	$\Q(\sqrt{-1}) $	None		✓			1850.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+2 i q^{3}-q^{4}+2 q^{6}+i q^{8}+\cdots$
1850.2.b.i	$1850$	$2$	1850.b	5.b	$2$	$4$	$4$	$14.772$	$\Q(i, \sqrt{13})$	None					74.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-q^{4}+(-2+\cdots)q^{6}+\cdots$
1850.2.b.j	$1850$	$2$	1850.b	5.b	$2$	$4$	$4$	$14.772$	$\Q(i, \sqrt{5})$	None					74.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{2}q^{6}-2\beta _{1}q^{7}+\cdots$
1850.2.b.k	$1850$	$2$	1850.b	5.b	$2$	$4$	$4$	$14.772$	$\Q(i, \sqrt{6})$	None		✓			1850.2.a.r	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}-q^{4}+(1+\beta _{3})q^{6}+\cdots$
1850.2.b.l	$1850$	$2$	1850.b	5.b	$2$	$4$	$4$	$14.772$	$\Q(\zeta_{12})$	None					370.2.a.e	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{2}+(-\beta_{2}+\beta_1)q^{3}-q^{4}+\cdots$
1850.2.b.m	$1850$	$2$	1850.b	5.b	$2$	$4$	$4$	$14.772$	$\Q(i, \sqrt{33})$	None					370.2.a.f	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+2\beta _{2}q^{3}-q^{4}+2q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots$
1850.2.b.n	$1850$	$2$	1850.b	5.b	$2$	$6$	$6$	$14.772$	6.0.350464.1	None		✓			1850.2.a.ba	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(\beta _{3}-\beta _{5})q^{3}-q^{4}+(-1+\cdots)q^{6}+\cdots$
1850.2.b.o	$1850$	$2$	1850.b	5.b	$2$	$6$	$6$	$14.772$	6.0.3182656.1	None					370.2.a.g	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}-\beta _{3}q^{3}-q^{4}+\beta _{2}q^{6}-\beta _{5}q^{7}+\cdots$
1850.2.b.p	$1850$	$2$	1850.b	5.b	$2$	$6$	$6$	$14.772$	6.0.37161216.1	None		✓			1850.2.a.y	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{2}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots$
1850.2.c.a	$1850$	$2$	1850.c	185.d	$2$	$2$	$2$	$14.772$	$\Q(\sqrt{-1}) $	None					370.2.d.a	$2$	$1$	$-2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+\beta q^{7}-q^{8}+3 q^{9}+\cdots$
1850.2.c.b	$1850$	$2$	1850.c	185.d	$2$	$2$	$2$	$14.772$	$\Q(\sqrt{-1}) $	None					370.2.d.b	$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+5 i q^{7}-q^{8}+3 q^{9}+\cdots$
1850.2.c.c	$1850$	$2$	1850.c	185.d	$2$	$2$	$2$	$14.772$	$\Q(\sqrt{-1}) $	None		✓			1850.2.d.b	$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}-2 i q^{7}-q^{8}+3 q^{9}+\cdots$

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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.