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 213 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
1638.2.a.a	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓				546.2.a.e	$1$	$0$	$-1$	$0$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}-q^{7}-q^{8}+3q^{10}+\cdots$
1638.2.a.b	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓	✓			1638.2.a.b	$1$	$1$	$-1$	$0$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots$
1638.2.a.c	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓				182.2.a.c	$1$	$0$	$-1$	$0$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots$
1638.2.a.d	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓				546.2.a.g	$1$	$1$	$-1$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}+2q^{10}+\cdots$
1638.2.a.e	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓	✓			1638.2.a.e	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}+q^{13}-q^{14}+\cdots$
1638.2.a.f	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓				182.2.a.d	$1$	$0$	$-1$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}+q^{13}+\cdots$
1638.2.a.g	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓	✓	✓	✓	1638.2.a.g	$1$	$0$	$-1$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
1638.2.a.h	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓				546.2.a.f	$1$	$1$	$-1$	$0$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots$
1638.2.a.i	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓	✓	✓	✓	1638.2.a.i	$1$	$0$	$-1$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots$
1638.2.a.j	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓				182.2.a.e	$1$	$0$	$-1$	$0$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}-q^{7}-q^{8}-4q^{10}+\cdots$
1638.2.a.k	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓				182.2.a.a	$1$	$0$	$1$	$0$	$-4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{5}-q^{7}+q^{8}-4q^{10}+\cdots$
1638.2.a.l	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓		✓	✓	546.2.a.d	$1$	$1$	$1$	$0$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots$
1638.2.a.m	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓	✓	✓	✓	1638.2.a.i	$1$	$1$	$1$	$0$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots$
1638.2.a.n	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓	✓	✓	✓	1638.2.a.g	$1$	$1$	$1$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots$
1638.2.a.o	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓		✓	✓	546.2.a.c	$1$	$1$	$1$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots$
1638.2.a.p	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓	✓			1638.2.a.e	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}+q^{13}+q^{14}+\cdots$
1638.2.a.q	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓				182.2.a.b	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{11}-q^{13}+\cdots$
1638.2.a.r	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓				546.2.a.a	$1$	$0$	$1$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
1638.2.a.s	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓				546.2.a.b	$1$	$0$	$1$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots$
1638.2.a.t	$1638$	$2$	1638.a	1.a	$1$	$1$	$1$	$13.079$	$\Q$	None	✓	✓			1638.2.a.b	$1$	$0$	$1$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots$
1638.2.a.u	$1638$	$2$	1638.a	1.a	$1$	$2$	$2$	$13.079$	$\Q(\sqrt{17})$	None	✓		✓	✓	546.2.a.j	$1$	$1$	$-2$	$0$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta )q^{5}-q^{7}-q^{8}+\cdots$
1638.2.a.v	$1638$	$2$	1638.a	1.a	$1$	$2$	$2$	$13.079$	$\Q(\sqrt{33})$	None	✓	✓	✓	✓	1638.2.a.v	$1$	$1$	$-2$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta q^{5}-q^{7}-q^{8}+\beta q^{10}+\cdots$
1638.2.a.w	$1638$	$2$	1638.a	1.a	$1$	$2$	$2$	$13.079$	$\Q(\sqrt{41})$	None	✓		✓		546.2.a.i	$1$	$0$	$-2$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots$
1638.2.a.x	$1638$	$2$	1638.a	1.a	$1$	$2$	$2$	$13.079$	$\Q(\sqrt{33})$	None	✓	✓	✓	✓	1638.2.a.v	$1$	$0$	$2$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}-q^{7}+q^{8}+\beta q^{10}+\cdots$
1638.2.a.y	$1638$	$2$	1638.a	1.a	$1$	$2$	$2$	$13.079$	$\Q(\sqrt{57})$	None	✓		✓		546.2.a.h	$1$	$0$	$2$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+q^{7}+q^{8}+\beta q^{10}+\cdots$
1638.2.c.a	$1638$	$2$	1638.c	13.b	$2$	$2$	$2$	$13.079$	$\Q(\sqrt{-1})$	None					182.2.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+2 i q^{5}-i q^{7}-i q^{8}+\cdots$
1638.2.c.b	$1638$	$2$	1638.c	13.b	$2$	$2$	$2$	$13.079$	$\Q(\sqrt{-1})$	None					546.2.c.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+2 i q^{5}-i q^{7}-i q^{8}+\cdots$
1638.2.c.c	$1638$	$2$	1638.c	13.b	$2$	$2$	$2$	$13.079$	$\Q(\sqrt{-1})$	None		✓			1638.2.c.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+2 i q^{5}+i q^{7}-i q^{8}+\cdots$
1638.2.c.d	$1638$	$2$	1638.c	13.b	$2$	$2$	$2$	$13.079$	$\Q(\sqrt{-1})$	None		✓			1638.2.c.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+2 i q^{5}-i q^{7}-i q^{8}+\cdots$
1638.2.c.e	$1638$	$2$	1638.c	13.b	$2$	$2$	$2$	$13.079$	$\Q(\sqrt{-1})$	None					546.2.c.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+i q^{5}-i q^{7}+i q^{8}+\cdots$
1638.2.c.f	$1638$	$2$	1638.c	13.b	$2$	$2$	$2$	$13.079$	$\Q(\sqrt{-1})$	None					546.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+i q^{5}+i q^{7}+i q^{8}+\cdots$
1638.2.c.g	$1638$	$2$	1638.c	13.b	$2$	$2$	$2$	$13.079$	$\Q(\sqrt{-1})$	None					546.2.c.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+3 i q^{5}+i q^{7}+i q^{8}+\cdots$
1638.2.c.h	$1638$	$2$	1638.c	13.b	$2$	$4$	$4$	$13.079$	$\Q(i, \sqrt{17})$	None					546.2.c.e	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-q^{4}+(\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+\cdots$
1638.2.c.i	$1638$	$2$	1638.c	13.b	$2$	$6$	$6$	$13.079$	6.0.30647296.1	None					182.2.d.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{4}q^{7}+\cdots$
1638.2.c.j	$1638$	$2$	1638.c	13.b	$2$	$6$	$6$	$13.079$	6.0.3356224.1	None		✓			1638.2.c.j	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{4}+(-\beta _{1}-\beta _{4})q^{5}+\beta _{1}q^{7}+\cdots$
1638.2.c.k	$1638$	$2$	1638.c	13.b	$2$	$6$	$6$	$13.079$	6.0.3356224.1	None		✓			1638.2.c.j	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{4}+(-\beta _{1}-\beta _{4})q^{5}-\beta _{1}q^{7}+\cdots$
1638.2.e.a	$1638$	$2$	1638.e	273.g	$2$	$16$	$16$	$13.079$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			1638.2.e.a	$4$	$0$	$-16$	$0$	$0$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+\beta _{6}q^{5}+\beta _{1}q^{7}-q^{8}+\cdots$
1638.2.e.b	$1638$	$2$	1638.e	273.g	$2$	$16$	$16$	$13.079$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			1638.2.e.a	$4$	$0$	$16$	$0$	$0$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+\beta _{6}q^{5}-\beta _{2}q^{7}+q^{8}+\cdots$
1638.2.g.a	$1638$	$2$	1638.g	21.c	$2$	$8$	$8$	$13.079$	8.0.40960000.1	None		✓			1638.2.g.a	$2$	$0$	$0$	$0$	$-8$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{4}+(-1-\beta _{3})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots$
1638.2.g.b	$1638$	$2$	1638.g	21.c	$2$	$8$	$8$	$13.079$	8.0.836829184.2	None		✓			1638.2.g.b	$2$	$0$	$0$	$0$	$-8$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-q^{4}+(-2-\beta _{1}-\beta _{6}+\beta _{7})q^{5}+\cdots$
1638.2.g.c	$1638$	$2$	1638.g	21.c	$2$	$8$	$8$	$13.079$	8.0.40960000.1	None		✓			1638.2.g.a	$2$	$0$	$0$	$0$	$8$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-q^{4}+(1-\beta _{3})q^{5}+(\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots$
1638.2.g.d	$1638$	$2$	1638.g	21.c	$2$	$8$	$8$	$13.079$	8.0.836829184.2	None		✓			1638.2.g.b	$2$	$0$	$0$	$0$	$8$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-q^{4}+(2+\beta _{1}+\beta _{6}-\beta _{7})q^{5}+\cdots$
1638.2.j.a	$1638$	$2$	1638.j	7.c	$3$	$2$	$1$	$13.079$	$\Q(\sqrt{-3})$	None					546.2.i.e	$2$	$0$	$-1$	$0$	$-2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots$
1638.2.j.b	$1638$	$2$	1638.j	7.c	$3$	$2$	$1$	$13.079$	$\Q(\sqrt{-3})$	None					546.2.i.g	$2$	$0$	$-1$	$0$	$-2$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots$
1638.2.j.c	$1638$	$2$	1638.j	7.c	$3$	$2$	$1$	$13.079$	$\Q(\sqrt{-3})$	None					182.2.f.a	$2$	$0$	$-1$	$0$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(2+\zeta_{6})q^{7}+\cdots$
1638.2.j.d	$1638$	$2$	1638.j	7.c	$3$	$2$	$1$	$13.079$	$\Q(\sqrt{-3})$	None		✓			1638.2.j.d	$2$	$1$	$-1$	$0$	$1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots$
1638.2.j.e	$1638$	$2$	1638.j	7.c	$3$	$2$	$1$	$13.079$	$\Q(\sqrt{-3})$	None					546.2.i.f	$2$	$0$	$-1$	$0$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$
1638.2.j.f	$1638$	$2$	1638.j	7.c	$3$	$2$	$1$	$13.079$	$\Q(\sqrt{-3})$	None					546.2.i.c	$2$	$0$	$1$	$0$	$-4$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-4\zeta_{6}q^{5}+\cdots$
1638.2.j.g	$1638$	$2$	1638.j	7.c	$3$	$2$	$1$	$13.079$	$\Q(\sqrt{-3})$	None		✓			1638.2.j.d	$2$	$0$	$1$	$0$	$-1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots$
1638.2.j.h	$1638$	$2$	1638.j	7.c	$3$	$2$	$1$	$13.079$	$\Q(\sqrt{-3})$	None					546.2.i.b	$2$	$0$	$1$	$0$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$

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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.