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 163 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
1530.2.a.a	$1530$	$2$	1530.a	1.a	$1$	$1$	$1$	$12.217$	$\Q$	None	✓	✓	✓	✓	1530.2.a.a	$1$	$0$	$-1$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots$
1530.2.a.b	$1530$	$2$	1530.a	1.a	$1$	$1$	$1$	$12.217$	$\Q$	None	✓				510.2.a.e	$1$	$0$	$-1$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots$
1530.2.a.c	$1530$	$2$	1530.a	1.a	$1$	$1$	$1$	$12.217$	$\Q$	None	✓		✓	✓	510.2.a.g	$1$	$1$	$-1$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots$
1530.2.a.d	$1530$	$2$	1530.a	1.a	$1$	$1$	$1$	$12.217$	$\Q$	None	✓				510.2.a.c	$1$	$1$	$-1$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots$
1530.2.a.e	$1530$	$2$	1530.a	1.a	$1$	$1$	$1$	$12.217$	$\Q$	None	✓	✓	✓	✓	1530.2.a.e	$1$	$1$	$-1$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots$
1530.2.a.f	$1530$	$2$	1530.a	1.a	$1$	$1$	$1$	$12.217$	$\Q$	None	✓				510.2.a.f	$1$	$1$	$-1$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-4q^{11}+\cdots$
1530.2.a.g	$1530$	$2$	1530.a	1.a	$1$	$1$	$1$	$12.217$	$\Q$	None	✓				170.2.a.e	$1$	$0$	$-1$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots$
1530.2.a.h	$1530$	$2$	1530.a	1.a	$1$	$1$	$1$	$12.217$	$\Q$	None	✓				510.2.a.d	$1$	$0$	$-1$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots$
1530.2.a.i	$1530$	$2$	1530.a	1.a	$1$	$1$	$1$	$12.217$	$\Q$	None	✓				510.2.a.b	$1$	$1$	$1$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots$
1530.2.a.j	$1530$	$2$	1530.a	1.a	$1$	$1$	$1$	$12.217$	$\Q$	None	✓				170.2.a.b	$1$	$1$	$1$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots$
1530.2.a.k	$1530$	$2$	1530.a	1.a	$1$	$1$	$1$	$12.217$	$\Q$	None	✓	✓	✓	✓	1530.2.a.e	$1$	$0$	$1$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots$
1530.2.a.l	$1530$	$2$	1530.a	1.a	$1$	$1$	$1$	$12.217$	$\Q$	None	✓				170.2.a.c	$1$	$0$	$1$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots$
1530.2.a.m	$1530$	$2$	1530.a	1.a	$1$	$1$	$1$	$12.217$	$\Q$	None	✓	✓	✓	✓	1530.2.a.a	$1$	$1$	$1$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots$
1530.2.a.n	$1530$	$2$	1530.a	1.a	$1$	$1$	$1$	$12.217$	$\Q$	None	✓				170.2.a.a	$1$	$0$	$1$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots$
1530.2.a.o	$1530$	$2$	1530.a	1.a	$1$	$1$	$1$	$12.217$	$\Q$	None	✓				170.2.a.d	$1$	$0$	$1$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots$
1530.2.a.p	$1530$	$2$	1530.a	1.a	$1$	$1$	$1$	$12.217$	$\Q$	None	✓				510.2.a.a	$1$	$0$	$1$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots$
1530.2.a.q	$1530$	$2$	1530.a	1.a	$1$	$2$	$2$	$12.217$	$\Q(\sqrt{5}) $	None	✓	✓	✓	✓	1530.2.a.q	$1$	$1$	$-2$	$0$	$-2$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+(1+\beta )q^{7}-q^{8}+\cdots$
1530.2.a.r	$1530$	$2$	1530.a	1.a	$1$	$2$	$2$	$12.217$	$\Q(\sqrt{17}) $	None	✓		✓		170.2.a.f	$1$	$0$	$-2$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+2\beta q^{7}-q^{8}+q^{10}+\cdots$
1530.2.a.s	$1530$	$2$	1530.a	1.a	$1$	$2$	$2$	$12.217$	$\Q(\sqrt{6}) $	None	✓		✓		510.2.a.h	$1$	$0$	$2$	$0$	$-2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+\beta q^{7}+q^{8}-q^{10}+\cdots$
1530.2.a.t	$1530$	$2$	1530.a	1.a	$1$	$2$	$2$	$12.217$	$\Q(\sqrt{5}) $	None	✓	✓	✓	✓	1530.2.a.q	$1$	$0$	$2$	$0$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+(1+\beta )q^{7}+q^{8}+\cdots$
1530.2.c.a	$1530$	$2$	1530.c	17.b	$2$	$2$	$2$	$12.217$	$\Q(\sqrt{-1}) $	None					170.2.b.c	$2$	$1$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}-i q^{5}+2 i q^{7}-q^{8}+\cdots$
1530.2.c.b	$1530$	$2$	1530.c	17.b	$2$	$2$	$2$	$12.217$	$\Q(\sqrt{-1}) $	None					170.2.b.b	$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+i q^{5}+4 i q^{7}-q^{8}+\cdots$
1530.2.c.c	$1530$	$2$	1530.c	17.b	$2$	$2$	$2$	$12.217$	$\Q(\sqrt{-1}) $	None					510.2.c.b	$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}-i q^{5}+2 i q^{7}-q^{8}+\cdots$
1530.2.c.d	$1530$	$2$	1530.c	17.b	$2$	$2$	$2$	$12.217$	$\Q(\sqrt{-1}) $	None					170.2.b.a	$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}-i q^{5}+q^{8}-i q^{10}+\cdots$
1530.2.c.e	$1530$	$2$	1530.c	17.b	$2$	$2$	$2$	$12.217$	$\Q(\sqrt{-1}) $	None					510.2.c.a	$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}-i q^{5}+q^{8}-i q^{10}+\cdots$
1530.2.c.f	$1530$	$2$	1530.c	17.b	$2$	$4$	$4$	$12.217$	$\Q(\zeta_{8})$	None					510.2.c.d	$2$	$0$	$-4$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}-\beta_1 q^{5}+(\beta_{2}+2\beta_1)q^{7}+\cdots$
1530.2.c.g	$1530$	$2$	1530.c	17.b	$2$	$4$	$4$	$12.217$	$\Q(i, \sqrt{13})$	None					510.2.c.c	$2$	$0$	$4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots$
1530.2.c.h	$1530$	$2$	1530.c	17.b	$2$	$6$	$6$	$12.217$	6.0.5089536.1	None		✓			1530.2.c.h	$2$	$0$	$-6$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots$
1530.2.c.i	$1530$	$2$	1530.c	17.b	$2$	$6$	$6$	$12.217$	6.0.5089536.1	None		✓			1530.2.c.h	$2$	$0$	$6$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots$
1530.2.d.a	$1530$	$2$	1530.d	5.b	$2$	$2$	$2$	$12.217$	$\Q(\sqrt{-1}) $	None		✓			1530.2.d.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+(i-2)q^{5}+i q^{8}+\cdots$
1530.2.d.b	$1530$	$2$	1530.d	5.b	$2$	$2$	$2$	$12.217$	$\Q(\sqrt{-1}) $	None					170.2.c.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+(-2 i-1)q^{5}+i q^{8}+\cdots$
1530.2.d.c	$1530$	$2$	1530.d	5.b	$2$	$2$	$2$	$12.217$	$\Q(\sqrt{-1}) $	None					510.2.d.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+(i+2)q^{5}+4 i q^{7}+\cdots$
1530.2.d.d	$1530$	$2$	1530.d	5.b	$2$	$2$	$2$	$12.217$	$\Q(\sqrt{-1}) $	None		✓			1530.2.d.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+(i+2)q^{5}+i q^{8}+\cdots$
1530.2.d.e	$1530$	$2$	1530.d	5.b	$2$	$4$	$4$	$12.217$	$\Q(i, \sqrt{6})$	None					510.2.d.c	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-q^{4}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots$
1530.2.d.f	$1530$	$2$	1530.d	5.b	$2$	$4$	$4$	$12.217$	$\Q(i, \sqrt{5})$	None					510.2.d.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
1530.2.d.g	$1530$	$2$	1530.d	5.b	$2$	$6$	$6$	$12.217$	6.0.5161984.1	None					170.2.c.b	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-q^{4}+(\beta _{1}+\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
1530.2.d.h	$1530$	$2$	1530.d	5.b	$2$	$6$	$6$	$12.217$	6.0.350464.1	None		✓			1530.2.d.h	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\cdots$
1530.2.d.i	$1530$	$2$	1530.d	5.b	$2$	$6$	$6$	$12.217$	6.0.5161984.1	None					510.2.d.d	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-q^{4}-\beta _{4}q^{5}+(\beta _{1}+\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots$
1530.2.d.j	$1530$	$2$	1530.d	5.b	$2$	$6$	$6$	$12.217$	6.0.350464.1	None		✓			1530.2.d.h	$2$	$0$	$0$	$0$	$2$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{4}+\beta _{2}q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\cdots$
1530.2.f.a	$1530$	$2$	1530.f	85.c	$2$	$2$	$2$	$12.217$	$\Q(\sqrt{-1}) $	None		✓			1530.2.f.a	$2$	$0$	$0$	$0$	$-4$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+(i-2)q^{5}-4 q^{7}+\cdots$
1530.2.f.b	$1530$	$2$	1530.f	85.c	$2$	$2$	$2$	$12.217$	$\Q(\sqrt{-1}) $	None					170.2.d.a	$2$	$0$	$0$	$0$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+(-i-2)q^{5}+2 q^{7}+\cdots$
1530.2.f.c	$1530$	$2$	1530.f	85.c	$2$	$2$	$2$	$12.217$	$\Q(\sqrt{-1}) $	None		✓			1530.2.f.a	$2$	$0$	$0$	$0$	$-4$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+(i-2)q^{5}+4 q^{7}+\cdots$
1530.2.f.d	$1530$	$2$	1530.f	85.c	$2$	$2$	$2$	$12.217$	$\Q(\sqrt{-1}) $	None		✓			1530.2.f.a	$2$	$0$	$0$	$0$	$4$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+(i+2)q^{5}-4 q^{7}+\cdots$
1530.2.f.e	$1530$	$2$	1530.f	85.c	$2$	$2$	$2$	$12.217$	$\Q(\sqrt{-1}) $	None					170.2.d.a	$2$	$0$	$0$	$0$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+(i+2)q^{5}-2 q^{7}+\cdots$
1530.2.f.f	$1530$	$2$	1530.f	85.c	$2$	$2$	$2$	$12.217$	$\Q(\sqrt{-1}) $	None		✓			1530.2.f.a	$2$	$0$	$0$	$0$	$4$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+(i+2)q^{5}+4 q^{7}+\cdots$
1530.2.f.g	$1530$	$2$	1530.f	85.c	$2$	$4$	$4$	$12.217$	$\Q(i, \sqrt{6})$	None					510.2.f.a	$2$	$0$	$0$	$0$	$-4$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-q^{4}+(-1-\beta _{2}+\beta _{3})q^{5}+\cdots$
1530.2.f.h	$1530$	$2$	1530.f	85.c	$2$	$4$	$4$	$12.217$	$\Q(\zeta_{8})$	None					170.2.d.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}^{2}q^{2}-q^{4}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+(3\zeta_{8}+\cdots)q^{7}+\cdots$
1530.2.f.i	$1530$	$2$	1530.f	85.c	$2$	$4$	$4$	$12.217$	$\Q(i, \sqrt{6})$	None					510.2.f.a	$2$	$0$	$0$	$0$	$4$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+(2+\cdots)q^{7}+\cdots$
1530.2.f.j	$1530$	$2$	1530.f	85.c	$2$	$6$	$6$	$12.217$	6.0.350464.1	None					510.2.f.c	$2$	$0$	$0$	$0$	$-2$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-q^{4}+(\beta _{1}+\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots$
1530.2.f.k	$1530$	$2$	1530.f	85.c	$2$	$6$	$6$	$12.217$	6.0.350464.1	None					510.2.f.c	$2$	$0$	$0$	$0$	$2$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-q^{4}+(-\beta _{1}-\beta _{5})q^{5}+(1+\cdots)q^{7}+\cdots$

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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.