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 200 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	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
1680.1.bb.a	$1680$	$1$	1680.bb	420.o	$2$	$1$	$1$	$0.838$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-105}) $	$\Q(\sqrt{21}) $	✓	✓			1680.1.bb.a	$4$	$0$	$0$	$-1$	$-1$	$-1$		$1$		$q-q^{3}-q^{5}-q^{7}+q^{9}+q^{15}+q^{21}+\cdots$
1680.1.bb.b	$1680$	$1$	1680.bb	420.o	$2$	$1$	$1$	$0.838$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-105}) $	$\Q(\sqrt{21}) $	✓	✓			1680.1.bb.a	$4$	$0$	$0$	$-1$	$1$	$1$		$1$		$q-q^{3}+q^{5}+q^{7}+q^{9}-q^{15}-q^{21}+\cdots$
1680.1.bb.c	$1680$	$1$	1680.bb	420.o	$2$	$1$	$1$	$0.838$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-105}) $	$\Q(\sqrt{21}) $	✓	✓			1680.1.bb.a	$4$	$0$	$0$	$1$	$-1$	$1$		$1$		$q+q^{3}-q^{5}+q^{7}+q^{9}-q^{15}+q^{21}+\cdots$
1680.1.bb.d	$1680$	$1$	1680.bb	420.o	$2$	$1$	$1$	$0.838$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-105}) $	$\Q(\sqrt{21}) $	✓	✓			1680.1.bb.a	$4$	$0$	$0$	$1$	$1$	$-1$		$1$		$q+q^{3}+q^{5}-q^{7}+q^{9}+q^{15}-q^{21}+\cdots$
1680.1.bb.e	$1680$	$1$	1680.bb	420.o	$2$	$2$	$2$	$0.838$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{15}) $		✓			1680.1.bb.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{3}-iq^{5}-iq^{7}-q^{9}-q^{11}+\cdots$
1680.1.bb.f	$1680$	$1$	1680.bb	420.o	$2$	$2$	$2$	$0.838$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{15}) $		✓			1680.1.bb.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}-iq^{5}+iq^{7}-q^{9}+q^{11}+\cdots$
1680.1.bb.g	$1680$	$1$	1680.bb	420.o	$2$	$4$	$4$	$0.838$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-35}) $	None		✓			1680.1.bb.g	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{3}q^{7}+\cdots$
1680.1.bb.h	$1680$	$1$	1680.bb	420.o	$2$	$4$	$4$	$0.838$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-35}) $	None		✓			1680.1.bb.g	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}q^{3}+\zeta_{12}^{3}q^{5}+\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{9}+\cdots$
1680.1.dp.a	$1680$	$1$	1680.dp	420.ae	$6$	$2$	$1$	$0.838$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-5}) $	None		✓			1680.1.dp.a	$4$	$0$	$0$	$-2$	$-1$	$-1$		$1$		$q-q^{3}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+q^{9}+\zeta_{6}q^{15}+\cdots$
1680.1.dp.b	$1680$	$1$	1680.dp	420.ae	$6$	$2$	$1$	$0.838$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-5}) $	None		✓			1680.1.dp.a	$4$	$0$	$0$	$-1$	$1$	$-1$		$1$		$q-\zeta_{6}q^{3}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
1680.1.dp.c	$1680$	$1$	1680.dp	420.ae	$6$	$2$	$1$	$0.838$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-5}) $	None		✓			1680.1.dp.a	$4$	$0$	$0$	$1$	$1$	$1$		$1$		$q+\zeta_{6}q^{3}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
1680.1.dp.d	$1680$	$1$	1680.dp	420.ae	$6$	$2$	$1$	$0.838$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-5}) $	None		✓			1680.1.dp.a	$4$	$0$	$0$	$2$	$-1$	$1$		$1$		$q+q^{3}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+q^{9}-\zeta_{6}q^{15}+\cdots$
1680.2.a.a	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓				420.2.a.c	$1$	$0$	$0$	$-1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots$
1680.2.a.b	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓				210.2.a.d	$1$	$0$	$0$	$-1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}+q^{9}+2q^{13}+q^{15}+\cdots$
1680.2.a.c	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓		✓	✓	840.2.a.i	$1$	$1$	$0$	$-1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}+q^{9}+2q^{13}+q^{15}+\cdots$
1680.2.a.d	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓				840.2.a.h	$1$	$0$	$0$	$-1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}+q^{9}+6q^{13}+q^{15}+\cdots$
1680.2.a.e	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓				840.2.a.g	$1$	$0$	$0$	$-1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots$
1680.2.a.f	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓				105.2.a.a	$1$	$1$	$0$	$-1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-q^{7}+q^{9}-6q^{13}-q^{15}+\cdots$
1680.2.a.g	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓				210.2.a.b	$1$	$1$	$0$	$-1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-q^{7}+q^{9}+2q^{13}-q^{15}+\cdots$
1680.2.a.h	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓		✓	✓	840.2.a.j	$1$	$1$	$0$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$
1680.2.a.i	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓				420.2.a.d	$1$	$0$	$0$	$-1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots$
1680.2.a.j	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓				210.2.a.e	$1$	$0$	$0$	$-1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
1680.2.a.k	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓				840.2.a.c	$1$	$0$	$0$	$1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}+q^{9}-2q^{13}-q^{15}+\cdots$
1680.2.a.l	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓				840.2.a.b	$1$	$0$	$0$	$1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
1680.2.a.m	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓		✓	✓	840.2.a.a	$1$	$1$	$0$	$1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$
1680.2.a.n	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓				420.2.a.a	$1$	$0$	$0$	$1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots$
1680.2.a.o	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓				210.2.a.a	$1$	$0$	$0$	$1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
1680.2.a.p	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓		✓	✓	840.2.a.f	$1$	$1$	$0$	$1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$
1680.2.a.q	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓				210.2.a.c	$1$	$0$	$0$	$1$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$
1680.2.a.r	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓				420.2.a.b	$1$	$0$	$0$	$1$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots$
1680.2.a.s	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓				840.2.a.e	$1$	$0$	$0$	$1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{7}+q^{9}+2q^{13}+q^{15}+\cdots$
1680.2.a.t	$1680$	$2$	1680.a	1.a	$1$	$1$	$1$	$13.415$	$\Q$	$_{}$	None	None	✓				840.2.a.d	$1$	$0$	$0$	$1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
1680.2.a.u	$1680$	$2$	1680.a	1.a	$1$	$2$	$2$	$13.415$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		✓	✓	840.2.a.k	$1$	$0$	$0$	$-2$	$2$	$-2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-q^{7}+q^{9}+\beta q^{11}+2q^{13}+\cdots$
1680.2.a.v	$1680$	$2$	1680.a	1.a	$1$	$2$	$2$	$13.415$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		✓	✓	105.2.a.b	$1$	$1$	$0$	$2$	$-2$	$-2$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots$
1680.2.d.a	$1680$	$2$	1680.d	28.d	$2$	$4$	$4$	$13.415$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			1680.2.d.a	$2$	$0$	$0$	$-4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+\beta _{1}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+q^{9}+\cdots$
1680.2.d.b	$1680$	$2$	1680.d	28.d	$2$	$4$	$4$	$13.415$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			1680.2.d.a	$2$	$0$	$0$	$4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}-\beta _{1}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+q^{9}+\cdots$
1680.2.d.c	$1680$	$2$	1680.d	28.d	$2$	$12$	$12$	$13.415$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			1680.2.d.c	$2$	$0$	$0$	$-12$	$0$	$4$		$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\beta _{1}q^{5}-\beta _{9}q^{7}+q^{9}-\beta _{7}q^{11}+\cdots$
1680.2.d.d	$1680$	$2$	1680.d	28.d	$2$	$12$	$12$	$13.415$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			1680.2.d.c	$2$	$0$	$0$	$12$	$0$	$-4$		$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta _{1}q^{5}+\beta _{8}q^{7}+q^{9}-\beta _{7}q^{11}+\cdots$
1680.2.f.a	$1680$	$2$	1680.f	21.c	$2$	$2$	$2$	$13.415$	$\Q(\sqrt{-3}) $	$_{}$	None	None					420.2.d.a	$2$	$1$	$0$	$-3$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+\zeta_{6})q^{3}+q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$
1680.2.f.b	$1680$	$2$	1680.f	21.c	$2$	$2$	$2$	$13.415$	$\Q(\sqrt{-3}) $	$_{}$	None	None					105.2.b.a	$2$	$0$	$0$	$0$	$-2$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{6}q^{3}-q^{5}+(-2-\zeta_{6})q^{7}-3q^{9}+\cdots$
1680.2.f.c	$1680$	$2$	1680.f	21.c	$2$	$2$	$2$	$13.415$	$\Q(\sqrt{-3}) $	$_{}$	None	None					105.2.b.a	$2$	$1$	$0$	$0$	$2$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{6}q^{3}+q^{5}+(-2+\zeta_{6})q^{7}-3q^{9}+\cdots$
1680.2.f.d	$1680$	$2$	1680.f	21.c	$2$	$2$	$2$	$13.415$	$\Q(\sqrt{-3}) $	$_{}$	None	None					420.2.d.a	$2$	$0$	$0$	$3$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2-\zeta_{6})q^{3}-q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$
1680.2.f.e	$1680$	$2$	1680.f	21.c	$2$	$4$	$4$	$13.415$	$\Q(i, \sqrt{5})$	$_{}$	None	None					210.2.b.a	$2$	$0$	$0$	$-2$	$-4$	$-6$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{2})q^{3}-q^{5}+(-1+\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots$
1680.2.f.f	$1680$	$2$	1680.f	21.c	$2$	$4$	$4$	$13.415$	$\Q(i, \sqrt{5})$	$_{}$	None	None					420.2.d.c	$2$	$0$	$0$	$-2$	$-4$	$6$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1})q^{3}-q^{5}+(1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
1680.2.f.g	$1680$	$2$	1680.f	21.c	$2$	$4$	$4$	$13.415$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None					105.2.b.c	$2$	$0$	$0$	$-1$	$4$	$8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+q^{5}+(2+\beta _{2})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots$
1680.2.f.h	$1680$	$2$	1680.f	21.c	$2$	$4$	$4$	$13.415$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None					105.2.b.c	$2$	$0$	$0$	$1$	$-4$	$8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-q^{5}+(2-\beta _{2})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots$
1680.2.f.i	$1680$	$2$	1680.f	21.c	$2$	$4$	$4$	$13.415$	$\Q(i, \sqrt{5})$	$_{}$	None	None					210.2.b.a	$2$	$0$	$0$	$2$	$4$	$-6$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-\beta _{2})q^{3}+q^{5}+(-1-2\beta _{2}+\cdots)q^{7}+\cdots$
1680.2.f.j	$1680$	$2$	1680.f	21.c	$2$	$4$	$4$	$13.415$	$\Q(i, \sqrt{5})$	$_{}$	None	None					420.2.d.c	$2$	$0$	$0$	$2$	$4$	$6$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{3}+q^{5}+(1+\beta _{2}+\beta _{3})q^{7}+\cdots$
1680.2.f.k	$1680$	$2$	1680.f	21.c	$2$	$16$	$16$	$13.415$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					840.2.f.a	$2$	$0$	$0$	$0$	$-16$	$-2$		$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}-q^{5}-\beta _{9}q^{7}+\beta _{7}q^{9}+\beta _{8}q^{11}+\cdots$
1680.2.f.l	$1680$	$2$	1680.f	21.c	$2$	$16$	$16$	$13.415$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					840.2.f.a	$2$	$0$	$0$	$0$	$16$	$-2$		$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+q^{5}-\beta _{4}q^{7}+\beta _{7}q^{9}+\beta _{8}q^{11}+\cdots$

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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.