LMFDB - Newform search results

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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 203 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2016.1.e.a	$2016$	$1$	2016.e	168.e	$2$	$4$	$4$	$1.006$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+\zeta_{8}^{2}q^{7}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+(-\zeta_{8}+\cdots)q^{23}+\cdots$
2016.1.f.a	$2016$	$1$	2016.f	7.b	$2$	$4$	$4$	$1.006$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-21}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+(-\zeta_{8}+\cdots)q^{11}+\cdots$
2016.1.l.a	$2016$	$1$	2016.l	56.h	$2$	$1$	$1$	$1.006$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q+q^{7}+2q^{23}-q^{25}+q^{49}-2q^{71}+\cdots$
2016.1.l.b	$2016$	$1$	2016.l	56.h	$2$	$2$	$2$	$1.006$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{42}) $		$8$	$0$	$0$	$0$	$0$	$-2$		$2$		$q-q^{7}-iq^{11}-q^{25}-iq^{29}+q^{49}+\cdots$
2016.1.bi.a	$2016$	$1$	2016.bi	504.aa	$6$	$4$	$2$	$1.006$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-\zeta_{12}^{2}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+\zeta_{12}^{4}q^{9}+\cdots$
2016.1.bv.a	$2016$	$1$	2016.bv	504.an	$6$	$2$	$1$	$1.006$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$0$	$-2$	$1$	$1$		$1$		$q-q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+q^{9}+\zeta_{6}^{2}q^{13}+\cdots$
2016.1.bv.b	$2016$	$1$	2016.bv	504.an	$6$	$2$	$1$	$1.006$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$0$	$2$	$-1$	$1$		$1$		$q+q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+q^{9}-\zeta_{6}^{2}q^{13}+\cdots$
2016.1.bv.c	$2016$	$1$	2016.bv	504.an	$6$	$4$	$2$	$1.006$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{12}^{3}q^{3}+(-\zeta_{12}-\zeta_{12}^{3})q^{5}+\zeta_{12}^{4}q^{7}+\cdots$
2016.1.bw.a	$2016$	$1$	2016.bw	252.u	$6$	$4$	$2$	$1.006$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{3}-\zeta_{12}q^{7}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{4}q^{13}+\cdots$
2016.1.cd.a	$2016$	$1$	2016.cd	28.g	$6$	$4$	$2$	$1.006$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}q^{11}+\cdots$
2016.1.ce.a	$2016$	$1$	2016.ce	56.j	$6$	$4$	$2$	$1.006$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$2$		$1$		$q+(\zeta_{12}^{3}+\zeta_{12}^{5})q^{5}+\zeta_{12}^{2}q^{7}+\zeta_{12}^{5}q^{11}+\cdots$
2016.1.cm.a	$2016$	$1$	2016.cm	504.be	$6$	$4$	$2$	$1.006$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$4$	$0$	$0$		$1$		$q+q^{3}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{7}+q^{9}+\cdots$
2016.1.dd.a	$2016$	$1$	2016.dd	252.al	$6$	$4$	$2$	$1.006$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{3}-\zeta_{12}^{3}q^{7}-q^{9}-\zeta_{12}^{2}q^{13}+\cdots$
2016.1.dn.a	$2016$	$1$	2016.dn	672.ar	$8$	$4$	$1$	$1.006$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-4$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}+\zeta_{8}^{3}q^{7}-q^{8}+(-\zeta_{8}^{2}+\cdots)q^{11}+\cdots$
2016.1.dn.b	$2016$	$1$	2016.dn	672.ar	$8$	$4$	$1$	$1.006$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}^{2}q^{8}+\cdots$
2016.1.dn.c	$2016$	$1$	2016.dn	672.ar	$8$	$4$	$1$	$1.006$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{8}+\cdots$
2016.1.dn.d	$2016$	$1$	2016.dn	672.ar	$8$	$4$	$1$	$1.006$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$4$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+\zeta_{8}^{3}q^{7}+q^{8}+(\zeta_{8}^{2}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots$
2016.1.dp.a	$2016$	$1$	2016.dp	224.v	$8$	$4$	$1$	$1.006$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}^{3}q^{8}+\cdots$
2016.1.dp.b	$2016$	$1$	2016.dp	224.v	$8$	$4$	$1$	$1.006$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{7}+\zeta_{8}q^{8}+\cdots$
2016.1.dp.c	$2016$	$1$	2016.dp	224.v	$8$	$4$	$1$	$1.006$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{3}q^{8}+\cdots$
2016.2.a.a	$2016$	$2$	2016.a	1.a	$1$	$1$	$1$	$16.098$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}+2q^{13}-2q^{17}+4q^{19}+\cdots$
2016.2.a.b	$2016$	$2$	2016.a	1.a	$1$	$1$	$1$	$16.098$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}+2q^{13}-2q^{17}-4q^{19}+\cdots$
2016.2.a.c	$2016$	$2$	2016.a	1.a	$1$	$1$	$1$	$16.098$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-4q^{11}+2q^{13}+4q^{17}-4q^{23}+\cdots$
2016.2.a.d	$2016$	$2$	2016.a	1.a	$1$	$1$	$1$	$16.098$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+2q^{11}-2q^{13}-4q^{17}-4q^{19}+\cdots$
2016.2.a.e	$2016$	$2$	2016.a	1.a	$1$	$1$	$1$	$16.098$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+4q^{11}-4q^{13}+2q^{17}-6q^{19}+\cdots$
2016.2.a.f	$2016$	$2$	2016.a	1.a	$1$	$1$	$1$	$16.098$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+4q^{11}+2q^{13}-4q^{17}+4q^{23}+\cdots$
2016.2.a.g	$2016$	$2$	2016.a	1.a	$1$	$1$	$1$	$16.098$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-4q^{11}-4q^{13}+2q^{17}+6q^{19}+\cdots$
2016.2.a.h	$2016$	$2$	2016.a	1.a	$1$	$1$	$1$	$16.098$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-4q^{11}+2q^{13}-4q^{17}-4q^{23}+\cdots$
2016.2.a.i	$2016$	$2$	2016.a	1.a	$1$	$1$	$1$	$16.098$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-2q^{11}-2q^{13}-4q^{17}+4q^{19}+\cdots$
2016.2.a.j	$2016$	$2$	2016.a	1.a	$1$	$1$	$1$	$16.098$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+4q^{11}+2q^{13}+4q^{17}+4q^{23}+\cdots$
2016.2.a.k	$2016$	$2$	2016.a	1.a	$1$	$1$	$1$	$16.098$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}+4q^{11}-6q^{13}+2q^{17}+\cdots$
2016.2.a.l	$2016$	$2$	2016.a	1.a	$1$	$1$	$1$	$16.098$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-4q^{11}-6q^{13}+2q^{17}+\cdots$
2016.2.a.m	$2016$	$2$	2016.a	1.a	$1$	$1$	$1$	$16.098$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-q^{7}-2q^{11}-2q^{13}+4q^{19}+\cdots$
2016.2.a.n	$2016$	$2$	2016.a	1.a	$1$	$1$	$1$	$16.098$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+q^{7}+2q^{11}-2q^{13}-4q^{19}+\cdots$
2016.2.a.o	$2016$	$2$	2016.a	1.a	$1$	$2$	$2$	$16.098$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}-q^{7}+(-2-2\beta )q^{11}+\cdots$
2016.2.a.p	$2016$	$2$	2016.a	1.a	$1$	$2$	$2$	$16.098$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}-q^{7}+(1+\beta )q^{11}+2\beta q^{13}+\cdots$
2016.2.a.q	$2016$	$2$	2016.a	1.a	$1$	$2$	$2$	$16.098$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+q^{7}+(-1-\beta )q^{11}+\cdots$
2016.2.a.r	$2016$	$2$	2016.a	1.a	$1$	$2$	$2$	$16.098$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+q^{7}+(2+2\beta )q^{11}+\cdots$
2016.2.a.s	$2016$	$2$	2016.a	1.a	$1$	$2$	$2$	$16.098$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}-q^{7}+(-2-\beta )q^{11}+2q^{13}+\cdots$
2016.2.a.t	$2016$	$2$	2016.a	1.a	$1$	$2$	$2$	$16.098$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}+q^{7}+(2+\beta )q^{11}+2q^{13}+\cdots$
2016.2.a.u	$2016$	$2$	2016.a	1.a	$1$	$2$	$2$	$16.098$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}-q^{7}+(-1-\beta )q^{11}+2\beta q^{13}+\cdots$
2016.2.a.v	$2016$	$2$	2016.a	1.a	$1$	$2$	$2$	$16.098$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+q^{7}+(1+\beta )q^{11}+2\beta q^{13}+\cdots$
2016.2.b.a	$2016$	$2$	2016.b	28.d	$2$	$8$	$8$	$16.098$	8.0.836829184.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}+\beta _{4}q^{7}+(\beta _{2}+\beta _{4}+\beta _{7})q^{11}+\cdots$
2016.2.b.b	$2016$	$2$	2016.b	28.d	$2$	$8$	$8$	$16.098$	$\Q(\zeta_{16})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{16}^{5}q^{5}+\zeta_{16}^{6}q^{7}-\zeta_{16}q^{11}+\cdots$
2016.2.b.c	$2016$	$2$	2016.b	28.d	$2$	$8$	$8$	$16.098$	8.0.836829184.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}-\beta _{4}q^{7}+(-\beta _{2}-\beta _{4}-\beta _{7})q^{11}+\cdots$
2016.2.b.d	$2016$	$2$	2016.b	28.d	$2$	$16$	$16$	$16.098$	16.0.$\cdots$.7	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{30}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{5}-\beta _{8}q^{7}+(\beta _{7}+\beta _{11})q^{11}+\cdots$
2016.2.c.a	$2016$	$2$	2016.c	8.b	$2$	$2$	$2$	$16.098$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-q^{7}+2\beta q^{11}-3\beta q^{13}+6q^{17}+\cdots$
2016.2.c.b	$2016$	$2$	2016.c	8.b	$2$	$4$	$4$	$16.098$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}-q^{7}+\beta _{1}q^{11}+\beta _{2}q^{17}+\cdots$
2016.2.c.c	$2016$	$2$	2016.c	8.b	$2$	$4$	$4$	$16.098$	4.0.2312.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{5}+q^{7}+(-\beta _{1}+\beta _{2})q^{11}+\beta _{2}q^{13}+\cdots$
2016.2.c.d	$2016$	$2$	2016.c	8.b	$2$	$4$	$4$	$16.098$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{12}^{3}q^{5}+q^{7}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{11}+\cdots$

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Elliptic curves over $\Q$
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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.