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 240 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
588.1.c.a	$588$	$1$	588.c	3.b	$2$	$1$	$1$	$0.293$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}+q^{9}+q^{13}+q^{19}+q^{25}-q^{27}+\cdots$
588.1.c.b	$588$	$1$	588.c	3.b	$2$	$1$	$1$	$0.293$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}+q^{9}-q^{13}-q^{19}+q^{25}+q^{27}+\cdots$
588.1.p.a	$588$	$1$	588.p	21.h	$6$	$2$	$1$	$0.293$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+q^{13}-\zeta_{6}q^{19}+\cdots$
588.1.z.a	$588$	$1$	588.z	147.n	$42$	$12$	$1$	$0.293$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$1$		$1$		$q+\zeta_{42}^{10}q^{3}+\zeta_{42}^{8}q^{7}+\zeta_{42}^{20}q^{9}+\cdots$
588.2.a.a	$588$	$2$	588.a	1.a	$1$	$1$	$1$	$4.695$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}+2q^{11}-3q^{13}+\cdots$
588.2.a.b	$588$	$2$	588.a	1.a	$1$	$1$	$1$	$4.695$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots$
588.2.a.c	$588$	$2$	588.a	1.a	$1$	$1$	$1$	$4.695$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}-6q^{11}-2q^{13}+4q^{19}+\cdots$
588.2.a.d	$588$	$2$	588.a	1.a	$1$	$1$	$1$	$4.695$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}+q^{9}+2q^{11}+6q^{13}+\cdots$
588.2.a.e	$588$	$2$	588.a	1.a	$1$	$1$	$1$	$4.695$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots$
588.2.a.f	$588$	$2$	588.a	1.a	$1$	$1$	$1$	$4.695$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}+2q^{11}+3q^{13}+\cdots$
588.2.b.a	$588$	$2$	588.b	28.d	$2$	$8$	$8$	$4.695$	8.0.562828176.1	$_{}$	None	None		$2$	$0$	$-2$	$-8$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{5}+\cdots$
588.2.b.b	$588$	$2$	588.b	28.d	$2$	$8$	$8$	$4.695$	8.0.562828176.1	$_{}$	None	None		$2$	$0$	$-2$	$8$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots$
588.2.b.c	$588$	$2$	588.b	28.d	$2$	$12$	$12$	$4.695$	12.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$4$	$-12$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{3}+(\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots$
588.2.b.d	$588$	$2$	588.b	28.d	$2$	$12$	$12$	$4.695$	12.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$4$	$12$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+q^{3}+(\beta _{5}+\beta _{6})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
588.2.e.a	$588$	$2$	588.e	12.b	$2$	$4$	$4$	$4.695$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-21}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}+\beta _{3}q^{5}+\beta _{3}q^{6}+\cdots$
588.2.e.b	$588$	$2$	588.e	12.b	$2$	$8$	$8$	$4.695$	8.0.3317760000.1	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}-\beta _{2}q^{3}+(-1-\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
588.2.e.c	$588$	$2$	588.e	12.b	$2$	$12$	$12$	$4.695$	12.0.$\cdots$.2	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{10}q^{3}+(-\beta _{3}+\beta _{5})q^{4}+\cdots$
588.2.e.d	$588$	$2$	588.e	12.b	$2$	$12$	$12$	$4.695$	12.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{8}q^{3}+\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots$
588.2.e.e	$588$	$2$	588.e	12.b	$2$	$12$	$12$	$4.695$	12.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{8}q^{3}+\beta _{2}q^{4}+\beta _{3}q^{5}+\cdots$
588.2.e.f	$588$	$2$	588.e	12.b	$2$	$24$	$24$	$4.695$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
588.2.f.a	$588$	$2$	588.f	21.c	$2$	$2$	$2$	$4.695$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-3$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\zeta_{6})q^{3}+3q^{5}+3\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots$
588.2.f.b	$588$	$2$	588.f	21.c	$2$	$2$	$2$	$4.695$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\zeta_{6}q^{3}-3q^{9}-3\zeta_{6}q^{13}-5\zeta_{6}q^{19}+\cdots$
588.2.f.c	$588$	$2$	588.f	21.c	$2$	$2$	$2$	$4.695$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$3$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{6})q^{3}-3q^{5}+3\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots$
588.2.f.d	$588$	$2$	588.f	21.c	$2$	$8$	$8$	$4.695$	8.0.3288334336.2	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{6})q^{3}+(-\beta _{1}-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots$
588.2.i.a	$588$	$2$	588.i	7.c	$3$	$2$	$1$	$4.695$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-1$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$
588.2.i.b	$588$	$2$	588.i	7.c	$3$	$2$	$1$	$4.695$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$
588.2.i.c	$588$	$2$	588.i	7.c	$3$	$2$	$1$	$4.695$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}+(6-6\zeta_{6})q^{11}+\cdots$
588.2.i.d	$588$	$2$	588.i	7.c	$3$	$2$	$1$	$4.695$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$
588.2.i.e	$588$	$2$	588.i	7.c	$3$	$2$	$1$	$4.695$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots$
588.2.i.f	$588$	$2$	588.i	7.c	$3$	$2$	$1$	$4.695$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}+(6-6\zeta_{6})q^{11}+\cdots$
588.2.i.g	$588$	$2$	588.i	7.c	$3$	$2$	$1$	$4.695$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots$
588.2.k.a	$588$	$2$	588.k	21.g	$6$	$2$	$1$	$4.695$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-3$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-1-\zeta_{6})q^{3}+3\zeta_{6}q^{9}+(4-8\zeta_{6})q^{13}+\cdots$
588.2.k.b	$588$	$2$	588.k	21.g	$6$	$2$	$1$	$4.695$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-3$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-1-\zeta_{6})q^{3}+3\zeta_{6}q^{9}+(-3+6\zeta_{6})q^{13}+\cdots$
588.2.k.c	$588$	$2$	588.k	21.g	$6$	$2$	$1$	$4.695$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+2\zeta_{6})q^{3}+3\zeta_{6}q^{5}-3q^{9}+\cdots$
588.2.k.d	$588$	$2$	588.k	21.g	$6$	$2$	$1$	$4.695$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$3$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(3-3\zeta_{6})q^{9}+\cdots$
588.2.k.e	$588$	$2$	588.k	21.g	$6$	$2$	$1$	$4.695$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$3$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(1+\zeta_{6})q^{3}+3\zeta_{6}q^{9}+(-4+8\zeta_{6})q^{13}+\cdots$
588.2.k.f	$588$	$2$	588.k	21.g	$6$	$16$	$8$	$4.695$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}-\beta _{5}-\beta _{8})q^{3}+(\beta _{1}-2\beta _{7}+\cdots)q^{5}+\cdots$
588.2.n.a	$588$	$2$	588.n	84.n	$6$	$4$	$2$	$4.695$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-21}) $	None		$8$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$
588.2.n.b	$588$	$2$	588.n	84.n	$6$	$4$	$2$	$4.695$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-21}) $	None		$8$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
588.2.n.c	$588$	$2$	588.n	84.n	$6$	$16$	$8$	$4.695$	16.0.$\cdots$.1	$_{}$	None	None		$16$	$0$	$0$	$0$	$0$	$0$		$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{9}q^{2}+(-\beta _{1}+\beta _{5}+\beta _{15})q^{3}-\beta _{3}q^{4}+\cdots$
588.2.n.d	$588$	$2$	588.n	84.n	$6$	$24$	$12$	$4.695$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
588.2.n.e	$588$	$2$	588.n	84.n	$6$	$24$	$12$	$4.695$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
588.2.n.f	$588$	$2$	588.n	84.n	$6$	$24$	$12$	$4.695$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
588.2.n.g	$588$	$2$	588.n	84.n	$6$	$24$	$12$	$4.695$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
588.2.n.h	$588$	$2$	588.n	84.n	$6$	$24$	$12$	$4.695$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
588.2.o.a	$588$	$2$	588.o	28.f	$6$	$8$	$4$	$4.695$	8.0.432972864.2	$_{}$	None	None		$4$	$0$	$1$	$-4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}-\beta _{6})q^{2}+\beta _{2}q^{3}+\beta _{5}q^{4}+\cdots$
588.2.o.b	$588$	$2$	588.o	28.f	$6$	$8$	$4$	$4.695$	8.0.562828176.1	$_{}$	None	None		$2$	$0$	$1$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{6}q^{2}-\beta _{3}q^{3}+(\beta _{1}-\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
588.2.o.c	$588$	$2$	588.o	28.f	$6$	$8$	$4$	$4.695$	8.0.432972864.2	$_{}$	None	None		$4$	$0$	$1$	$4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}-\beta _{6})q^{2}-\beta _{2}q^{3}+\beta _{5}q^{4}+\cdots$
588.2.o.d	$588$	$2$	588.o	28.f	$6$	$8$	$4$	$4.695$	8.0.562828176.1	$_{}$	None	None		$2$	$0$	$1$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{4}q^{2}+(1-\beta _{3})q^{3}+(\beta _{2}+\beta _{5}-\beta _{7})q^{4}+\cdots$
588.2.o.e	$588$	$2$	588.o	28.f	$6$	$24$	$12$	$4.695$		$_{}$	None	None		$4$	$0$	$-4$	$-12$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$

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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.