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 (48 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
2601.1.b.a	$2601$	$1$	2601.b	3.b	$2$	$2$	$2$	$1.298$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\beta q^{2}-q^{4}-\beta q^{5}-q^{7}-2q^{10}+\cdots$
2601.1.b.b	$2601$	$1$	2601.b	3.b	$2$	$2$	$2$	$1.298$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\beta q^{2}-q^{4}-\beta q^{5}+q^{7}+2q^{10}+\cdots$
2601.1.c.a	$2601$	$1$	2601.c	51.c	$2$	$4$	$4$	$1.298$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}-q^{4}+(-\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{5}+\cdots$
2601.1.g.a	$2601$	$1$	2601.g	51.f	$4$	$4$	$2$	$1.298$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+q^{4}+(-1+\zeta_{8}^{2}+\cdots)q^{5}+\cdots$
2601.1.g.b	$2601$	$1$	2601.g	51.f	$4$	$4$	$2$	$1.298$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$4$	$0$		$1$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+q^{4}+(1-\zeta_{8}^{2})q^{5}+\cdots$
2601.1.k.a	$2601$	$1$	2601.k	51.g	$8$	$8$	$2$	$1.298$	$\Q(\zeta_{16})$	$S_{4}$	None	None		$8$	$0$	$-8$	$0$	$0$	$0$		$1$		$q+(-1+\zeta_{16}^{4})q^{2}-\zeta_{16}^{4}q^{4}+(\zeta_{16}+\cdots)q^{5}+\cdots$
2601.1.k.b	$2601$	$1$	2601.k	51.g	$8$	$8$	$2$	$1.298$	$\Q(\zeta_{16})$	$S_{4}$	None	None		$8$	$0$	$8$	$0$	$0$	$0$		$1$		$q+(1-\zeta_{16}^{4})q^{2}-\zeta_{16}^{4}q^{4}+(\zeta_{16}-\zeta_{16}^{5}+\cdots)q^{5}+\cdots$
2601.1.p.a	$2601$	$1$	2601.p	17.e	$16$	$8$	$1$	$1.298$	$\Q(\zeta_{16})$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-51}) $	$\Q(\sqrt{17}) $		$32$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{6}q^{4}-\zeta_{16}^{2}q^{13}-\zeta_{16}^{4}q^{16}+\cdots$
2601.1.p.b	$2601$	$1$	2601.p	17.e	$16$	$16$	$2$	$1.298$	16.0.$\cdots$.2	$D_{6}$	$\Q(\sqrt{-3}) $	None		$32$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta _{12}q^{4}+\beta _{3}q^{7}+\beta _{4}q^{13}-\beta _{8}q^{16}+\cdots$
2601.1.x.a	$2601$	$1$	2601.x	153.t	$48$	$32$	$2$	$1.298$	$\Q(\zeta_{96})$	$A_{4}$	None	None		$32$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{96}^{38}q^{2}-\zeta_{96}^{21}q^{3}+\zeta_{96}^{25}q^{5}+\cdots$
2601.2.a.a	$2601$	$2$	2601.a	1.a	$1$	$1$	$1$	$20.769$	$\Q$	$_{}$	None	None	✓	$1$	$2$	$-2$	$0$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-3q^{5}-2q^{7}+6q^{10}+\cdots$
2601.2.a.b	$2601$	$2$	2601.a	1.a	$1$	$1$	$1$	$20.769$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+q^{5}+2q^{7}-2q^{10}+\cdots$
2601.2.a.c	$2601$	$2$	2601.a	1.a	$1$	$1$	$1$	$20.769$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-2$	$0$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+3q^{5}+2q^{7}-6q^{10}+\cdots$
2601.2.a.d	$2601$	$2$	2601.a	1.a	$1$	$1$	$1$	$20.769$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{5}+q^{7}+3q^{8}+2q^{10}+\cdots$
2601.2.a.e	$2601$	$2$	2601.a	1.a	$1$	$1$	$1$	$20.769$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+2q^{5}-q^{7}+3q^{8}-2q^{10}+\cdots$
2601.2.a.f	$2601$	$2$	2601.a	1.a	$1$	$1$	$1$	$20.769$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+3q^{5}+4q^{7}-3q^{11}-q^{13}+\cdots$
2601.2.a.g	$2601$	$2$	2601.a	1.a	$1$	$1$	$1$	$20.769$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-2q^{5}-4q^{7}-3q^{8}-2q^{10}+\cdots$
2601.2.a.h	$2601$	$2$	2601.a	1.a	$1$	$1$	$1$	$20.769$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-2q^{5}-q^{7}-3q^{8}-2q^{10}+\cdots$
2601.2.a.i	$2601$	$2$	2601.a	1.a	$1$	$1$	$1$	$20.769$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-4q^{7}-3q^{8}-4q^{11}+\cdots$
2601.2.a.j	$2601$	$2$	2601.a	1.a	$1$	$1$	$1$	$20.769$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+4q^{7}-3q^{8}+4q^{11}+\cdots$
2601.2.a.k	$2601$	$2$	2601.a	1.a	$1$	$1$	$1$	$20.769$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{5}+q^{7}-3q^{8}+2q^{10}+\cdots$
2601.2.a.l	$2601$	$2$	2601.a	1.a	$1$	$1$	$1$	$20.769$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$2$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-q^{5}+2q^{7}-2q^{10}+\cdots$
2601.2.a.m	$2601$	$2$	2601.a	1.a	$1$	$2$	$2$	$20.769$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+2\beta q^{5}+\cdots$
2601.2.a.n	$2601$	$2$	2601.a	1.a	$1$	$2$	$2$	$20.769$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$-2$	$0$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-2\beta q^{5}+\cdots$
2601.2.a.o	$2601$	$2$	2601.a	1.a	$1$	$2$	$2$	$20.769$	$\Q(\sqrt{17}) $	$_{}$	$\Q(\sqrt{-51}) $	None	✓	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$2$	$N(\mathrm{U}(1))$	$q-2q^{4}-\beta q^{5}+\beta q^{11}-q^{13}+4q^{16}+\cdots$
2601.2.a.p	$2601$	$2$	2601.a	1.a	$1$	$2$	$2$	$20.769$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{5}+\beta q^{7}-2\beta q^{8}-\beta q^{10}+\cdots$
2601.2.a.q	$2601$	$2$	2601.a	1.a	$1$	$2$	$2$	$20.769$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{5}-\beta q^{7}-2\beta q^{8}+\beta q^{10}+\cdots$
2601.2.a.r	$2601$	$2$	2601.a	1.a	$1$	$2$	$2$	$20.769$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}-\beta q^{5}+(2-\beta )q^{7}+\cdots$
2601.2.a.s	$2601$	$2$	2601.a	1.a	$1$	$2$	$2$	$20.769$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}+\beta q^{5}+(-2+\beta )q^{7}+\cdots$
2601.2.a.t	$2601$	$2$	2601.a	1.a	$1$	$2$	$2$	$20.769$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2+\beta )q^{4}+(1+\beta )q^{5}+(4+\beta )q^{8}+\cdots$
2601.2.a.u	$2601$	$2$	2601.a	1.a	$1$	$3$	$3$	$20.769$	$\Q(\zeta_{18})^+$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+(3\beta _{1}-\beta _{2})q^{7}+(-4\beta _{1}+3\beta _{2})q^{13}+\cdots$
2601.2.a.v	$2601$	$2$	2601.a	1.a	$1$	$3$	$3$	$20.769$	$\Q(\zeta_{18})^+$	$_{}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+(-3\beta _{1}+\beta _{2})q^{7}+(-4\beta _{1}+\cdots)q^{13}+\cdots$
2601.2.a.w	$2601$	$2$	2601.a	1.a	$1$	$3$	$3$	$20.769$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-2+\beta _{1})q^{5}-\beta _{2}q^{7}+\cdots$
2601.2.a.x	$2601$	$2$	2601.a	1.a	$1$	$3$	$3$	$20.769$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(2-\beta _{1})q^{5}+\beta _{2}q^{7}+\cdots$
2601.2.a.y	$2601$	$2$	2601.a	1.a	$1$	$3$	$3$	$20.769$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$-3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
2601.2.a.z	$2601$	$2$	2601.a	1.a	$1$	$3$	$3$	$20.769$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$3$	$0$	$3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
2601.2.a.ba	$2601$	$2$	2601.a	1.a	$1$	$4$	$4$	$20.769$	$\Q(\zeta_{16})^+$	$_{}$	None	None	✓	$2$	$0$	$-4$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+(-\beta _{1}-2\beta _{3})q^{5}+2\beta _{1}q^{7}+\cdots$
2601.2.a.bb	$2601$	$2$	2601.a	1.a	$1$	$4$	$4$	$20.769$	$\Q(\zeta_{16})^+$	$_{}$	None	None	✓	$2$	$1$	$-4$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(1+2\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
2601.2.a.bc	$2601$	$2$	2601.a	1.a	$1$	$4$	$4$	$20.769$	$\Q(\zeta_{16})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-4$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1+\beta _{1}+\beta _{3})q^{5}+\cdots$
2601.2.a.bd	$2601$	$2$	2601.a	1.a	$1$	$4$	$4$	$20.769$	$\Q(\zeta_{16})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$4$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{1}-\beta _{3})q^{5}+\cdots$
2601.2.a.be	$2601$	$2$	2601.a	1.a	$1$	$4$	$4$	$20.769$	4.4.7232.1	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$-6$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{3})q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
2601.2.a.bf	$2601$	$2$	2601.a	1.a	$1$	$4$	$4$	$20.769$	4.4.7232.1	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$6$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{3})q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
2601.2.a.bg	$2601$	$2$	2601.a	1.a	$1$	$4$	$4$	$20.769$	$\Q(\zeta_{16})^+$	$_{}$	None	None	✓	$2$	$0$	$4$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+(-\beta _{1}-2\beta _{3})q^{5}-2\beta _{1}q^{7}+\cdots$
2601.2.a.bh	$2601$	$2$	2601.a	1.a	$1$	$6$	$6$	$20.769$	6.6.3418281.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$0$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+(1+\beta _{1}+\beta _{2}-\beta _{4}+2\beta _{5})q^{4}+\cdots$
2601.2.a.bi	$2601$	$2$	2601.a	1.a	$1$	$6$	$6$	$20.769$	6.6.3418281.1	$_{}$	None	None	✓	$1$	$0$	$-3$	$0$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+(1+\beta _{1}+\beta _{2}-\beta _{4}+2\beta _{5})q^{4}+\cdots$
2601.2.a.bj	$2601$	$2$	2601.a	1.a	$1$	$6$	$6$	$20.769$	6.6.45769536.1	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$-18$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}-\beta _{3}q^{5}+(-3+\cdots)q^{7}+\cdots$
2601.2.a.bk	$2601$	$2$	2601.a	1.a	$1$	$6$	$6$	$20.769$	6.6.45769536.1	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$18$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+\beta _{3}q^{5}+(3-\beta _{2}+\cdots)q^{7}+\cdots$
2601.2.a.bl	$2601$	$2$	2601.a	1.a	$1$	$8$	$8$	$20.769$	8.8.4848615424.1	$_{}$	None	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}+(4-\beta _{2})q^{4}-\beta _{1}q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots$

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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.