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 97 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
129.1.l.a	$129$	$1$	129.l	129.l	$14$	$6$	$1$	$0.064$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	129.1.l.a	$4$	$0$	$0$	$-1$	$0$	$-2$		$1$		$q-\zeta_{14}^{5}q^{3}+\zeta_{14}^{4}q^{4}+(-\zeta_{14}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots$
129.2.a.a	$129$	$2$	129.a	1.a	$1$	$1$	$1$	$1.030$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	129.2.a.a	$1$	$1$	$0$	$-1$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-2q^{5}-2q^{7}+q^{9}-5q^{11}+\cdots$
129.2.a.b	$129$	$2$	129.a	1.a	$1$	$1$	$1$	$1.030$	$\Q$	$_{}$	None	None	✓	✓			129.2.a.b	$1$	$0$	$1$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+2q^{5}+q^{6}-3q^{8}+\cdots$
129.2.a.c	$129$	$2$	129.a	1.a	$1$	$2$	$2$	$1.030$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓	✓	129.2.a.c	$1$	$0$	$2$	$-2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+(1-\beta )q^{5}+\cdots$
129.2.a.d	$129$	$2$	129.a	1.a	$1$	$3$	$3$	$1.030$	3.3.568.1	$_{}$	None	None	✓	✓	✓		129.2.a.d	$1$	$0$	$-2$	$3$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(3+\beta _{2})q^{4}+\cdots$
129.2.d.a	$129$	$2$	129.d	129.d	$2$	$12$	$12$	$1.030$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓	✓	129.2.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+\beta _{6}q^{3}+\beta _{9}q^{4}+\beta _{11}q^{5}+\cdots$
129.2.e.a	$129$	$2$	129.e	43.c	$3$	$2$	$1$	$1.030$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			129.2.e.a	$2$	$1$	$-4$	$-1$	$-2$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2q^{2}+(-1+\zeta_{6})q^{3}+2q^{4}+(-2+\cdots)q^{5}+\cdots$
129.2.e.b	$129$	$2$	129.e	43.c	$3$	$6$	$3$	$1.030$	6.0.1783323.2	$_{}$	None	None		✓			129.2.e.b	$2$	$0$	$-2$	$3$	$-3$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+\beta _{4}q^{3}+(1+\beta _{3})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$
129.2.e.c	$129$	$2$	129.e	43.c	$3$	$6$	$3$	$1.030$	6.0.64827.1	$_{}$	None	None		✓			129.2.e.c	$2$	$0$	$2$	$-3$	$1$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}-\beta _{5}q^{3}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
129.2.h.a	$129$	$2$	129.h	129.h	$6$	$2$	$1$	$1.030$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			129.2.h.a	$4$	$1$	$0$	$-3$	$0$	$-9$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-1-\zeta_{6})q^{3}-2q^{4}+(-6+3\zeta_{6})q^{7}+\cdots$
129.2.h.b	$129$	$2$	129.h	129.h	$6$	$24$	$12$	$1.030$		$_{}$	None	None		✓	✓		129.2.h.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
129.2.i.a	$129$	$2$	129.i	43.e	$7$	$6$	$1$	$1.030$	$\Q(\zeta_{14})$	$_{}$	None	None		✓			129.2.i.a	$2$	$0$	$-5$	$1$	$10$	$0$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-\zeta_{14}+\zeta_{14}^{2}-\zeta_{14}^{3}+\zeta_{14}^{4}+\cdots)q^{2}+\cdots$
129.2.i.b	$129$	$2$	129.i	43.e	$7$	$12$	$2$	$1.030$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			129.2.i.b	$2$	$0$	$3$	$2$	$-10$	$14$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(1-\beta _{2}-\beta _{6}-\beta _{7}-\beta _{8}+\beta _{9}+\beta _{11})q^{2}+\cdots$
129.2.i.c	$129$	$2$	129.i	43.e	$7$	$30$	$5$	$1.030$		$_{}$	None	None		✓	✓		129.2.i.c	$2$	$0$	$-2$	$-5$	$-4$	$2$			$\mathrm{SU}(2)[C_{7}]$
129.2.j.a	$129$	$2$	129.j	129.j	$14$	$72$	$12$	$1.030$		$_{}$	None	None		✓	✓	✓	129.2.j.a	$4$	$0$	$0$	$-7$	$0$	$0$			$\mathrm{SU}(2)[C_{14}]$
129.2.m.a	$129$	$2$	129.m	43.g	$21$	$36$	$3$	$1.030$		$_{}$	None	None		✓			129.2.m.a	$2$	$0$	$2$	$-3$	$3$	$-11$			$\mathrm{SU}(2)[C_{21}]$
129.2.m.b	$129$	$2$	129.m	43.g	$21$	$48$	$4$	$1.030$		$_{}$	None	None		✓	✓		129.2.m.b	$2$	$0$	$2$	$4$	$1$	$-16$			$\mathrm{SU}(2)[C_{21}]$
129.2.n.a	$129$	$2$	129.n	129.n	$42$	$12$	$1$	$1.030$	$\Q(\zeta_{21})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			129.2.n.a	$4$	$0$	$0$	$3$	$0$	$9$		$1$	$\mathrm{U}(1)[D_{42}]$	$q+(2\zeta_{21}+\zeta_{21}^{8})q^{3}+(2-2\zeta_{21}+2\zeta_{21}^{3}+\cdots)q^{4}+\cdots$
129.2.n.b	$129$	$2$	129.n	129.n	$42$	$144$	$12$	$1.030$		$_{}$	None	None		✓	✓		129.2.n.b	$4$	$0$	$0$	$-14$	$0$	$-42$			$\mathrm{SU}(2)[C_{42}]$
129.3.b.a	$129$	$3$	129.b	43.b	$2$	$14$	$14$	$3.515$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		✓	✓	✓	129.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-\beta _{9}q^{3}+(-3+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots$
129.3.c.a	$129$	$3$	129.c	3.b	$2$	$28$	$28$	$3.515$		$_{}$	None	None		✓	✓	✓	129.3.c.a	$2$	$0$	$0$	$2$	$0$	$8$			$\mathrm{SU}(2)[C_{2}]$
129.3.f.a	$129$	$3$	129.f	129.f	$6$	$2$	$1$	$3.515$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			129.3.f.a	$4$	$0$	$0$	$3$	$0$	$13$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+3\zeta_{6}q^{3}+4q^{4}+(13-13\zeta_{6})q^{7}+\cdots$
129.3.f.b	$129$	$3$	129.f	129.f	$6$	$52$	$26$	$3.515$		$_{}$	None	None		✓	✓		129.3.f.b	$4$	$0$	$0$	$-8$	$0$	$-16$			$\mathrm{SU}(2)[C_{6}]$
129.3.g.a	$129$	$3$	129.g	43.d	$6$	$2$	$1$	$3.515$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			129.3.g.a	$2$	$0$	$0$	$-3$	$0$	$18$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+2\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+\cdots$
129.3.g.b	$129$	$3$	129.g	43.d	$6$	$14$	$7$	$3.515$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		✓			129.3.g.b	$2$	$0$	$0$	$-21$	$3$	$-36$		$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-1-\beta _{8})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots$
129.3.g.c	$129$	$3$	129.g	43.d	$6$	$14$	$7$	$3.515$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		✓			129.3.g.c	$2$	$0$	$0$	$21$	$-3$	$15$		$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{3}-\beta _{4})q^{2}+(2-\beta _{2})q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots$
129.3.k.a	$129$	$3$	129.k	43.f	$14$	$84$	$14$	$3.515$		$_{}$	None	None		✓	✓	✓	129.3.k.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{14}]$
129.3.l.a	$129$	$3$	129.l	129.l	$14$	$168$	$28$	$3.515$		$_{}$	None	None		✓	✓	✓	129.3.l.a	$4$	$0$	$0$	$-9$	$0$	$-36$			$\mathrm{SU}(2)[C_{14}]$
129.3.o.a	$129$	$3$	129.o	129.o	$42$	$12$	$1$	$3.515$	$\Q(\zeta_{21})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			129.3.o.a	$4$	$0$	$0$	$-3$	$0$	$-13$		$1$	$\mathrm{U}(1)[D_{42}]$	$q+(3\zeta_{21}^{2}+3\zeta_{21}^{9})q^{3}+4\zeta_{21}^{3}q^{4}+\cdots$
129.3.o.b	$129$	$3$	129.o	129.o	$42$	$312$	$26$	$3.515$		$_{}$	None	None		✓	✓		129.3.o.b	$4$	$0$	$0$	$-6$	$0$	$2$			$\mathrm{SU}(2)[C_{42}]$
129.3.p.a	$129$	$3$	129.p	43.h	$42$	$84$	$7$	$3.515$		$_{}$	None	None		✓			129.3.p.a	$2$	$0$	$0$	$-21$	$3$	$-15$			$\mathrm{SU}(2)[C_{42}]$
129.3.p.b	$129$	$3$	129.p	43.h	$42$	$96$	$8$	$3.515$		$_{}$	None	None		✓	✓		129.3.p.b	$2$	$0$	$0$	$24$	$-3$	$18$			$\mathrm{SU}(2)[C_{42}]$
129.4.a.a	$129$	$4$	129.a	1.a	$1$	$1$	$1$	$7.611$	$\Q$	$_{}$	None	None	✓	✓			129.4.a.a	$1$	$1$	$-1$	$3$	$-2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}-7q^{4}-2q^{5}-3q^{6}+\cdots$
129.4.a.b	$129$	$4$	129.a	1.a	$1$	$1$	$1$	$7.611$	$\Q$	$_{}$	None	None	✓	✓			129.4.a.b	$1$	$0$	$4$	$-3$	$11$	$9$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}-3q^{3}+8q^{4}+11q^{5}-12q^{6}+\cdots$
129.4.a.c	$129$	$4$	129.a	1.a	$1$	$2$	$2$	$7.611$	$\Q(\sqrt{10}) $	$_{}$	None	None	✓	✓	✓		129.4.a.c	$1$	$1$	$-2$	$6$	$-14$	$-38$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+3q^{3}+(3-2\beta )q^{4}+\cdots$
129.4.a.d	$129$	$4$	129.a	1.a	$1$	$5$	$5$	$7.611$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	129.4.a.d	$1$	$1$	$-3$	$-15$	$-12$	$-18$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-3q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
129.4.a.e	$129$	$4$	129.a	1.a	$1$	$5$	$5$	$7.611$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	✓	✓		129.4.a.e	$1$	$0$	$-3$	$-15$	$-3$	$1$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-3q^{3}+(5+\beta _{2}+\beta _{4})q^{4}+\cdots$
129.4.a.f	$129$	$4$	129.a	1.a	$1$	$8$	$8$	$7.611$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	129.4.a.f	$1$	$0$	$1$	$24$	$4$	$52$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+3q^{3}+(7+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots$
129.4.d.a	$129$	$4$	129.d	129.d	$2$	$2$	$2$	$7.611$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			129.4.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{3}-8 q^{4}+6\beta q^{7}-27 q^{9}+\cdots$
129.4.d.b	$129$	$4$	129.d	129.d	$2$	$40$	$40$	$7.611$		$_{}$	None	None		✓	✓		129.4.d.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
129.4.e.a	$129$	$4$	129.e	43.c	$3$	$20$	$10$	$7.611$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓			129.4.e.a	$2$	$0$	$2$	$-30$	$6$	$24$		$2^{6}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{3})q^{2}-3\beta _{4}q^{3}+(3+\beta _{2})q^{4}+\cdots$
129.4.e.b	$129$	$4$	129.e	43.c	$3$	$24$	$12$	$7.611$		$_{}$	None	None		✓	✓		129.4.e.b	$2$	$0$	$2$	$36$	$10$	$30$			$\mathrm{SU}(2)[C_{3}]$
129.4.h.a	$129$	$4$	129.h	129.h	$6$	$84$	$42$	$7.611$		$_{}$	None	None		✓	✓	✓	129.4.h.a	$4$	$0$	$0$	$-3$	$0$	$-24$			$\mathrm{SU}(2)[C_{6}]$
129.4.i.a	$129$	$4$	129.i	43.e	$7$	$66$	$11$	$7.611$		$_{}$	None	None		✓			129.4.i.a	$2$	$0$	$2$	$-33$	$12$	$-118$			$\mathrm{SU}(2)[C_{7}]$
129.4.i.b	$129$	$4$	129.i	43.e	$7$	$66$	$11$	$7.611$		$_{}$	None	None		✓			129.4.i.b	$2$	$0$	$2$	$33$	$4$	$-90$			$\mathrm{SU}(2)[C_{7}]$
129.4.j.a	$129$	$4$	129.j	129.j	$14$	$12$	$2$	$7.611$	$\Q(\zeta_{21})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			129.4.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 3^{6}$	$\mathrm{U}(1)[D_{14}]$	$q+\beta_{11} q^{3}+8\beta_{5} q^{4}+(3\beta_{11}-3\beta_{10}+\cdots+10\beta_{2})q^{7}+\cdots$
129.4.j.b	$129$	$4$	129.j	129.j	$14$	$240$	$40$	$7.611$		$_{}$	None	None		✓	✓		129.4.j.b	$4$	$0$	$0$	$-7$	$0$	$0$			$\mathrm{SU}(2)[C_{14}]$
129.4.m.a	$129$	$4$	129.m	43.g	$21$	$120$	$10$	$7.611$		$_{}$	None	None		✓			129.4.m.a	$2$	$0$	$-2$	$30$	$-6$	$74$			$\mathrm{SU}(2)[C_{21}]$
129.4.m.b	$129$	$4$	129.m	43.g	$21$	$144$	$12$	$7.611$		$_{}$	None	None		✓	✓		129.4.m.b	$2$	$0$	$-2$	$-36$	$-10$	$68$			$\mathrm{SU}(2)[C_{21}]$
129.4.n.a	$129$	$4$	129.n	129.n	$42$	$504$	$42$	$7.611$		$_{}$	None	None		✓	✓	✓	129.4.n.a	$4$	$0$	$0$	$-11$	$0$	$-18$			$\mathrm{SU}(2)[C_{42}]$

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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.