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 130 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
435.1.b.a	$435$	$1$	435.b	435.b	$2$	$4$	$4$	$0.217$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{145}) $		✓	✓	✓	435.1.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-\zeta_{8}q^{3}-q^{4}+\zeta_{8}^{2}q^{5}+\cdots$
435.2.a.a	$435$	$2$	435.a	1.a	$1$	$1$	$1$	$3.473$	$\Q$	$_{}$	None	None	✓	✓			435.2.a.a	$1$	$0$	$-1$	$1$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}-4q^{7}+\cdots$
435.2.a.b	$435$	$2$	435.a	1.a	$1$	$1$	$1$	$3.473$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	435.2.a.b	$1$	$0$	$0$	$-1$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{5}-2q^{7}+q^{9}+q^{11}+\cdots$
435.2.a.c	$435$	$2$	435.a	1.a	$1$	$1$	$1$	$3.473$	$\Q$	$_{}$	None	None	✓	✓			435.2.a.c	$1$	$0$	$0$	$1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}+2q^{7}+q^{9}+3q^{11}+\cdots$
435.2.a.d	$435$	$2$	435.a	1.a	$1$	$1$	$1$	$3.473$	$\Q$	$_{}$	None	None	✓	✓			435.2.a.d	$1$	$0$	$1$	$1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+4q^{7}+\cdots$
435.2.a.e	$435$	$2$	435.a	1.a	$1$	$2$	$2$	$3.473$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓	✓	435.2.a.e	$1$	$1$	$-1$	$2$	$-2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots$
435.2.a.f	$435$	$2$	435.a	1.a	$1$	$2$	$2$	$3.473$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓	✓			435.2.a.f	$1$	$0$	$-1$	$2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(3+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots$
435.2.a.g	$435$	$2$	435.a	1.a	$1$	$2$	$2$	$3.473$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓		435.2.a.g	$1$	$0$	$0$	$2$	$-2$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+3q^{4}-q^{5}-\beta q^{6}+2q^{7}+\cdots$
435.2.a.h	$435$	$2$	435.a	1.a	$1$	$2$	$2$	$3.473$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			435.2.a.h	$1$	$0$	$1$	$2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots$
435.2.a.i	$435$	$2$	435.a	1.a	$1$	$3$	$3$	$3.473$	3.3.469.1	$_{}$	None	None	✓	✓	✓	✓	435.2.a.i	$1$	$0$	$1$	$-3$	$3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
435.2.a.j	$435$	$2$	435.a	1.a	$1$	$4$	$4$	$3.473$	4.4.2225.1	$_{}$	None	None	✓	✓	✓	✓	435.2.a.j	$1$	$1$	$-3$	$-4$	$-4$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
435.2.c.a	$435$	$2$	435.c	5.b	$2$	$2$	$2$	$3.473$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			435.2.c.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}+iq^{3}-2q^{4}+(-2-i)q^{5}+\cdots$
435.2.c.b	$435$	$2$	435.c	5.b	$2$	$2$	$2$	$3.473$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			435.2.c.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-iq^{3}+q^{4}+(1-2i)q^{5}+q^{6}+\cdots$
435.2.c.c	$435$	$2$	435.c	5.b	$2$	$4$	$4$	$3.473$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			435.2.c.c	$2$	$0$	$0$	$0$	$-4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}q^{2}+\zeta_{8}q^{3}+q^{4}+(-1+2\zeta_{8}+\cdots)q^{5}+\cdots$
435.2.c.d	$435$	$2$	435.c	5.b	$2$	$10$	$10$	$3.473$	10.0.$\cdots$.1	$_{}$	None	None		✓			435.2.c.d	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{2}+\beta _{9})q^{2}-\beta _{4}q^{3}+(-1+\cdots)q^{4}+\cdots$
435.2.c.e	$435$	$2$	435.c	5.b	$2$	$10$	$10$	$3.473$	10.0.$\cdots$.1	$_{}$	None	None		✓			435.2.c.e	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{4}+\beta _{6})q^{2}-\beta _{6}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
435.2.d.a	$435$	$2$	435.d	29.b	$2$	$10$	$10$	$3.473$	10.0.$\cdots$.1	$_{}$	None	None		✓			435.2.d.a	$2$	$0$	$0$	$0$	$-10$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2})q^{4}-q^{5}+\cdots$
435.2.d.b	$435$	$2$	435.d	29.b	$2$	$10$	$10$	$3.473$	10.0.$\cdots$.1	$_{}$	None	None		✓			435.2.d.b	$2$	$0$	$0$	$0$	$10$	$8$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{7}q^{3}+(-1+\beta _{2})q^{4}+q^{5}+\cdots$
435.2.f.a	$435$	$2$	435.f	145.d	$2$	$2$	$2$	$3.473$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			435.2.f.a	$2$	$0$	$-4$	$2$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2q^{2}+q^{3}+2q^{4}+(2+i)q^{5}-2q^{6}+\cdots$
435.2.f.b	$435$	$2$	435.f	145.d	$2$	$2$	$2$	$3.473$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			435.2.f.b	$2$	$1$	$-2$	$-2$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-q^{3}-q^{4}+(-1+i)q^{5}+q^{6}+\cdots$
435.2.f.c	$435$	$2$	435.f	145.d	$2$	$2$	$2$	$3.473$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			435.2.f.b	$2$	$0$	$2$	$2$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{3}-q^{4}+(-1+i)q^{5}+q^{6}+\cdots$
435.2.f.d	$435$	$2$	435.f	145.d	$2$	$2$	$2$	$3.473$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			435.2.f.a	$2$	$0$	$4$	$-2$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{2}-q^{3}+2q^{4}+(2+i)q^{5}-2q^{6}+\cdots$
435.2.f.e	$435$	$2$	435.f	145.d	$2$	$12$	$12$	$3.473$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			435.2.f.e	$2$	$0$	$0$	$-12$	$-6$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}-q^{3}+(1-\beta _{3})q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots$
435.2.f.f	$435$	$2$	435.f	145.d	$2$	$12$	$12$	$3.473$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓			435.2.f.e	$2$	$0$	$0$	$12$	$-6$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+q^{3}+(1-\beta _{3})q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots$
435.2.j.a	$435$	$2$	435.j	145.e	$4$	$2$	$1$	$3.473$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			435.2.j.a	$2$	$0$	$0$	$-2$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+iq^{2}-q^{3}+q^{4}+(2+i)q^{5}-iq^{6}+\cdots$
435.2.j.b	$435$	$2$	435.j	145.e	$4$	$4$	$2$	$3.473$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			435.2.j.b	$2$	$0$	$0$	$-4$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{12}^{2}q^{2}-q^{3}-q^{4}+(-1-2\zeta_{12}+\cdots)q^{5}+\cdots$
435.2.j.c	$435$	$2$	435.j	145.e	$4$	$24$	$12$	$3.473$		$_{}$	None	None		✓			435.2.j.c	$2$	$0$	$0$	$-24$	$-4$	$0$			$\mathrm{SU}(2)[C_{4}]$
435.2.j.d	$435$	$2$	435.j	145.e	$4$	$30$	$15$	$3.473$		$_{}$	None	None		✓	✓		435.2.j.d	$2$	$0$	$0$	$30$	$4$	$0$			$\mathrm{SU}(2)[C_{4}]$
435.2.l.a	$435$	$2$	435.l	435.l	$4$	$112$	$56$	$3.473$		$_{}$	None	None		✓	✓	✓	435.2.l.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
435.2.m.a	$435$	$2$	435.m	15.e	$4$	$4$	$2$	$3.473$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			435.2.m.a	$2$	$1$	$-4$	$-4$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}^{2}+\cdots)q^{3}+\cdots$
435.2.m.b	$435$	$2$	435.m	15.e	$4$	$4$	$2$	$3.473$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			435.2.m.a	$2$	$0$	$4$	$4$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots$
435.2.m.c	$435$	$2$	435.m	15.e	$4$	$52$	$26$	$3.473$		$_{}$	None	None		✓			435.2.m.c	$2$	$0$	$-4$	$-6$	$-4$	$0$			$\mathrm{SU}(2)[C_{4}]$
435.2.m.d	$435$	$2$	435.m	15.e	$4$	$52$	$26$	$3.473$		$_{}$	None	None		✓			435.2.m.c	$2$	$0$	$4$	$2$	$4$	$0$			$\mathrm{SU}(2)[C_{4}]$
435.2.p.a	$435$	$2$	435.p	435.p	$4$	$112$	$56$	$3.473$		$_{}$	None	None		✓	✓	✓	435.2.p.a	$8$	$0$	$0$	$0$	$0$	$-16$			$\mathrm{SU}(2)[C_{4}]$
435.2.q.a	$435$	$2$	435.q	87.f	$4$	$4$	$2$	$3.473$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			435.2.q.a	$2$	$1$	$-4$	$-4$	$4$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}^{2}+\cdots)q^{3}+\cdots$
435.2.q.b	$435$	$2$	435.q	87.f	$4$	$4$	$2$	$3.473$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			435.2.q.a	$2$	$0$	$4$	$-4$	$-4$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}^{2}+\cdots)q^{3}+\cdots$
435.2.q.c	$435$	$2$	435.q	87.f	$4$	$36$	$18$	$3.473$		$_{}$	None	None		✓			435.2.q.c	$2$	$0$	$-4$	$6$	$-36$	$8$			$\mathrm{SU}(2)[C_{4}]$
435.2.q.d	$435$	$2$	435.q	87.f	$4$	$36$	$18$	$3.473$		$_{}$	None	None		✓			435.2.q.c	$2$	$0$	$4$	$2$	$36$	$8$			$\mathrm{SU}(2)[C_{4}]$
435.2.s.a	$435$	$2$	435.s	145.j	$4$	$2$	$1$	$3.473$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			435.2.j.a	$2$	$1$	$2$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}-iq^{3}-q^{4}+(-2+i)q^{5}-iq^{6}+\cdots$
435.2.s.b	$435$	$2$	435.s	145.j	$4$	$4$	$2$	$3.473$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			435.2.j.b	$2$	$0$	$0$	$0$	$4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}+q^{4}+(1-2\zeta_{12}+\cdots)q^{5}+\cdots$
435.2.s.c	$435$	$2$	435.s	145.j	$4$	$24$	$12$	$3.473$		$_{}$	None	None		✓			435.2.j.c	$2$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{4}]$
435.2.s.d	$435$	$2$	435.s	145.j	$4$	$30$	$15$	$3.473$		$_{}$	None	None		✓	✓		435.2.j.d	$2$	$0$	$2$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{4}]$
435.2.u.a	$435$	$2$	435.u	29.d	$7$	$30$	$5$	$3.473$		$_{}$	None	None		✓			435.2.u.a	$2$	$0$	$1$	$-5$	$5$	$0$			$\mathrm{SU}(2)[C_{7}]$
435.2.u.b	$435$	$2$	435.u	29.d	$7$	$30$	$5$	$3.473$		$_{}$	None	None		✓			435.2.u.b	$2$	$0$	$1$	$5$	$-5$	$4$			$\mathrm{SU}(2)[C_{7}]$
435.2.u.c	$435$	$2$	435.u	29.d	$7$	$30$	$5$	$3.473$		$_{}$	None	None		✓			435.2.u.c	$2$	$0$	$3$	$-5$	$-5$	$4$			$\mathrm{SU}(2)[C_{7}]$
435.2.u.d	$435$	$2$	435.u	29.d	$7$	$30$	$5$	$3.473$		$_{}$	None	None		✓			435.2.u.d	$2$	$0$	$3$	$5$	$5$	$0$			$\mathrm{SU}(2)[C_{7}]$
435.2.x.a	$435$	$2$	435.x	145.l	$14$	$96$	$16$	$3.473$		$_{}$	None	None		✓			435.2.x.a	$2$	$0$	$-2$	$16$	$-3$	$0$			$\mathrm{SU}(2)[C_{14}]$
435.2.x.b	$435$	$2$	435.x	145.l	$14$	$96$	$16$	$3.473$		$_{}$	None	None		✓			435.2.x.a	$2$	$0$	$2$	$-16$	$11$	$0$			$\mathrm{SU}(2)[C_{14}]$
435.2.z.a	$435$	$2$	435.z	29.e	$14$	$60$	$10$	$3.473$		$_{}$	None	None		✓			435.2.z.a	$2$	$0$	$0$	$0$	$-10$	$-8$			$\mathrm{SU}(2)[C_{14}]$
435.2.z.b	$435$	$2$	435.z	29.e	$14$	$60$	$10$	$3.473$		$_{}$	None	None		✓			435.2.z.b	$2$	$0$	$0$	$0$	$10$	$0$			$\mathrm{SU}(2)[C_{14}]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
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Abelian varieties over $\F_{q}$

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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.