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 61 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
460.1.d.a	$460$	$1$	460.d	115.c	$2$	$1$	$1$	$0.230$	$\Q$	$D_{3}$	$\Q(\sqrt{-115}) $	None	✓	✓			460.1.d.a	$2$	$0$	$0$	$0$	$-1$	$1$		$1$		$q-q^{5}+q^{7}+q^{9}+q^{17}-q^{23}+q^{25}+\cdots$
460.1.d.b	$460$	$1$	460.d	115.c	$2$	$1$	$1$	$0.230$	$\Q$	$D_{3}$	$\Q(\sqrt{-115}) $	None	✓	✓			460.1.d.a	$2$	$0$	$0$	$0$	$1$	$-1$		$1$		$q+q^{5}-q^{7}+q^{9}-q^{17}+q^{23}+q^{25}+\cdots$
460.1.n.a	$460$	$1$	460.n	460.n	$22$	$10$	$1$	$0.230$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-5}) $	None		✓			460.1.n.a	$4$	$0$	$-1$	$-2$	$-1$	$9$		$1$		$q+\zeta_{22}^{10}q^{2}+(\zeta_{22}^{2}+\zeta_{22}^{4})q^{3}-\zeta_{22}^{9}q^{4}+\cdots$
460.1.n.b	$460$	$1$	460.n	460.n	$22$	$10$	$1$	$0.230$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-5}) $	None		✓			460.1.n.a	$4$	$0$	$1$	$2$	$-1$	$-9$		$1$		$q-\zeta_{22}^{10}q^{2}+(-\zeta_{22}^{2}-\zeta_{22}^{4})q^{3}+\cdots$
460.2.a.a	$460$	$2$	460.a	1.a	$1$	$1$	$1$	$3.673$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	460.2.a.a	$1$	$1$	$0$	$-1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{7}-2q^{9}-4q^{11}+\cdots$
460.2.a.b	$460$	$2$	460.a	1.a	$1$	$1$	$1$	$3.673$	$\Q$	$_{}$	None	None	✓	✓			460.2.a.b	$1$	$0$	$0$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}-3q^{9}+6q^{11}+6q^{13}+\cdots$
460.2.a.c	$460$	$2$	460.a	1.a	$1$	$1$	$1$	$3.673$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	460.2.a.c	$1$	$1$	$0$	$1$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-4q^{7}-2q^{9}-6q^{11}+\cdots$
460.2.a.d	$460$	$2$	460.a	1.a	$1$	$1$	$1$	$3.673$	$\Q$	$_{}$	None	None	✓	✓			460.2.a.d	$1$	$0$	$0$	$3$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-q^{5}+2q^{7}+6q^{9}-3q^{13}+\cdots$
460.2.a.e	$460$	$2$	460.a	1.a	$1$	$2$	$2$	$3.673$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓	✓	460.2.a.e	$1$	$0$	$0$	$1$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}+(1-\beta )q^{7}+(1+\beta )q^{9}+\cdots$
460.2.c.a	$460$	$2$	460.c	5.b	$2$	$12$	$12$	$3.673$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓	✓	460.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{5}+\beta _{6})q^{3}+\beta _{9}q^{5}+(-\beta _{1}-\beta _{6}+\cdots)q^{7}+\cdots$
460.2.e.a	$460$	$2$	460.e	92.b	$2$	$16$	$16$	$3.673$	16.0.$\cdots$.3	$_{}$	None	None		✓			460.2.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+\beta _{8}q^{3}+(-\beta _{2}+\beta _{8})q^{4}+\cdots$
460.2.e.b	$460$	$2$	460.e	92.b	$2$	$32$	$32$	$3.673$		$_{}$	None	None		✓	✓		460.2.e.b	$4$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
460.2.g.a	$460$	$2$	460.g	460.g	$2$	$4$	$4$	$3.673$	$\Q(\sqrt{2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5}) $	None		✓			460.2.g.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}-\beta _{2}q^{3}+2q^{4}+\beta _{3}q^{5}+2q^{6}+\cdots$
460.2.g.b	$460$	$2$	460.g	460.g	$2$	$8$	$8$	$3.673$	8.0.207360000.1	$_{}$	None	None		✓			460.2.g.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(\beta _{2}-\beta _{4})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots$
460.2.g.c	$460$	$2$	460.g	460.g	$2$	$56$	$56$	$3.673$		$_{}$	None	None		✓	✓		460.2.g.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
460.2.i.a	$460$	$2$	460.i	115.e	$4$	$8$	$4$	$3.673$	8.0.$\cdots$.3	$_{}$	None	None		✓			460.2.i.a	$4$	$0$	$0$	$-8$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{3})q^{3}+(-\beta _{1}+\beta _{6})q^{5}-\beta _{2}q^{7}+\cdots$
460.2.i.b	$460$	$2$	460.i	115.e	$4$	$16$	$8$	$3.673$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		460.2.i.b	$4$	$0$	$0$	$4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{6}q^{3}-\beta _{3}q^{5}+(-\beta _{3}+\beta _{15})q^{7}+\cdots$
460.2.j.a	$460$	$2$	460.j	20.e	$4$	$132$	$66$	$3.673$		$_{}$	None	None		✓	✓	✓	460.2.j.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
460.2.m.a	$460$	$2$	460.m	23.c	$11$	$30$	$3$	$3.673$		$_{}$	None	None		✓			460.2.m.a	$2$	$0$	$0$	$0$	$-3$	$1$			$\mathrm{SU}(2)[C_{11}]$
460.2.m.b	$460$	$2$	460.m	23.c	$11$	$50$	$5$	$3.673$		$_{}$	None	None		✓	✓		460.2.m.b	$2$	$0$	$0$	$0$	$5$	$-1$			$\mathrm{SU}(2)[C_{11}]$
460.2.o.a	$460$	$2$	460.o	460.o	$22$	$40$	$4$	$3.673$		$_{}$	$\Q(\sqrt{-5}) $	None		✓			460.2.o.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{22}]$
460.2.o.b	$460$	$2$	460.o	460.o	$22$	$640$	$64$	$3.673$		$_{}$	None	None		✓	✓		460.2.o.b	$8$	$0$	$0$	$0$	$-22$	$0$			$\mathrm{SU}(2)[C_{22}]$
460.2.q.a	$460$	$2$	460.q	92.h	$22$	$480$	$48$	$3.673$		$_{}$	None	None		✓	✓	✓	460.2.q.a	$4$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
460.2.s.a	$460$	$2$	460.s	115.j	$22$	$120$	$12$	$3.673$		$_{}$	None	None		✓	✓	✓	460.2.s.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
460.2.w.a	$460$	$2$	460.w	460.w	$44$	$1360$	$68$	$3.673$		$_{}$	None	None		✓	✓	✓	460.2.w.a	$8$	$0$	$-18$	$0$	$-36$	$0$			$\mathrm{SU}(2)[C_{44}]$
460.2.x.a	$460$	$2$	460.x	115.l	$44$	$240$	$12$	$3.673$		$_{}$	None	None		✓	✓	✓	460.2.x.a	$4$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{44}]$
460.3.b.a	$460$	$3$	460.b	4.b	$2$	$88$	$88$	$12.534$		$_{}$	None	None		✓	✓	✓	460.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
460.3.d.a	$460$	$3$	460.d	115.c	$2$	$2$	$2$	$12.534$	$\Q(\sqrt{345}) $	$_{}$	$\Q(\sqrt{-115}) $	None	✓	✓			460.3.d.a	$2$	$0$	$0$	$0$	$-10$	$-9$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-5q^{5}+(-4-\beta )q^{7}+9q^{9}+(4+3\beta )q^{17}+\cdots$
460.3.d.b	$460$	$3$	460.d	115.c	$2$	$2$	$2$	$12.534$	$\Q(\sqrt{345}) $	$_{}$	$\Q(\sqrt{-115}) $	None	✓	✓			460.3.d.a	$2$	$0$	$0$	$0$	$10$	$9$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+5q^{5}+(4+\beta )q^{7}+9q^{9}+(-4-3\beta )q^{17}+\cdots$
460.3.d.c	$460$	$3$	460.d	115.c	$2$	$20$	$20$	$12.534$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓	✓		460.3.d.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}+\beta _{1}q^{5}-\beta _{16}q^{7}+(-4+\beta _{11}+\cdots)q^{9}+\cdots$
460.3.f.a	$460$	$3$	460.f	23.b	$2$	$16$	$16$	$12.534$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓	✓	460.3.f.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+\beta _{4}q^{5}-\beta _{7}q^{7}+(4+\beta _{2}+\cdots)q^{9}+\cdots$
460.3.l.a	$460$	$3$	460.l	5.c	$4$	$44$	$22$	$12.534$		$_{}$	None	None		✓	✓	✓	460.3.l.a	$2$	$0$	$0$	$0$	$8$	$16$			$\mathrm{SU}(2)[C_{4}]$
460.4.a.a	$460$	$4$	460.a	1.a	$1$	$5$	$5$	$27.141$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	460.4.a.a	$1$	$1$	$0$	$-7$	$25$	$-20$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3})q^{3}+5q^{5}+(-5-\beta _{1}+\cdots)q^{7}+\cdots$
460.4.a.b	$460$	$4$	460.a	1.a	$1$	$5$	$5$	$27.141$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	460.4.a.b	$1$	$1$	$0$	$-3$	$-25$	$8$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-5q^{5}+(2-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
460.4.a.c	$460$	$4$	460.a	1.a	$1$	$6$	$6$	$27.141$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	460.4.a.c	$1$	$0$	$0$	$-1$	$30$	$24$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+5q^{5}+(4+\beta _{3}-\beta _{4})q^{7}+\cdots$
460.4.a.d	$460$	$4$	460.a	1.a	$1$	$6$	$6$	$27.141$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	460.4.a.d	$1$	$0$	$0$	$3$	$-30$	$20$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-5q^{5}+(3+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
460.4.c.a	$460$	$4$	460.c	5.b	$2$	$32$	$32$	$27.141$		$_{}$	None	None		✓	✓	✓	460.4.c.a	$2$	$0$	$0$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{2}]$
460.4.i.a	$460$	$4$	460.i	115.e	$4$	$72$	$36$	$27.141$		$_{}$	None	None		✓	✓	✓	460.4.i.a	$4$	$0$	$0$	$8$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
460.5.d.a	$460$	$5$	460.d	115.c	$2$	$2$	$2$	$47.550$	$\Q(\sqrt{345}) $	$_{}$	$\Q(\sqrt{-115}) $	None	✓	✓			460.5.d.a	$2$	$0$	$0$	$0$	$-50$	$-17$		$3$	$\mathrm{U}(1)[D_{2}]$	$q-5^{2}q^{5}+(-10-3\beta )q^{7}+3^{4}q^{9}+\cdots$
460.5.d.b	$460$	$5$	460.d	115.c	$2$	$2$	$2$	$47.550$	$\Q(\sqrt{345}) $	$_{}$	$\Q(\sqrt{-115}) $	None	✓	✓			460.5.d.a	$2$	$0$	$0$	$0$	$50$	$17$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+5^{2}q^{5}+(10+3\beta )q^{7}+3^{4}q^{9}+(234+\cdots)q^{17}+\cdots$
460.5.d.c	$460$	$5$	460.d	115.c	$2$	$44$	$44$	$47.550$		$_{}$	None	None		✓	✓		460.5.d.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
460.5.f.a	$460$	$5$	460.f	23.b	$2$	$32$	$32$	$47.550$		$_{}$	None	None		✓	✓	✓	460.5.f.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
460.5.l.a	$460$	$5$	460.l	5.c	$4$	$88$	$44$	$47.550$		$_{}$	None	None		✓	✓	✓	460.5.l.a	$2$	$0$	$0$	$0$	$48$	$-160$			$\mathrm{SU}(2)[C_{4}]$
460.6.a.a	$460$	$6$	460.a	1.a	$1$	$9$	$9$	$73.777$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	460.6.a.a	$1$	$1$	$0$	$-31$	$-225$	$-319$	$+$	$2^{5}$	$\mathrm{SU}(2)$	$q+(-3-\beta _{1})q^{3}-5^{2}q^{5}+(-35-\beta _{1}+\cdots)q^{7}+\cdots$
460.6.a.b	$460$	$6$	460.a	1.a	$1$	$9$	$9$	$73.777$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	460.6.a.b	$1$	$1$	$0$	$-9$	$225$	$-95$	$+$	$2^{5}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}+5^{2}q^{5}+(-11+2\beta _{1}+\cdots)q^{7}+\cdots$
460.6.a.c	$460$	$6$	460.a	1.a	$1$	$10$	$10$	$73.777$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	460.6.a.c	$1$	$0$	$0$	$-13$	$-250$	$-28$	$-$	$2^{7}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}-5^{2}q^{5}+(-3+2\beta _{1}+\cdots)q^{7}+\cdots$
460.6.a.d	$460$	$6$	460.a	1.a	$1$	$10$	$10$	$73.777$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	460.6.a.d	$1$	$0$	$0$	$9$	$250$	$6$	$-$	$2^{7}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+5^{2}q^{5}+(1-\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots$
460.6.c.a	$460$	$6$	460.c	5.b	$2$	$56$	$56$	$73.777$		$_{}$	None	None		✓	✓	✓	460.6.c.a	$2$	$0$	$0$	$0$	$-60$	$0$			$\mathrm{SU}(2)[C_{2}]$
460.7.d.a	$460$	$7$	460.d	115.c	$2$	$2$	$2$	$105.825$	$\Q(\sqrt{345}) $	$_{}$	$\Q(\sqrt{-115}) $	None	✓	✓			460.7.d.a	$2$	$0$	$0$	$0$	$-250$	$594$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q-5^{3}q^{5}+(297-4\beta )q^{7}+3^{6}q^{9}+(-4103+\cdots)q^{17}+\cdots$
460.7.d.b	$460$	$7$	460.d	115.c	$2$	$2$	$2$	$105.825$	$\Q(\sqrt{345}) $	$_{}$	$\Q(\sqrt{-115}) $	None	✓	✓			460.7.d.a	$2$	$0$	$0$	$0$	$250$	$-594$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+5^{3}q^{5}+(-297-4\beta )q^{7}+3^{6}q^{9}+\cdots$

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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.