LMFDB - Newform search results

Refine search

Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is twist minimal	Is self-dual

$Nk^2$	Coefficient ring index	Coefficient ring gens.	Projective image	Projective image type

				Sort order	Select

Results (1-50 of 57 matches)

Next Download displayed columns for results to

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	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	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1656.1.l.a	$1656$	$1$	1656.l	184.e	$2$	$1$	$1$	$0.826$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-46}) $	$\Q(\sqrt{2}) $	✓		184.1.e.a	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}+q^{16}+q^{23}-q^{25}+\cdots$
1656.1.l.b	$1656$	$1$	1656.l	184.e	$2$	$2$	$2$	$0.826$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-46}) $	None	✓	✓	1656.1.l.b	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-\beta q^{5}-q^{8}+\beta q^{10}+\beta q^{11}+\cdots$
1656.1.l.c	$1656$	$1$	1656.l	184.e	$2$	$2$	$2$	$0.826$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-23}) $	None			184.1.e.b	$4$	$0$	$-1$	$0$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{13}+\cdots$
1656.1.l.d	$1656$	$1$	1656.l	184.e	$2$	$2$	$2$	$0.826$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-46}) $	None	✓	✓	1656.1.l.b	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}-\beta q^{5}+q^{8}-\beta q^{10}+\beta q^{11}+\cdots$
1656.1.v.a	$1656$	$1$	1656.v	1656.v	$6$	$6$	$3$	$0.826$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-23}) $	None		✓	1656.1.v.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{2}q^{2}+\zeta_{18}q^{3}+\zeta_{18}^{4}q^{4}-\zeta_{18}^{3}q^{6}+\cdots$
1656.1.v.b	$1656$	$1$	1656.v	1656.v	$6$	$6$	$3$	$0.826$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-23}) $	None		✓	1656.1.v.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{7}q^{2}+\zeta_{18}^{4}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
1656.1.z.a	$1656$	$1$	1656.z	1656.z	$6$	$6$	$3$	$0.826$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-23}) $	None		✓	1656.1.z.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{2}q^{2}+\zeta_{18}^{5}q^{3}+\zeta_{18}^{4}q^{4}+\cdots$
1656.1.z.b	$1656$	$1$	1656.z	1656.z	$6$	$6$	$3$	$0.826$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-23}) $	None		✓	1656.1.z.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{4}q^{2}-\zeta_{18}^{2}q^{3}+\zeta_{18}^{8}q^{4}+\cdots$
1656.2.a.a	$1656$	$2$	1656.a	1.a	$1$	$1$	$1$	$13.223$	$\Q$	$_{}$	None	None	✓		552.2.a.d	$1$	$1$	$0$	$0$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+2q^{7}+2q^{13}+4q^{17}-6q^{19}+\cdots$
1656.2.a.b	$1656$	$2$	1656.a	1.a	$1$	$1$	$1$	$13.223$	$\Q$	$_{}$	None	None	✓		552.2.a.c	$1$	$0$	$0$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{7}+4q^{11}-2q^{13}+2q^{17}+\cdots$
1656.2.a.c	$1656$	$2$	1656.a	1.a	$1$	$1$	$1$	$13.223$	$\Q$	$_{}$	None	None	✓		184.2.a.d	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-5q^{13}+6q^{17}+6q^{19}-q^{23}+\cdots$
1656.2.a.d	$1656$	$2$	1656.a	1.a	$1$	$1$	$1$	$13.223$	$\Q$	$_{}$	None	None	✓		552.2.a.b	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+2q^{13}-8q^{17}+6q^{19}-q^{23}+\cdots$
1656.2.a.e	$1656$	$2$	1656.a	1.a	$1$	$1$	$1$	$13.223$	$\Q$	$_{}$	None	None	✓		184.2.a.c	$1$	$1$	$0$	$0$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}-6q^{11}-2q^{13}-6q^{17}-6q^{19}+\cdots$
1656.2.a.f	$1656$	$2$	1656.a	1.a	$1$	$1$	$1$	$13.223$	$\Q$	$_{}$	None	None	✓		552.2.a.e	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}-2q^{13}+2q^{17}-4q^{19}+\cdots$
1656.2.a.g	$1656$	$2$	1656.a	1.a	$1$	$1$	$1$	$13.223$	$\Q$	$_{}$	None	None	✓		184.2.a.b	$1$	$0$	$0$	$0$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}+2q^{11}+7q^{13}+4q^{17}+\cdots$
1656.2.a.h	$1656$	$2$	1656.a	1.a	$1$	$1$	$1$	$13.223$	$\Q$	$_{}$	None	None	✓		552.2.a.a	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2q^{7}+2q^{11}-2q^{13}+4q^{17}+\cdots$
1656.2.a.i	$1656$	$2$	1656.a	1.a	$1$	$1$	$1$	$13.223$	$\Q$	$_{}$	None	None	✓		184.2.a.a	$1$	$0$	$0$	$0$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+2q^{7}+4q^{11}-5q^{13}+2q^{17}+\cdots$
1656.2.a.j	$1656$	$2$	1656.a	1.a	$1$	$2$	$2$	$13.223$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		184.2.a.e	$1$	$1$	$0$	$0$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+(-2+2\beta )q^{11}+(3-\beta )q^{13}+\cdots$
1656.2.a.k	$1656$	$2$	1656.a	1.a	$1$	$2$	$2$	$13.223$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓	1656.2.a.k	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{5}+(-1+\beta )q^{7}+(2-2\beta )q^{11}+\cdots$
1656.2.a.l	$1656$	$2$	1656.a	1.a	$1$	$2$	$2$	$13.223$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		552.2.a.f	$1$	$0$	$0$	$0$	$-2$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+2q^{7}+(-1-\beta )q^{11}+\cdots$
1656.2.a.m	$1656$	$2$	1656.a	1.a	$1$	$2$	$2$	$13.223$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓	1656.2.a.k	$1$	$1$	$0$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+(-1-\beta )q^{7}+(-2-2\beta )q^{11}+\cdots$
1656.2.a.n	$1656$	$2$	1656.a	1.a	$1$	$3$	$3$	$13.223$	3.3.148.1	$_{}$	None	None	✓		552.2.a.g	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}+(1+\beta _{1})q^{7}+(-1+\beta _{1}+\beta _{2})q^{11}+\cdots$
1656.2.a.o	$1656$	$2$	1656.a	1.a	$1$	$4$	$4$	$13.223$	4.4.44688.2	$_{}$	None	None	✓	✓	1656.2.a.o	$1$	$0$	$0$	$0$	$-4$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{5}-\beta _{1}q^{7}+(-\beta _{2}+\beta _{3})q^{11}+\cdots$
1656.2.a.p	$1656$	$2$	1656.a	1.a	$1$	$4$	$4$	$13.223$	4.4.44688.2	$_{}$	None	None	✓	✓	1656.2.a.o	$1$	$0$	$0$	$0$	$4$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{5}-\beta _{1}q^{7}+(\beta _{2}-\beta _{3})q^{11}+\cdots$
1656.2.b.a	$1656$	$2$	1656.b	552.b	$2$	$8$	$8$	$13.223$	8.0.$\cdots$.17	$_{}$	$\Q(\sqrt{-46}) $	None		✓	1656.2.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-2q^{4}+\beta _{5}q^{5}-2\beta _{1}q^{8}+\cdots$
1656.2.b.b	$1656$	$2$	1656.b	552.b	$2$	$8$	$8$	$13.223$	8.0.$\cdots$.17	$_{}$	$\Q(\sqrt{-46}) $	None		✓	1656.2.b.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-2q^{4}-\beta _{4}q^{5}-2\beta _{1}q^{8}+\cdots$
1656.2.b.c	$1656$	$2$	1656.b	552.b	$2$	$80$	$80$	$13.223$		$_{}$	None	None		✓	1656.2.b.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1656.2.j.a	$1656$	$2$	1656.j	24.f	$2$	$44$	$44$	$13.223$		$_{}$	None	None		✓	1656.2.j.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1656.2.j.b	$1656$	$2$	1656.j	24.f	$2$	$44$	$44$	$13.223$		$_{}$	None	None		✓	1656.2.j.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1656.2.m.a	$1656$	$2$	1656.m	69.c	$2$	$24$	$24$	$13.223$		$_{}$	None	None		✓	1656.2.m.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1656.3.c.a	$1656$	$3$	1656.c	23.b	$2$	$12$	$12$	$45.123$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None			184.3.f.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{14}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{5}-\beta _{9}q^{7}+\beta _{4}q^{11}-\beta _{8}q^{13}+\cdots$
1656.3.c.b	$1656$	$3$	1656.c	23.b	$2$	$24$	$24$	$45.123$		$_{}$	None	None		✓	1656.3.c.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1656.3.c.c	$1656$	$3$	1656.c	23.b	$2$	$24$	$24$	$45.123$		$_{}$	None	None			552.3.c.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1656.3.g.a	$1656$	$3$	1656.g	3.b	$2$	$20$	$20$	$45.123$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓	1656.3.g.a	$2$	$0$	$0$	$0$	$0$	$-32$		$2^{14}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{11})q^{5}+(-2+\beta _{9})q^{7}+(-\beta _{11}+\cdots)q^{11}+\cdots$
1656.3.g.b	$1656$	$3$	1656.g	3.b	$2$	$24$	$24$	$45.123$		$_{}$	None	None		✓	1656.3.g.b	$2$	$0$	$0$	$0$	$0$	$-16$			$\mathrm{SU}(2)[C_{2}]$
1656.4.a.a	$1656$	$4$	1656.a	1.a	$1$	$1$	$1$	$97.707$	$\Q$	$_{}$	None	None	✓		184.4.a.a	$1$	$1$	$0$	$0$	$-22$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q-22q^{5}+8q^{7}+20q^{11}+22q^{13}+\cdots$
1656.4.a.b	$1656$	$4$	1656.a	1.a	$1$	$1$	$1$	$97.707$	$\Q$	$_{}$	None	None	✓		552.4.a.b	$1$	$1$	$0$	$0$	$-8$	$-22$	$-$	$1$	$\mathrm{SU}(2)$	$q-8q^{5}-22q^{7}+4q^{11}-14q^{13}+\cdots$
1656.4.a.c	$1656$	$4$	1656.a	1.a	$1$	$1$	$1$	$97.707$	$\Q$	$_{}$	None	None	✓		184.4.a.b	$1$	$1$	$0$	$0$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-4q^{7}-26q^{11}+70q^{13}+\cdots$
1656.4.a.d	$1656$	$4$	1656.a	1.a	$1$	$1$	$1$	$97.707$	$\Q$	$_{}$	None	None	✓		552.4.a.a	$1$	$1$	$0$	$0$	$14$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+14q^{5}+2q^{7}-58q^{11}-50q^{13}+\cdots$
1656.4.a.e	$1656$	$4$	1656.a	1.a	$1$	$2$	$2$	$97.707$	$\Q(\sqrt{93}) $	$_{}$	None	None	✓		552.4.a.d	$1$	$1$	$0$	$0$	$-2$	$10$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+(5-\beta )q^{7}+(8-4\beta )q^{11}+\cdots$
1656.4.a.f	$1656$	$4$	1656.a	1.a	$1$	$2$	$2$	$97.707$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		552.4.a.f	$1$	$1$	$0$	$0$	$4$	$-8$	$-$	$3$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}+(-4-3\beta )q^{7}+(2^{5}-4\beta )q^{11}+\cdots$
1656.4.a.g	$1656$	$4$	1656.a	1.a	$1$	$2$	$2$	$97.707$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		552.4.a.c	$1$	$1$	$0$	$0$	$8$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(4+4\beta )q^{5}+(2-9\beta )q^{7}+(-20+7\beta )q^{11}+\cdots$
1656.4.a.h	$1656$	$4$	1656.a	1.a	$1$	$2$	$2$	$97.707$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓		552.4.a.e	$1$	$1$	$0$	$0$	$14$	$10$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	$q+(7+\beta )q^{5}+(5+\beta )q^{7}+(10-2\beta )q^{11}+\cdots$
1656.4.a.i	$1656$	$4$	1656.a	1.a	$1$	$3$	$3$	$97.707$	3.3.761.1	$_{}$	None	None	✓		184.4.a.d	$1$	$1$	$0$	$0$	$-16$	$18$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(-5-2\beta _{1}-\beta _{2})q^{5}+(5+3\beta _{1})q^{7}+\cdots$
1656.4.a.j	$1656$	$4$	1656.a	1.a	$1$	$3$	$3$	$97.707$	3.3.761.1	$_{}$	None	None	✓		184.4.a.c	$1$	$0$	$0$	$0$	$-2$	$-28$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}+\beta _{2})q^{5}+(-10+2\beta _{1}+\cdots)q^{7}+\cdots$
1656.4.a.k	$1656$	$4$	1656.a	1.a	$1$	$4$	$4$	$97.707$	4.4.2239521.1	$_{}$	None	None	✓		552.4.a.h	$1$	$0$	$0$	$0$	$-2$	$50$	$+$	$2^{5}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3})q^{5}+(12-\beta _{2})q^{7}+(-5+\cdots)q^{11}+\cdots$
1656.4.a.l	$1656$	$4$	1656.a	1.a	$1$	$4$	$4$	$97.707$	4.4.2822449.1	$_{}$	None	None	✓		184.4.a.f	$1$	$1$	$0$	$0$	$2$	$-32$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(1+\beta _{1}-\beta _{3})q^{5}+(-8-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
1656.4.a.m	$1656$	$4$	1656.a	1.a	$1$	$4$	$4$	$97.707$	4.4.1623576.1	$_{}$	None	None	✓		552.4.a.g	$1$	$0$	$0$	$0$	$14$	$14$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q+(3-\beta _{3})q^{5}+(4-\beta _{1}+\beta _{2})q^{7}+(5+\cdots)q^{11}+\cdots$
1656.4.a.n	$1656$	$4$	1656.a	1.a	$1$	$4$	$4$	$97.707$	4.4.167313.1	$_{}$	None	None	✓		184.4.a.e	$1$	$0$	$0$	$0$	$20$	$-10$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+(5-\beta _{2}-\beta _{3})q^{5}+(-1-\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots$
1656.4.a.o	$1656$	$4$	1656.a	1.a	$1$	$5$	$5$	$97.707$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓		552.4.a.j	$1$	$1$	$0$	$0$	$-16$	$0$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+(-3+\beta _{2})q^{5}-\beta _{3}q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 57 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.