LMFDB - Newform search results

Refine search

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
		Only for weight 1:

				Sort order	Select

Results (1-50 of 125 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	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
2064.1.p.a	$2064$	$1$	2064.p	516.h	$2$	$1$	$1$	$1.030$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-129}) $	$\Q(\sqrt{43}) $	✓	$4$	$0$	$0$	$-1$	$0$	$2$		$1$		$q-q^{3}+2q^{7}+q^{9}+2q^{13}-2q^{19}+\cdots$
2064.1.p.b	$2064$	$1$	2064.p	516.h	$2$	$1$	$1$	$1.030$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-129}) $	$\Q(\sqrt{43}) $	✓	$4$	$0$	$0$	$1$	$0$	$-2$		$1$		$q+q^{3}-2q^{7}+q^{9}+2q^{13}+2q^{19}+\cdots$
2064.1.p.c	$2064$	$1$	2064.p	516.h	$2$	$2$	$2$	$1.030$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-129}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$-2$		$1$		$q-q^{3}-\beta q^{5}-q^{7}+q^{9}-\beta q^{11}-q^{13}+\cdots$
2064.1.p.d	$2064$	$1$	2064.p	516.h	$2$	$2$	$2$	$1.030$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-129}) $	None	✓	$4$	$0$	$0$	$2$	$0$	$2$		$1$		$q+q^{3}-\beta q^{5}+q^{7}+q^{9}+\beta q^{11}-q^{13}+\cdots$
2064.1.z.a	$2064$	$1$	2064.z	516.j	$6$	$2$	$1$	$1.030$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{13}+\cdots$
2064.1.z.b	$2064$	$1$	2064.z	516.j	$6$	$2$	$1$	$1.030$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$1$		$1$		$q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{13}+\cdots$
2064.1.bh.a	$2064$	$1$	2064.bh	129.f	$6$	$2$	$1$	$1.030$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{13}+\cdots$
2064.1.cb.a	$2064$	$1$	2064.cb	516.t	$14$	$6$	$1$	$1.030$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$2$		$1$		$q-\zeta_{14}^{5}q^{3}+(\zeta_{14}-\zeta_{14}^{6})q^{7}-\zeta_{14}^{3}q^{9}+\cdots$
2064.1.cb.b	$2064$	$1$	2064.cb	516.t	$14$	$6$	$1$	$1.030$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-2$		$1$		$q+\zeta_{14}^{5}q^{3}+(-\zeta_{14}+\zeta_{14}^{6})q^{7}-\zeta_{14}^{3}q^{9}+\cdots$
2064.1.cj.a	$2064$	$1$	2064.cj	129.l	$14$	$6$	$1$	$1.030$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$		$1$		$q-\zeta_{14}^{4}q^{3}+(-\zeta_{14}^{2}+\zeta_{14}^{5})q^{7}+\cdots$
2064.1.cx.a	$2064$	$1$	2064.cx	129.o	$42$	$12$	$1$	$1.030$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$1$		$1$		$q-\zeta_{42}^{16}q^{3}+(\zeta_{42}^{13}+\zeta_{42}^{15})q^{7}+\cdots$
2064.1.df.a	$2064$	$1$	2064.df	516.ad	$42$	$12$	$1$	$1.030$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q+\zeta_{42}^{11}q^{3}+(-\zeta_{42}^{5}-\zeta_{42}^{9})q^{7}+\cdots$
2064.1.df.b	$2064$	$1$	2064.df	516.ad	$42$	$12$	$1$	$1.030$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$1$		$1$		$q-\zeta_{42}^{11}q^{3}+(\zeta_{42}^{5}+\zeta_{42}^{9})q^{7}-\zeta_{42}q^{9}+\cdots$
2064.2.a.a	$2064$	$2$	2064.a	1.a	$1$	$1$	$1$	$16.481$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}+3q^{7}+q^{9}-3q^{11}+\cdots$
2064.2.a.b	$2064$	$2$	2064.a	1.a	$1$	$1$	$1$	$16.481$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}+3q^{7}+q^{9}+5q^{11}+\cdots$
2064.2.a.c	$2064$	$2$	2064.a	1.a	$1$	$1$	$1$	$16.481$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}-7q^{13}+\cdots$
2064.2.a.d	$2064$	$2$	2064.a	1.a	$1$	$1$	$1$	$16.481$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}+2q^{11}+6q^{13}+6q^{17}+\cdots$
2064.2.a.e	$2064$	$2$	2064.a	1.a	$1$	$1$	$1$	$16.481$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots$
2064.2.a.f	$2064$	$2$	2064.a	1.a	$1$	$1$	$1$	$16.481$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots$
2064.2.a.g	$2064$	$2$	2064.a	1.a	$1$	$1$	$1$	$16.481$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$3$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}-5q^{7}+q^{9}+3q^{11}+\cdots$
2064.2.a.h	$2064$	$2$	2064.a	1.a	$1$	$1$	$1$	$16.481$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots$
2064.2.a.i	$2064$	$2$	2064.a	1.a	$1$	$1$	$1$	$16.481$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-2q^{7}+q^{9}+2q^{13}+\cdots$
2064.2.a.j	$2064$	$2$	2064.a	1.a	$1$	$1$	$1$	$16.481$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-2q^{7}+q^{9}+3q^{11}+\cdots$
2064.2.a.k	$2064$	$2$	2064.a	1.a	$1$	$1$	$1$	$16.481$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+2q^{7}+q^{9}+5q^{11}+\cdots$
2064.2.a.l	$2064$	$2$	2064.a	1.a	$1$	$1$	$1$	$16.481$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}+q^{9}-3q^{11}-3q^{13}+\cdots$
2064.2.a.m	$2064$	$2$	2064.a	1.a	$1$	$1$	$1$	$16.481$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-3q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
2064.2.a.n	$2064$	$2$	2064.a	1.a	$1$	$1$	$1$	$16.481$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+5q^{7}+q^{9}-q^{11}-3q^{13}+\cdots$
2064.2.a.o	$2064$	$2$	2064.a	1.a	$1$	$1$	$1$	$16.481$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}+q^{7}+q^{9}+q^{11}+q^{13}+\cdots$
2064.2.a.p	$2064$	$2$	2064.a	1.a	$1$	$1$	$1$	$16.481$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}+q^{7}+q^{9}+q^{11}+7q^{13}+\cdots$
2064.2.a.q	$2064$	$2$	2064.a	1.a	$1$	$2$	$2$	$16.481$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-3$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta )q^{5}+(3-\beta )q^{7}+q^{9}+\cdots$
2064.2.a.r	$2064$	$2$	2064.a	1.a	$1$	$2$	$2$	$16.481$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta )q^{5}+(1+2\beta )q^{7}+q^{9}+\cdots$
2064.2.a.s	$2064$	$2$	2064.a	1.a	$1$	$2$	$2$	$16.481$	$\Q(\sqrt{57}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}-5q^{11}+\cdots$
2064.2.a.t	$2064$	$2$	2064.a	1.a	$1$	$2$	$2$	$16.481$	$\Q(\sqrt{41}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-2q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots$
2064.2.a.u	$2064$	$2$	2064.a	1.a	$1$	$2$	$2$	$16.481$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta q^{5}+\beta q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots$
2064.2.a.v	$2064$	$2$	2064.a	1.a	$1$	$2$	$2$	$16.481$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{5}+(-1-2\beta )q^{7}+q^{9}+\cdots$
2064.2.a.w	$2064$	$2$	2064.a	1.a	$1$	$2$	$2$	$16.481$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+(-2+2\beta )q^{7}+q^{9}+\cdots$
2064.2.a.x	$2064$	$2$	2064.a	1.a	$1$	$3$	$3$	$16.481$	3.3.568.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+\cdots$
2064.2.a.y	$2064$	$2$	2064.a	1.a	$1$	$3$	$3$	$16.481$	3.3.568.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{1})q^{5}+(-1-\beta _{2})q^{7}+\cdots$
2064.2.a.z	$2064$	$2$	2064.a	1.a	$1$	$3$	$3$	$16.481$	3.3.3592.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta _{1})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots$
2064.2.a.ba	$2064$	$2$	2064.a	1.a	$1$	$3$	$3$	$16.481$	3.3.568.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta _{1})q^{5}+(1-\beta _{2})q^{7}+q^{9}+\cdots$
2064.2.d.a	$2064$	$2$	2064.d	12.b	$2$	$8$	$8$	$16.481$	$\Q(\zeta_{24})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{24}+\zeta_{24}^{5}+\zeta_{24}^{6})q^{3}+\zeta_{24}^{7}q^{5}+\cdots$
2064.2.d.b	$2064$	$2$	2064.d	12.b	$2$	$28$	$28$	$16.481$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2064.2.d.c	$2064$	$2$	2064.d	12.b	$2$	$48$	$48$	$16.481$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2064.2.i.a	$2064$	$2$	2064.i	172.d	$2$	$8$	$8$	$16.481$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-8$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+\beta _{1}q^{5}+(1-\beta _{2})q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$
2064.2.i.b	$2064$	$2$	2064.i	172.d	$2$	$8$	$8$	$16.481$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$8$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+q^{9}+\cdots$
2064.2.i.c	$2064$	$2$	2064.i	172.d	$2$	$14$	$14$	$16.481$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-14$	$0$	$-8$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+\beta _{5}q^{5}+(-1-\beta _{9})q^{7}+q^{9}+\cdots$
2064.2.i.d	$2064$	$2$	2064.i	172.d	$2$	$14$	$14$	$16.481$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$14$	$0$	$8$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta _{5}q^{5}+(1+\beta _{9})q^{7}+q^{9}+\beta _{7}q^{11}+\cdots$
2064.2.l.a	$2064$	$2$	2064.l	129.d	$2$	$2$	$2$	$16.481$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta )q^{3}+2q^{5}-3\beta q^{7}+(-1+\cdots)q^{9}+\cdots$
2064.2.l.b	$2064$	$2$	2064.l	129.d	$2$	$2$	$2$	$16.481$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-6$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{6}q^{3}-3q^{5}-\zeta_{6}q^{7}-3q^{9}+\zeta_{6}q^{11}+\cdots$
2064.2.l.c	$2064$	$2$	2064.l	129.d	$2$	$2$	$2$	$16.481$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\zeta_{6}q^{3}-2\zeta_{6}q^{7}-3q^{9}-2q^{13}+\cdots$

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 125 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.