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 68 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
1264.1.e.a	$1264$	$1$	1264.e	79.b	$2$	$2$	$2$	$0.631$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-79}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$0$		$1$		$q-\beta q^{5}+q^{9}+(1-\beta )q^{11}+(-1+\beta )q^{13}+\cdots$
1264.1.l.a	$1264$	$1$	1264.l	1264.l	$4$	$2$	$1$	$0.631$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$-2$	$0$	$-2$	$0$		$1$		$q-q^{2}+q^{4}+(-1-i)q^{5}-q^{8}-iq^{9}+\cdots$
1264.1.l.b	$1264$	$1$	1264.l	1264.l	$4$	$8$	$4$	$0.631$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$2$	$0$	$2$	$0$		$1$		$q-\zeta_{20}^{8}q^{2}-\zeta_{20}^{6}q^{4}+(\zeta_{20}^{6}-\zeta_{20}^{9}+\cdots)q^{5}+\cdots$
1264.1.v.a	$1264$	$1$	1264.v	1264.v	$12$	$4$	$1$	$0.631$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$2$	$0$	$2$		$1$		$q-\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{4})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
1264.1.v.b	$1264$	$1$	1264.v	1264.v	$12$	$4$	$1$	$0.631$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$2$	$-2$	$0$	$2$		$1$		$q-\zeta_{12}^{4}q^{2}+(-\zeta_{12}+\zeta_{12}^{4})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
1264.2.a.a	$1264$	$2$	1264.a	1.a	$1$	$1$	$1$	$10.093$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
1264.2.a.b	$1264$	$2$	1264.a	1.a	$1$	$1$	$1$	$10.093$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+5q^{7}-2q^{9}-4q^{11}+\cdots$
1264.2.a.c	$1264$	$2$	1264.a	1.a	$1$	$1$	$1$	$10.093$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}+q^{7}-2q^{9}+5q^{13}+\cdots$
1264.2.a.d	$1264$	$2$	1264.a	1.a	$1$	$1$	$1$	$10.093$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+q^{7}-2q^{9}+2q^{11}+\cdots$
1264.2.a.e	$1264$	$2$	1264.a	1.a	$1$	$1$	$1$	$10.093$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+3q^{7}-2q^{9}-4q^{11}+\cdots$
1264.2.a.f	$1264$	$2$	1264.a	1.a	$1$	$1$	$1$	$10.093$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots$
1264.2.a.g	$1264$	$2$	1264.a	1.a	$1$	$1$	$1$	$10.093$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots$
1264.2.a.h	$1264$	$2$	1264.a	1.a	$1$	$1$	$1$	$10.093$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-3q^{5}+3q^{7}+6q^{9}+2q^{11}+\cdots$
1264.2.a.i	$1264$	$2$	1264.a	1.a	$1$	$1$	$1$	$10.093$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}-q^{7}+6q^{9}+6q^{11}+\cdots$
1264.2.a.j	$1264$	$2$	1264.a	1.a	$1$	$2$	$2$	$10.093$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+(1+\beta )q^{5}+q^{9}+(-2+\beta )q^{11}+\cdots$
1264.2.a.k	$1264$	$2$	1264.a	1.a	$1$	$2$	$2$	$10.093$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-5$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-3+\beta )q^{5}+2\beta q^{7}-3q^{9}+(2+\beta )q^{11}+\cdots$
1264.2.a.l	$1264$	$2$	1264.a	1.a	$1$	$2$	$2$	$10.093$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-4$	$-8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2q^{5}-4q^{7}+3q^{9}+(2+2\beta )q^{13}+\cdots$
1264.2.a.m	$1264$	$2$	1264.a	1.a	$1$	$2$	$2$	$10.093$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{3}+(-1+\beta )q^{5}+2q^{7}+(1+4\beta )q^{9}+\cdots$
1264.2.a.n	$1264$	$2$	1264.a	1.a	$1$	$2$	$2$	$10.093$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$4$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(2+\beta )q^{5}+(2+\beta )q^{7}-2q^{9}+\cdots$
1264.2.a.o	$1264$	$2$	1264.a	1.a	$1$	$3$	$3$	$10.093$	3.3.229.1	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-6$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{2})q^{3}+(-2+\beta _{1})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
1264.2.a.p	$1264$	$2$	1264.a	1.a	$1$	$5$	$5$	$10.093$	5.5.81589.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$7$	$5$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2}+\beta _{3})q^{3}+(1+\beta _{3})q^{5}+\cdots$
1264.2.a.q	$1264$	$2$	1264.a	1.a	$1$	$6$	$6$	$10.093$	6.6.24544216.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$-5$	$-6$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}+(-1-\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots$
1264.2.a.r	$1264$	$2$	1264.a	1.a	$1$	$6$	$6$	$10.093$	6.6.22234984.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$9$	$-6$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+(2+\beta _{2})q^{5}+(-1-\beta _{5})q^{7}+\cdots$
1264.2.h.a	$1264$	$2$	1264.h	316.d	$2$	$12$	$12$	$10.093$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{3}-\beta _{1}q^{5}-\beta _{8}q^{7}+\beta _{2}q^{9}+\cdots$
1264.2.h.b	$1264$	$2$	1264.h	316.d	$2$	$28$	$28$	$10.093$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1264.2.i.a	$1264$	$2$	1264.i	79.c	$3$	$2$	$1$	$10.093$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$1$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}-3\zeta_{6}q^{7}+\cdots$
1264.2.i.b	$1264$	$2$	1264.i	79.c	$3$	$2$	$1$	$10.093$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-4\zeta_{6}q^{5}+\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(4-4\zeta_{6})q^{13}+\cdots$
1264.2.i.c	$1264$	$2$	1264.i	79.c	$3$	$2$	$1$	$10.093$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-3\zeta_{6}q^{7}+3\zeta_{6}q^{9}-2\zeta_{6}q^{11}+(2+\cdots)q^{13}+\cdots$
1264.2.i.d	$1264$	$2$	1264.i	79.c	$3$	$4$	$2$	$10.093$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$3$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(-1+\beta _{1}-2\beta _{2}+\beta _{3})q^{5}+\cdots$
1264.2.i.e	$1264$	$2$	1264.i	79.c	$3$	$4$	$2$	$10.093$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None		$2$	$0$	$0$	$1$	$1$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
1264.2.i.f	$1264$	$2$	1264.i	79.c	$3$	$8$	$4$	$10.093$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$2$	$2$	$7$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{1}+\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
1264.2.i.g	$1264$	$2$	1264.i	79.c	$3$	$12$	$6$	$10.093$	12.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{4}+\beta _{5}-2\beta _{6}-\beta _{7}+\beta _{8}+\cdots)q^{3}+\cdots$
1264.2.i.h	$1264$	$2$	1264.i	79.c	$3$	$12$	$6$	$10.093$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{2}-\beta _{9})q^{3}+(\beta _{1}-\beta _{8})q^{5}+\cdots$
1264.2.i.i	$1264$	$2$	1264.i	79.c	$3$	$12$	$6$	$10.093$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$2$	$-1$	$4$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{9}q^{5}+(1-\beta _{7}+\cdots)q^{7}+\cdots$
1264.2.i.j	$1264$	$2$	1264.i	79.c	$3$	$20$	$10$	$10.093$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{3}+(\beta _{5}+\beta _{12})q^{5}+(\beta _{8}-\beta _{14}+\cdots)q^{7}+\cdots$
1264.2.n.a	$1264$	$2$	1264.n	316.f	$6$	$2$	$1$	$10.093$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-2$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
1264.2.n.b	$1264$	$2$	1264.n	316.f	$6$	$2$	$1$	$10.093$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-2$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
1264.2.n.c	$1264$	$2$	1264.n	316.f	$6$	$2$	$1$	$10.093$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-3$	$1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\zeta_{6})q^{3}-3\zeta_{6}q^{5}+\zeta_{6}q^{7}+\cdots$
1264.2.n.d	$1264$	$2$	1264.n	316.f	$6$	$2$	$1$	$10.093$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}-\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$
1264.2.n.e	$1264$	$2$	1264.n	316.f	$6$	$2$	$1$	$10.093$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+(-4+\cdots)q^{13}+\cdots$
1264.2.n.f	$1264$	$2$	1264.n	316.f	$6$	$2$	$1$	$10.093$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+(4+\cdots)q^{11}+\cdots$
1264.2.n.g	$1264$	$2$	1264.n	316.f	$6$	$20$	$10$	$10.093$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$3$	$-8$		$3^{9}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{7}q^{3}+(-\beta _{11}-\beta _{14})q^{5}+(\beta _{8}-\beta _{19})q^{7}+\cdots$
1264.2.n.h	$1264$	$2$	1264.n	316.f	$6$	$20$	$10$	$10.093$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$4$	$3$	$8$		$3^{9}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{7}q^{3}+(-\beta _{11}-\beta _{14})q^{5}+(-\beta _{8}+\cdots)q^{7}+\cdots$
1264.2.n.i	$1264$	$2$	1264.n	316.f	$6$	$28$	$14$	$10.093$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
1264.3.d.a	$1264$	$3$	1264.d	4.b	$2$	$26$	$26$	$34.442$		$_{}$	None	None		$2$	$0$	$0$	$0$	$12$	$0$			$\mathrm{SU}(2)[C_{2}]$
1264.3.d.b	$1264$	$3$	1264.d	4.b	$2$	$52$	$52$	$34.442$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1264.3.e.a	$1264$	$3$	1264.e	79.b	$2$	$5$	$5$	$34.442$	5.5.19503125.1	$_{}$	$\Q(\sqrt{-79}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{5}+9q^{9}+(2\beta _{2}+\beta _{3})q^{11}+(2\beta _{2}+\cdots)q^{13}+\cdots$
1264.3.e.b	$1264$	$3$	1264.e	79.b	$2$	$8$	$8$	$34.442$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-\beta _{3}+\beta _{4}-\beta _{6})q^{5}-\beta _{7}q^{7}+\cdots$
1264.3.e.c	$1264$	$3$	1264.e	79.b	$2$	$12$	$12$	$34.442$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(\beta _{2}+\beta _{10})q^{5}-\beta _{5}q^{7}+(-3+\cdots)q^{9}+\cdots$
1264.3.e.d	$1264$	$3$	1264.e	79.b	$2$	$14$	$14$	$34.442$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{5}q^{5}-\beta _{12}q^{7}+(-3+\beta _{2}+\cdots)q^{9}+\cdots$

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 68 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.