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 206 matches)

Next Download to Pari/GP SageMath Magma Oscar

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
585.1.o.a	$585$	$1$	585.o	65.h	$4$	$8$	$4$	$0.292$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{16}^{5}-\zeta_{16}^{7})q^{2}+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\cdots)q^{4}+\cdots$
585.2.a.a	$585$	$2$	585.a	1.a	$1$	$1$	$1$	$4.671$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}-3q^{7}+2q^{10}+\cdots$
585.2.a.b	$585$	$2$	585.a	1.a	$1$	$1$	$1$	$4.671$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-2$	$0$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}+3q^{7}+2q^{10}+\cdots$
585.2.a.c	$585$	$2$	585.a	1.a	$1$	$1$	$1$	$4.671$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+q^{5}-q^{7}-2q^{10}+\cdots$
585.2.a.d	$585$	$2$	585.a	1.a	$1$	$1$	$1$	$4.671$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}+2q^{7}+3q^{8}+q^{10}+\cdots$
585.2.a.e	$585$	$2$	585.a	1.a	$1$	$1$	$1$	$4.671$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{5}-q^{7}+3q^{11}+q^{13}+\cdots$
585.2.a.f	$585$	$2$	585.a	1.a	$1$	$1$	$1$	$4.671$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{5}-q^{7}-3q^{11}+q^{13}+\cdots$
585.2.a.g	$585$	$2$	585.a	1.a	$1$	$1$	$1$	$4.671$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}-4q^{11}+\cdots$
585.2.a.h	$585$	$2$	585.a	1.a	$1$	$1$	$1$	$4.671$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}-4q^{7}-3q^{8}+q^{10}+\cdots$
585.2.a.i	$585$	$2$	585.a	1.a	$1$	$1$	$1$	$4.671$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}+2q^{7}-3q^{8}+q^{10}+\cdots$
585.2.a.j	$585$	$2$	585.a	1.a	$1$	$2$	$2$	$4.671$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$-2$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+(-3+\beta )q^{7}+\cdots$
585.2.a.k	$585$	$2$	585.a	1.a	$1$	$2$	$2$	$4.671$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+q^{5}+2q^{7}-\beta q^{8}+\beta q^{10}+\cdots$
585.2.a.l	$585$	$2$	585.a	1.a	$1$	$2$	$2$	$4.671$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$2$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2+\beta )q^{4}+q^{5}+(-3+\beta )q^{7}+\cdots$
585.2.a.m	$585$	$2$	585.a	1.a	$1$	$2$	$2$	$4.671$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}-q^{5}+(2+2\beta )q^{7}+\cdots$
585.2.a.n	$585$	$2$	585.a	1.a	$1$	$3$	$3$	$4.671$	3.3.316.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$1$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+q^{5}-\beta _{2}q^{7}+\cdots$
585.2.b.a	$585$	$2$	585.b	13.b	$2$	$2$	$2$	$4.671$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{4}+iq^{5}+2iq^{7}+3iq^{8}+\cdots$
585.2.b.b	$585$	$2$	585.b	13.b	$2$	$2$	$2$	$4.671$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{4}+iq^{5}+4iq^{7}+3iq^{8}+\cdots$
585.2.b.c	$585$	$2$	585.b	13.b	$2$	$2$	$2$	$4.671$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{4}+iq^{5}-4iq^{7}+3iq^{8}+\cdots$
585.2.b.d	$585$	$2$	585.b	13.b	$2$	$2$	$2$	$4.671$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{4}+iq^{5}-3iq^{7}-3iq^{11}+(2+\cdots)q^{13}+\cdots$
585.2.b.e	$585$	$2$	585.b	13.b	$2$	$4$	$4$	$4.671$	$\Q(i, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
585.2.b.f	$585$	$2$	585.b	13.b	$2$	$4$	$4$	$4.671$	$\Q(i, \sqrt{13})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-2\beta _{1}q^{2}-2q^{4}+\beta _{1}q^{5}-\beta _{2}q^{7}+\cdots$
585.2.b.g	$585$	$2$	585.b	13.b	$2$	$6$	$6$	$4.671$	6.0.5089536.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(-2+\beta _{3})q^{4}+\beta _{4}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
585.2.c.a	$585$	$2$	585.c	5.b	$2$	$2$	$2$	$4.671$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{4}+(1+2i)q^{5}-iq^{7}+q^{11}+\cdots$
585.2.c.b	$585$	$2$	585.c	5.b	$2$	$6$	$6$	$4.671$	6.0.350464.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{3}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2})q^{4}+\cdots$
585.2.c.c	$585$	$2$	585.c	5.b	$2$	$10$	$10$	$4.671$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1-\beta _{4}+\beta _{6}+\beta _{7})q^{4}+\cdots$
585.2.c.d	$585$	$2$	585.c	5.b	$2$	$12$	$12$	$4.671$	12.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{2}+(-1-\beta _{9})q^{4}+(-\beta _{5}+\beta _{8}+\cdots)q^{5}+\cdots$
585.2.h.a	$585$	$2$	585.h	65.d	$2$	$2$	$2$	$4.671$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-4$	$0$	$-4$	$-6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2q^{2}+2q^{4}+(-2+i)q^{5}-3q^{7}+\cdots$
585.2.h.b	$585$	$2$	585.h	65.d	$2$	$2$	$2$	$4.671$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$-2$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-q^{4}+(-1-i)q^{5}+3q^{8}+(1+\cdots)q^{10}+\cdots$
585.2.h.c	$585$	$2$	585.h	65.d	$2$	$2$	$2$	$4.671$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-q^{4}+(1+i)q^{5}-3q^{8}+(1+i)q^{10}+\cdots$
585.2.h.d	$585$	$2$	585.h	65.d	$2$	$2$	$2$	$4.671$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$4$	$0$	$4$	$6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{2}+2q^{4}+(2-i)q^{5}+3q^{7}+(4+\cdots)q^{10}+\cdots$
585.2.h.e	$585$	$2$	585.h	65.d	$2$	$4$	$4$	$4.671$	$\Q(\sqrt{-5}, \sqrt{13})$	$_{}$	$\Q(\sqrt{-195}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}-\beta _{1}q^{5}+\beta _{3}q^{7}+\beta _{1}q^{11}+\cdots$
585.2.h.f	$585$	$2$	585.h	65.d	$2$	$8$	$8$	$4.671$	8.0.$\cdots$.21	$_{}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{4}q^{2}+(2-\beta _{2})q^{4}+\beta _{1}q^{5}+(\beta _{1}+\cdots)q^{8}+\cdots$
585.2.h.g	$585$	$2$	585.h	65.d	$2$	$12$	$12$	$4.671$	12.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{10}q^{2}+(1+\beta _{5}-\beta _{11})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
585.2.i.a	$585$	$2$	585.i	9.c	$3$	$2$	$1$	$4.671$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$3$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-\zeta_{6})q^{3}+2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots$
585.2.i.b	$585$	$2$	585.i	9.c	$3$	$2$	$1$	$4.671$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$0$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
585.2.i.c	$585$	$2$	585.i	9.c	$3$	$2$	$1$	$4.671$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$3$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
585.2.i.d	$585$	$2$	585.i	9.c	$3$	$2$	$1$	$4.671$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$2$	$-3$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$
585.2.i.e	$585$	$2$	585.i	9.c	$3$	$16$	$8$	$4.671$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$-3$	$1$	$8$	$11$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{6}q^{2}+(-\beta _{7}+\beta _{14})q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots$
585.2.i.f	$585$	$2$	585.i	9.c	$3$	$16$	$8$	$4.671$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$1$	$-2$	$-8$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3}-\beta _{4}-\beta _{5}-\beta _{6}+\cdots)q^{3}+\cdots$
585.2.i.g	$585$	$2$	585.i	9.c	$3$	$26$	$13$	$4.671$		$_{}$	None	None		$2$	$0$	$1$	$1$	$-13$	$-10$			$\mathrm{SU}(2)[C_{3}]$
585.2.i.h	$585$	$2$	585.i	9.c	$3$	$30$	$15$	$4.671$		$_{}$	None	None		$2$	$0$	$1$	$1$	$15$	$-10$			$\mathrm{SU}(2)[C_{3}]$
585.2.j.a	$585$	$2$	585.j	13.c	$3$	$2$	$1$	$4.671$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{4}+q^{5}+\zeta_{6}q^{7}+(6-6\zeta_{6})q^{11}+\cdots$
585.2.j.b	$585$	$2$	585.j	13.c	$3$	$2$	$1$	$4.671$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+q^{5}-5\zeta_{6}q^{7}+\cdots$
585.2.j.c	$585$	$2$	585.j	13.c	$3$	$4$	$2$	$4.671$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$-4$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}+\cdots)q^{4}+\cdots$
585.2.j.d	$585$	$2$	585.j	13.c	$3$	$4$	$2$	$4.671$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$-1$	$0$	$4$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$
585.2.j.e	$585$	$2$	585.j	13.c	$3$	$4$	$2$	$4.671$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$1$	$0$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}-q^{5}+\cdots$
585.2.j.f	$585$	$2$	585.j	13.c	$3$	$6$	$3$	$4.671$	6.0.1714608.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-6$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{3}-\beta _{5})q^{2}+(-2\beta _{1}-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
585.2.j.g	$585$	$2$	585.j	13.c	$3$	$6$	$3$	$4.671$	6.0.591408.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{5}q^{2}+(\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots$
585.2.j.h	$585$	$2$	585.j	13.c	$3$	$10$	$5$	$4.671$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$10$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{3})q^{2}+(-1+\beta _{4}-\beta _{8})q^{4}+\cdots$
585.2.j.i	$585$	$2$	585.j	13.c	$3$	$10$	$5$	$4.671$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$2$	$0$	$-10$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots$

Next Download to Pari/GP SageMath Magma Oscar

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 206 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.