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 75 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
1476.1.h.a	$1476$	$1$	1476.h	164.d	$2$	$1$	$1$	$0.737$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-41}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$-1$	$0$	$2$	$0$		$1$		$q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{16}+\cdots$
1476.1.h.b	$1476$	$1$	1476.h	164.d	$2$	$2$	$2$	$0.737$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-41}) $	None	✓	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}-\beta q^{7}+q^{8}+\beta q^{11}-\beta q^{14}+\cdots$
1476.1.j.a	$1476$	$1$	1476.j	164.e	$4$	$2$	$1$	$0.737$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{2}-q^{4}-iq^{8}+(1+i)q^{13}+q^{16}+\cdots$
1476.1.j.b	$1476$	$1$	1476.j	164.e	$4$	$2$	$1$	$0.737$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-q^{4}+iq^{8}+(1+i)q^{13}+q^{16}+\cdots$
1476.1.l.a	$1476$	$1$	1476.l	123.f	$4$	$4$	$2$	$0.737$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{3}q^{11}+\zeta_{8}q^{17}+\cdots$
1476.1.o.a	$1476$	$1$	1476.o	1476.o	$6$	$2$	$1$	$0.737$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-41}) $	None		$4$	$0$	$-1$	$-2$	$1$	$-1$		$1$		$q+\zeta_{6}^{2}q^{2}-q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{6}+\cdots$
1476.1.o.b	$1476$	$1$	1476.o	1476.o	$6$	$2$	$1$	$0.737$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-41}) $	None		$4$	$0$	$-1$	$2$	$1$	$1$		$1$		$q+\zeta_{6}^{2}q^{2}+q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{6}+\cdots$
1476.1.o.c	$1476$	$1$	1476.o	1476.o	$6$	$4$	$2$	$0.737$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-41}) $	None		$8$	$0$	$-2$	$0$	$-2$	$0$		$1$		$q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{4}+\cdots$
1476.1.o.d	$1476$	$1$	1476.o	1476.o	$6$	$8$	$4$	$0.737$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-41}) $	None		$8$	$0$	$4$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{4}q^{2}+\zeta_{24}^{9}q^{3}+\zeta_{24}^{8}q^{4}+\cdots$
1476.1.w.a	$1476$	$1$	1476.w	492.o	$8$	$4$	$1$	$0.737$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-1-\zeta_{8}^{2})q^{5}+\cdots$
1476.1.w.b	$1476$	$1$	1476.w	492.o	$8$	$4$	$1$	$0.737$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$4$	$0$		$1$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(1+\zeta_{8}^{2})q^{5}+\cdots$
1476.1.z.a	$1476$	$1$	1476.z	164.l	$10$	$4$	$1$	$0.737$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-2$	$0$		$1$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+(-\zeta_{10}^{3}+\zeta_{10}^{4}+\cdots)q^{5}+\cdots$
1476.1.ba.a	$1476$	$1$	1476.ba	164.j	$10$	$4$	$1$	$0.737$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$2$	$0$		$1$		$q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+(-\zeta_{10}^{2}-\zeta_{10}^{4}+\cdots)q^{5}+\cdots$
1476.1.bo.a	$1476$	$1$	1476.bo	164.n	$20$	$8$	$1$	$0.737$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{9}q^{2}-\zeta_{20}^{8}q^{4}+(-\zeta_{20}^{2}-\zeta_{20}^{4}+\cdots)q^{5}+\cdots$
1476.1.bo.b	$1476$	$1$	1476.bo	164.n	$20$	$8$	$1$	$0.737$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{20}^{9}q^{2}-\zeta_{20}^{8}q^{4}+(\zeta_{20}^{2}+\zeta_{20}^{4}+\cdots)q^{5}+\cdots$
1476.1.cc.a	$1476$	$1$	1476.cc	492.ae	$40$	$16$	$1$	$0.737$	$\Q(\zeta_{40})$	$D_{40}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+\zeta_{40}^{13}q^{2}-\zeta_{40}^{6}q^{4}+(\zeta_{40}^{8}+\zeta_{40}^{14}+\cdots)q^{5}+\cdots$
1476.1.cc.b	$1476$	$1$	1476.cc	492.ae	$40$	$16$	$1$	$0.737$	$\Q(\zeta_{40})$	$D_{40}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{40}^{13}q^{2}-\zeta_{40}^{6}q^{4}+(-\zeta_{40}^{8}+\cdots)q^{5}+\cdots$
1476.2.a.a	$1476$	$2$	1476.a	1.a	$1$	$1$	$1$	$11.786$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+q^{11}-2q^{13}+q^{17}-4q^{19}+\cdots$
1476.2.a.b	$1476$	$2$	1476.a	1.a	$1$	$1$	$1$	$11.786$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}+5q^{11}+4q^{13}+5q^{17}+\cdots$
1476.2.a.c	$1476$	$2$	1476.a	1.a	$1$	$2$	$2$	$11.786$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{5}+(1-\beta )q^{7}+(-2-\beta )q^{11}+\cdots$
1476.2.a.d	$1476$	$2$	1476.a	1.a	$1$	$2$	$2$	$11.786$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}+(2-\beta )q^{7}+(1-\beta )q^{11}+\cdots$
1476.2.a.e	$1476$	$2$	1476.a	1.a	$1$	$3$	$3$	$11.786$	3.3.404.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-4$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{5}+(1+\beta _{1})q^{7}+(-2+\cdots)q^{11}+\cdots$
1476.2.a.f	$1476$	$2$	1476.a	1.a	$1$	$3$	$3$	$11.786$	3.3.404.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{5}+(1+\beta _{1})q^{7}+(2+2\beta _{1}+\cdots)q^{11}+\cdots$
1476.2.a.g	$1476$	$2$	1476.a	1.a	$1$	$4$	$4$	$11.786$	4.4.25808.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta _{2}-\beta _{3})q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
1476.2.c.a	$1476$	$2$	1476.c	12.b	$2$	$80$	$80$	$11.786$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1476.2.d.a	$1476$	$2$	1476.d	492.d	$2$	$4$	$4$	$11.786$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\zeta_{8}^{2}q^{2}-2q^{4}-\zeta_{8}^{2}q^{5}+2\zeta_{8}^{2}q^{8}+\cdots$
1476.2.d.b	$1476$	$2$	1476.d	492.d	$2$	$8$	$8$	$11.786$	8.0.$\cdots$.5	$_{}$	None	None		$4$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{4})q^{2}+(-1-\beta _{4})q^{4}-2\beta _{6}q^{5}+\cdots$
1476.2.d.c	$1476$	$2$	1476.d	492.d	$2$	$8$	$8$	$11.786$	8.0.$\cdots$.5	$_{}$	None	None		$4$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+(-2+\beta _{4})q^{4}-2\beta _{6}q^{5}+\cdots$
1476.2.d.d	$1476$	$2$	1476.d	492.d	$2$	$64$	$64$	$11.786$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1476.2.f.a	$1476$	$2$	1476.f	41.b	$2$	$2$	$2$	$11.786$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-4q^{5}-4iq^{7}-3iq^{11}-4iq^{13}+\cdots$
1476.2.f.b	$1476$	$2$	1476.f	41.b	$2$	$2$	$2$	$11.786$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+4q^{5}-4iq^{7}+3iq^{11}-4iq^{13}+\cdots$
1476.2.f.c	$1476$	$2$	1476.f	41.b	$2$	$4$	$4$	$11.786$	$\Q(i, \sqrt{41})$	$_{}$	$\Q(\sqrt{-123}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{11}+(\beta _{1}-2\beta _{2})q^{17}-5q^{25}+\cdots$
1476.2.f.d	$1476$	$2$	1476.f	41.b	$2$	$4$	$4$	$11.786$	4.0.25088.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{2})q^{5}+\beta _{3}q^{7}+(2\beta _{1}+\beta _{3})q^{11}+\cdots$
1476.2.f.e	$1476$	$2$	1476.f	41.b	$2$	$6$	$6$	$11.786$	6.0.5089536.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1})q^{5}+(-\beta _{2}+\beta _{5})q^{7}+(\beta _{2}+\cdots)q^{11}+\cdots$
1476.2.i.a	$1476$	$2$	1476.i	9.c	$3$	$2$	$1$	$11.786$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$-1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-5+5\zeta_{6})q^{7}+\cdots$
1476.2.i.b	$1476$	$2$	1476.i	9.c	$3$	$32$	$16$	$11.786$		$_{}$	None	None		$2$	$0$	$0$	$-1$	$1$	$-1$			$\mathrm{SU}(2)[C_{3}]$
1476.2.i.c	$1476$	$2$	1476.i	9.c	$3$	$46$	$23$	$11.786$		$_{}$	None	None		$2$	$0$	$0$	$-1$	$2$	$4$			$\mathrm{SU}(2)[C_{3}]$
1476.2.k.a	$1476$	$2$	1476.k	41.c	$4$	$6$	$3$	$11.786$	6.0.5089536.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{4}-\beta _{5})q^{5}+(\beta _{1}+\beta _{2}-\beta _{5})q^{7}+\cdots$
1476.2.k.b	$1476$	$2$	1476.k	41.c	$4$	$12$	$6$	$11.786$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{6}q^{5}+(-\beta _{1}-\beta _{3}-\beta _{10})q^{7}+\beta _{11}q^{11}+\cdots$
1476.2.k.c	$1476$	$2$	1476.k	41.c	$4$	$16$	$8$	$11.786$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{5}-\beta _{9}q^{7}+(\beta _{3}-\beta _{4}-\beta _{7}-\beta _{10}+\cdots)q^{11}+\cdots$
1476.2.n.a	$1476$	$2$	1476.n	41.d	$5$	$4$	$1$	$11.786$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-7$	$9$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-3+3\zeta_{10}+2\zeta_{10}^{3})q^{5}+(3+3\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
1476.2.n.b	$1476$	$2$	1476.n	41.d	$5$	$4$	$1$	$11.786$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-5$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-2\zeta_{10}^{3})q^{5}+(-1-\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
1476.2.n.c	$1476$	$2$	1476.n	41.d	$5$	$4$	$1$	$11.786$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-1$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}+2\zeta_{10}^{3})q^{5}+(-1-\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
1476.2.n.d	$1476$	$2$	1476.n	41.d	$5$	$4$	$1$	$11.786$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$7$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(2-2\zeta_{10}+\zeta_{10}^{3})q^{5}+(2-2\zeta_{10}+\cdots)q^{7}+\cdots$
1476.2.n.e	$1476$	$2$	1476.n	41.d	$5$	$8$	$2$	$11.786$	8.0.2127515625.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$-7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{4}q^{5}+(-2+\beta _{1}+2\beta _{2}-\beta _{3})q^{7}+\cdots$
1476.2.n.f	$1476$	$2$	1476.n	41.d	$5$	$16$	$4$	$11.786$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{3}+\beta _{4}-\beta _{6}-\beta _{9})q^{5}+(-1+\cdots)q^{7}+\cdots$
1476.2.n.g	$1476$	$2$	1476.n	41.d	$5$	$32$	$8$	$11.786$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{5}]$
1476.2.q.a	$1476$	$2$	1476.q	369.i	$6$	$8$	$4$	$11.786$	$\Q(\zeta_{24})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{24}-\zeta_{24}^{5}-2\zeta_{24}^{6}+\zeta_{24}^{7})q^{3}+\cdots$
1476.2.q.b	$1476$	$2$	1476.q	369.i	$6$	$76$	$38$	$11.786$		$_{}$	None	None		$4$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{6}]$
1476.2.x.a	$1476$	$2$	1476.x	123.i	$8$	$28$	$7$	$11.786$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{8}]$

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 75 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.