LMFDB - Newform search results

Refine search

Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

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

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

				Sort order	Select

Results (1-50 of 147 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	Largest	Maximal	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	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
544.1.e.a	$544$	$1$	544.e	136.e	$2$	$1$	$1$	$0.271$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-34}) $	$\Q(\sqrt{17}) $	✓		✓	✓	136.1.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{9}-q^{17}+2q^{19}-q^{25}-2q^{43}+\cdots$
544.1.n.a	$544$	$1$	544.n	136.j	$4$	$2$	$1$	$0.271$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None			✓	✓	136.1.j.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(i+1)q^{3}+i q^{9}+(i-1)q^{11}+\cdots$
544.1.bl.a	$544$	$1$	544.bl	136.p	$8$	$4$	$1$	$0.271$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-2}) $	None			✓	✓	136.1.p.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-1-\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{9}+\cdots$
544.1.cd.a	$544$	$1$	544.cd	17.e	$16$	$8$	$1$	$0.271$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	544.1.cd.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{16}-\zeta_{16}^{6})q^{5}+\zeta_{16}^{3}q^{9}+(-\zeta_{16}^{5}+\cdots)q^{13}+\cdots$
544.2.a.a	$544$	$2$	544.a	1.a	$1$	$1$	$1$	$4.344$	$\Q$	$_{}$	None	None	✓	✓			544.2.a.a	$1$	$0$	$0$	$-2$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots$
544.2.a.b	$544$	$2$	544.a	1.a	$1$	$1$	$1$	$4.344$	$\Q$	$_{}$	None	None	✓	✓			544.2.a.b	$1$	$0$	$0$	$-2$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+4q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots$
544.2.a.c	$544$	$2$	544.a	1.a	$1$	$1$	$1$	$4.344$	$\Q$	$_{}$	None	None	✓	✓			544.2.a.c	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-3q^{9}-4q^{11}+2q^{13}-q^{17}+\cdots$
544.2.a.d	$544$	$2$	544.a	1.a	$1$	$1$	$1$	$4.344$	$\Q$	$_{}$	None	None	✓	✓			544.2.a.c	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-3q^{9}+4q^{11}+2q^{13}-q^{17}+\cdots$
544.2.a.e	$544$	$2$	544.a	1.a	$1$	$1$	$1$	$4.344$	$\Q$	$_{}$	None	None	✓	✓			544.2.a.a	$1$	$0$	$0$	$2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots$
544.2.a.f	$544$	$2$	544.a	1.a	$1$	$1$	$1$	$4.344$	$\Q$	$_{}$	None	None	✓	✓			544.2.a.b	$1$	$0$	$0$	$2$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+4q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots$
544.2.a.g	$544$	$2$	544.a	1.a	$1$	$2$	$2$	$4.344$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓		544.2.a.g	$2$	$1$	$0$	$0$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2q^{5}-3\beta q^{7}-q^{9}+\beta q^{11}+\cdots$
544.2.a.h	$544$	$2$	544.a	1.a	$1$	$2$	$2$	$4.344$	$\Q(\sqrt{10}) $	$_{}$	None	None	✓	✓	✓		544.2.a.h	$2$	$0$	$0$	$0$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2q^{5}+\beta q^{7}+7q^{9}+\beta q^{11}+\cdots$
544.2.a.i	$544$	$2$	544.a	1.a	$1$	$3$	$3$	$4.344$	3.3.148.1	$_{}$	None	None	✓	✓	✓	✓	544.2.a.i	$1$	$1$	$0$	$-2$	$-2$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$
544.2.a.j	$544$	$2$	544.a	1.a	$1$	$3$	$3$	$4.344$	3.3.148.1	$_{}$	None	None	✓	✓	✓		544.2.a.i	$1$	$0$	$0$	$2$	$-2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(1-\beta _{2})q^{7}+\cdots$
544.2.b.a	$544$	$2$	544.b	17.b	$2$	$2$	$2$	$4.344$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			544.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{5}+3 q^{9}-6 q^{13}+(\beta+1)q^{17}+\cdots$
544.2.b.b	$544$	$2$	544.b	17.b	$2$	$4$	$4$	$4.344$	4.0.2312.1	$_{}$	$\Q(\sqrt{-17}) $	None		✓			544.2.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{7}+(-4-\beta _{3})q^{9}+\cdots$
544.2.b.c	$544$	$2$	544.b	17.b	$2$	$4$	$4$	$4.344$	4.0.2312.1	$_{}$	$\Q(\sqrt{-17}) $	None		✓			544.2.b.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}-\beta _{1}q^{7}+(-2+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
544.2.b.d	$544$	$2$	544.b	17.b	$2$	$4$	$4$	$4.344$	4.0.2048.2	$_{}$	None	None		✓			544.2.b.d	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}+(-1+\cdots)q^{9}+\cdots$
544.2.b.e	$544$	$2$	544.b	17.b	$2$	$4$	$4$	$4.344$	4.0.2048.2	$_{}$	None	None		✓			544.2.b.d	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(-\beta _{1}-\beta _{2})q^{5}-\beta _{1}q^{7}+\cdots$
544.2.c.a	$544$	$2$	544.c	8.b	$2$	$8$	$8$	$4.344$	8.0.1649659456.5	$_{}$	None	None					136.2.c.a	$2$	$0$	$0$	$0$	$0$	$-8$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}-\beta _{7}q^{5}+(-1-\beta _{5})q^{7}+(-1+\cdots)q^{9}+\cdots$
544.2.c.b	$544$	$2$	544.c	8.b	$2$	$8$	$8$	$4.344$	8.0.4469724736.1	$_{}$	None	None					136.2.c.b	$2$	$0$	$0$	$0$	$0$	$12$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}-\beta _{2}q^{5}+(2+\beta _{1})q^{7}+(-2+\cdots)q^{9}+\cdots$
544.2.h.a	$544$	$2$	544.h	136.h	$2$	$16$	$16$	$4.344$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None			✓	✓	136.2.h.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{11}q^{3}+\beta _{7}q^{5}-\beta _{10}q^{7}+\beta _{4}q^{9}+\cdots$
544.2.m.a	$544$	$2$	544.m	136.i	$4$	$8$	$4$	$4.344$	8.0.342102016.5	$_{}$	None	None					136.2.i.a	$4$	$0$	$0$	$0$	$0$	$-4$		$2^{7}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{3}+(-1-\beta _{5})q^{7}+(2\beta _{2}-\beta _{5}+\cdots)q^{9}+\cdots$
544.2.m.b	$544$	$2$	544.m	136.i	$4$	$24$	$12$	$4.344$		$_{}$	None	None			✓		136.2.i.b	$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{4}]$
544.2.o.a	$544$	$2$	544.o	17.c	$4$	$2$	$1$	$4.344$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			544.2.o.a	$2$	$0$	$0$	$-4$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2 i-2)q^{3}+(-i-1)q^{5}+(2 i-2)q^{7}+\cdots$
544.2.o.b	$544$	$2$	544.o	17.c	$4$	$2$	$1$	$4.344$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			544.2.o.b	$2$	$1$	$0$	$-2$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{3}+(-2 i-2)q^{5}-i q^{9}+\cdots$
544.2.o.c	$544$	$2$	544.o	17.c	$4$	$2$	$1$	$4.344$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			544.2.o.c	$4$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i-1)q^{5}-3 i q^{9}-4 q^{13}+\cdots$
544.2.o.d	$544$	$2$	544.o	17.c	$4$	$2$	$1$	$4.344$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			544.2.o.d	$4$	$0$	$0$	$0$	$6$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(3 i+3)q^{5}-3 i q^{9}+4 q^{13}+(4 i-1)q^{17}+\cdots$
544.2.o.e	$544$	$2$	544.o	17.c	$4$	$2$	$1$	$4.344$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			544.2.o.b	$2$	$0$	$0$	$2$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{3}+(-2 i-2)q^{5}-i q^{9}+\cdots$
544.2.o.f	$544$	$2$	544.o	17.c	$4$	$2$	$1$	$4.344$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			544.2.o.a	$2$	$0$	$0$	$4$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(2 i+2)q^{3}+(-i-1)q^{5}+(-2 i+2)q^{7}+\cdots$
544.2.o.g	$544$	$2$	544.o	17.c	$4$	$6$	$3$	$4.344$	6.0.419904.1	$_{}$	None	None		✓			544.2.o.g	$2$	$0$	$0$	$0$	$6$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{4}q^{3}+(1+\beta _{2})q^{5}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$
544.2.o.h	$544$	$2$	544.o	17.c	$4$	$6$	$3$	$4.344$	6.0.419904.1	$_{}$	None	None		✓			544.2.o.g	$2$	$0$	$0$	$0$	$6$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{3}+(1+\beta _{1})q^{5}+(-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots$
544.2.o.i	$544$	$2$	544.o	17.c	$4$	$12$	$6$	$4.344$	12.0.$\cdots$.2	$_{}$	None	None		✓	✓		544.2.o.i	$4$	$0$	$0$	$0$	$0$	$0$		$2^{14}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{3}-\beta _{9}q^{5}+(\beta _{1}+\beta _{5})q^{7}+(-2\beta _{2}+\cdots)q^{9}+\cdots$
544.2.v.a	$544$	$2$	544.v	544.v	$8$	$280$	$70$	$4.344$		$_{}$	None	None		✓	✓	✓	544.2.v.a	$2$	$0$	$-4$	$0$	$-4$	$-4$			$\mathrm{SU}(2)[C_{8}]$
544.2.x.a	$544$	$2$	544.x	544.x	$8$	$280$	$70$	$4.344$		$_{}$	None	None		✓	✓	✓	544.2.v.a	$2$	$0$	$-4$	$-4$	$0$	$-4$			$\mathrm{SU}(2)[C_{8}]$
544.2.z.a	$544$	$2$	544.z	544.z	$8$	$280$	$70$	$4.344$		$_{}$	None	None		✓	✓	✓	544.2.z.a	$2$	$0$	$0$	$-4$	$-4$	$0$			$\mathrm{SU}(2)[C_{8}]$
544.2.bb.a	$544$	$2$	544.bb	17.d	$8$	$4$	$1$	$4.344$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			544.2.bb.a	$4$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{U}(1)[D_{8}]$	$q+(-2+2\zeta_{8}-\zeta_{8}^{2}-\zeta_{8}^{3})q^{5}-3\zeta_{8}q^{9}+\cdots$
544.2.bb.b	$544$	$2$	544.bb	17.d	$8$	$4$	$1$	$4.344$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			544.2.bb.b	$4$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{U}(1)[D_{8}]$	$q+(2-2\zeta_{8}-\zeta_{8}^{2}-\zeta_{8}^{3})q^{5}-3\zeta_{8}q^{9}+\cdots$
544.2.bb.c	$544$	$2$	544.bb	17.d	$8$	$8$	$2$	$4.344$	8.0.205520896.4	$_{}$	None	None		✓			544.2.bb.c	$4$	$0$	$0$	$0$	$-8$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{8}]$	$q-\beta _{3}q^{3}+(-1+\beta _{1})q^{5}+(-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots$
544.2.bb.d	$544$	$2$	544.bb	17.d	$8$	$16$	$4$	$4.344$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			544.2.bb.d	$4$	$0$	$0$	$0$	$8$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{8}]$	$q+\beta _{1}q^{3}+(-\beta _{4}+\beta _{14})q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots$
544.2.bb.e	$544$	$2$	544.bb	17.d	$8$	$20$	$5$	$4.344$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			544.2.bb.e	$2$	$0$	$0$	$0$	$0$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{8}]$	$q+\beta _{8}q^{3}+\beta _{14}q^{5}-\beta _{7}q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots$
544.2.bb.f	$544$	$2$	544.bb	17.d	$8$	$20$	$5$	$4.344$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		✓			544.2.bb.e	$2$	$0$	$0$	$0$	$0$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{8}]$	$q-\beta _{5}q^{3}+\beta _{15}q^{5}+\beta _{9}q^{7}+(\beta _{1}-\beta _{5}+\cdots)q^{9}+\cdots$
544.2.bc.a	$544$	$2$	544.bc	544.ac	$8$	$280$	$70$	$4.344$		$_{}$	None	None		✓	✓	✓	544.2.bc.a	$4$	$0$	$-8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
544.2.bd.a	$544$	$2$	544.bd	32.g	$8$	$128$	$32$	$4.344$		$_{}$	None	None		✓			544.2.bd.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
544.2.bd.b	$544$	$2$	544.bd	32.g	$8$	$128$	$32$	$4.344$		$_{}$	None	None		✓			544.2.bd.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
544.2.bk.a	$544$	$2$	544.bk	136.o	$8$	$64$	$16$	$4.344$		$_{}$	None	None			✓	✓	136.2.o.a	$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{8}]$
544.2.bn.a	$544$	$2$	544.bn	544.an	$8$	$280$	$70$	$4.344$		$_{}$	None	None		✓	✓	✓	544.2.z.a	$2$	$0$	$0$	$-4$	$-4$	$-8$			$\mathrm{SU}(2)[C_{8}]$
544.2.bp.a	$544$	$2$	544.bp	544.ap	$8$	$280$	$70$	$4.344$		$_{}$	None	None		✓	✓	✓	544.2.bp.a	$2$	$0$	$-4$	$-4$	$-8$	$-4$			$\mathrm{SU}(2)[C_{8}]$
544.2.bq.a	$544$	$2$	544.bq	544.aq	$8$	$280$	$70$	$4.344$		$_{}$	None	None		✓	✓	✓	544.2.bp.a	$2$	$0$	$-4$	$-8$	$-4$	$-4$			$\mathrm{SU}(2)[C_{8}]$
544.2.bu.a	$544$	$2$	544.bu	544.au	$16$	$560$	$70$	$4.344$		$_{}$	None	None		✓	✓	✓	544.2.bu.a	$2$	$0$	$-8$	$-8$	$-8$	$-8$			$\mathrm{SU}(2)[C_{16}]$

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 147 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.