LMFDB - Newform search results

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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

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Results (1-50 of 68 matches)

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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
1617.1.h.a	$1617$	$1$	1617.h	231.h	$2$	$8$	$8$	$0.807$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-11}) $	None		✓	✓	✓	1617.1.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}q^{3}-q^{4}+(-\zeta_{16}^{3}+\zeta_{16}^{5}+\cdots)q^{5}+\cdots$
1617.1.k.a	$1617$	$1$	1617.k	231.k	$6$	$2$	$1$	$0.807$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-231}) $	None					231.1.h.a	$4$	$0$	$-1$	$-1$	$1$	$0$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}+q^{6}-q^{8}+\cdots$
1617.1.k.b	$1617$	$1$	1617.k	231.k	$6$	$2$	$1$	$0.807$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-231}) $	None					231.1.h.a	$4$	$0$	$-1$	$1$	$-1$	$0$		$1$		$q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{5}-q^{6}-q^{8}+\cdots$
1617.1.k.c	$1617$	$1$	1617.k	231.k	$6$	$2$	$1$	$0.807$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-231}) $	None					231.1.h.a	$4$	$0$	$1$	$-1$	$1$	$0$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}-q^{6}+q^{8}+\cdots$
1617.1.k.d	$1617$	$1$	1617.k	231.k	$6$	$2$	$1$	$0.807$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-231}) $	None					231.1.h.a	$4$	$0$	$1$	$1$	$-1$	$0$		$1$		$q+\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{5}+q^{6}+q^{8}+\cdots$
1617.1.k.e	$1617$	$1$	1617.k	231.k	$6$	$16$	$8$	$0.807$	$\Q(\zeta_{48})$	$D_{8}$	$\Q(\sqrt{-11}) $	None		✓	✓		1617.1.h.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{48}^{5}q^{3}+\zeta_{48}^{8}q^{4}+(\zeta_{48}-\zeta_{48}^{7}+\cdots)q^{5}+\cdots$
1617.2.a.a	$1617$	$2$	1617.a	1.a	$1$	$1$	$1$	$12.912$	$\Q$	$_{}$	None	None	✓				231.2.i.c	$1$	$1$	$-2$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{9}-q^{11}+\cdots$
1617.2.a.b	$1617$	$2$	1617.a	1.a	$1$	$1$	$1$	$12.912$	$\Q$	$_{}$	None	None	✓				231.2.i.c	$1$	$1$	$-2$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-2q^{6}+q^{9}-q^{11}+\cdots$
1617.2.a.c	$1617$	$2$	1617.a	1.a	$1$	$1$	$1$	$12.912$	$\Q$	$_{}$	None	None	✓				231.2.i.b	$1$	$1$	$-1$	$-1$	$4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+4q^{5}+q^{6}+3q^{8}+\cdots$
1617.2.a.d	$1617$	$2$	1617.a	1.a	$1$	$1$	$1$	$12.912$	$\Q$	$_{}$	None	None	✓				231.2.i.b	$1$	$1$	$-1$	$1$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-4q^{5}-q^{6}+3q^{8}+\cdots$
1617.2.a.e	$1617$	$2$	1617.a	1.a	$1$	$1$	$1$	$12.912$	$\Q$	$_{}$	None	None	✓				231.2.a.a	$1$	$1$	$-1$	$1$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+2q^{5}-q^{6}+3q^{8}+\cdots$
1617.2.a.f	$1617$	$2$	1617.a	1.a	$1$	$1$	$1$	$12.912$	$\Q$	$_{}$	None	None	✓	✓			1617.2.a.f	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots$
1617.2.a.g	$1617$	$2$	1617.a	1.a	$1$	$1$	$1$	$12.912$	$\Q$	$_{}$	None	None	✓				231.2.i.a	$1$	$1$	$1$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots$
1617.2.a.h	$1617$	$2$	1617.a	1.a	$1$	$1$	$1$	$12.912$	$\Q$	$_{}$	None	None	✓				231.2.i.a	$1$	$1$	$1$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots$
1617.2.a.i	$1617$	$2$	1617.a	1.a	$1$	$1$	$1$	$12.912$	$\Q$	$_{}$	None	None	✓	✓			1617.2.a.f	$1$	$1$	$1$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots$
1617.2.a.j	$1617$	$2$	1617.a	1.a	$1$	$1$	$1$	$12.912$	$\Q$	$_{}$	None	None	✓				33.2.a.a	$1$	$0$	$1$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+2q^{5}+q^{6}-3q^{8}+\cdots$
1617.2.a.k	$1617$	$2$	1617.a	1.a	$1$	$2$	$2$	$12.912$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			1617.2.a.k	$1$	$0$	$-3$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(1-2\beta )q^{5}+\cdots$
1617.2.a.l	$1617$	$2$	1617.a	1.a	$1$	$2$	$2$	$12.912$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			1617.2.a.k	$1$	$1$	$-3$	$2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+(-1+\cdots)q^{5}+\cdots$
1617.2.a.m	$1617$	$2$	1617.a	1.a	$1$	$2$	$2$	$12.912$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				231.2.i.d	$1$	$1$	$-2$	$-2$	$4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+2q^{5}+\cdots$
1617.2.a.n	$1617$	$2$	1617.a	1.a	$1$	$2$	$2$	$12.912$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				231.2.i.d	$1$	$1$	$-2$	$2$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}-2q^{5}+\cdots$
1617.2.a.o	$1617$	$2$	1617.a	1.a	$1$	$2$	$2$	$12.912$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓				231.2.a.b	$1$	$1$	$-1$	$2$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(3+\beta )q^{4}-3q^{5}-\beta q^{6}+\cdots$
1617.2.a.p	$1617$	$2$	1617.a	1.a	$1$	$2$	$2$	$12.912$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				231.2.a.c	$1$	$1$	$1$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots$
1617.2.a.q	$1617$	$2$	1617.a	1.a	$1$	$3$	$3$	$12.912$	3.3.229.1	$_{}$	None	None	✓	✓	✓		1617.2.a.q	$1$	$1$	$0$	$-3$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
1617.2.a.r	$1617$	$2$	1617.a	1.a	$1$	$3$	$3$	$12.912$	3.3.229.1	$_{}$	None	None	✓	✓			1617.2.a.q	$1$	$0$	$0$	$3$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
1617.2.a.s	$1617$	$2$	1617.a	1.a	$1$	$3$	$3$	$12.912$	3.3.837.1	$_{}$	None	None	✓				231.2.a.d	$1$	$0$	$0$	$3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
1617.2.a.t	$1617$	$2$	1617.a	1.a	$1$	$3$	$3$	$12.912$	3.3.229.1	$_{}$	None	None	✓				231.2.a.e	$1$	$0$	$2$	$-3$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}-q^{3}+(2+\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots$
1617.2.a.u	$1617$	$2$	1617.a	1.a	$1$	$4$	$4$	$12.912$	4.4.2624.1	$_{}$	None	None	✓	✓			1617.2.a.u	$1$	$0$	$-2$	$-4$	$8$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
1617.2.a.v	$1617$	$2$	1617.a	1.a	$1$	$4$	$4$	$12.912$	4.4.2624.1	$_{}$	None	None	✓	✓	✓		1617.2.a.u	$1$	$1$	$-2$	$4$	$-8$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots$
1617.2.a.w	$1617$	$2$	1617.a	1.a	$1$	$4$	$4$	$12.912$	4.4.2624.1	$_{}$	None	None	✓	✓	✓		1617.2.a.w	$1$	$1$	$2$	$-4$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-q^{3}+\beta _{2}q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
1617.2.a.x	$1617$	$2$	1617.a	1.a	$1$	$4$	$4$	$12.912$	4.4.11344.1	$_{}$	None	None	✓		✓		231.2.i.e	$1$	$0$	$2$	$-4$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
1617.2.a.y	$1617$	$2$	1617.a	1.a	$1$	$4$	$4$	$12.912$	4.4.2624.1	$_{}$	None	None	✓	✓			1617.2.a.w	$1$	$0$	$2$	$4$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+q^{3}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
1617.2.a.z	$1617$	$2$	1617.a	1.a	$1$	$4$	$4$	$12.912$	4.4.11344.1	$_{}$	None	None	✓				231.2.i.e	$1$	$0$	$2$	$4$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
1617.2.a.ba	$1617$	$2$	1617.a	1.a	$1$	$5$	$5$	$12.912$	5.5.3676752.1	$_{}$	None	None	✓		✓		231.2.i.f	$1$	$0$	$2$	$-5$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-1+\beta _{4})q^{5}+\cdots$
1617.2.a.bb	$1617$	$2$	1617.a	1.a	$1$	$5$	$5$	$12.912$	5.5.3676752.1	$_{}$	None	None	✓		✓		231.2.i.f	$1$	$0$	$2$	$5$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{4})q^{5}+\cdots$
1617.2.c.a	$1617$	$2$	1617.c	77.b	$2$	$32$	$32$	$12.912$		$_{}$	None	None					231.2.p.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1617.2.c.b	$1617$	$2$	1617.c	77.b	$2$	$48$	$48$	$12.912$		$_{}$	None	None		✓	✓		1617.2.c.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1617.4.a.a	$1617$	$4$	1617.a	1.a	$1$	$1$	$1$	$95.406$	$\Q$	$_{}$	None	None	✓				33.4.a.a	$1$	$1$	$-5$	$-3$	$14$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-5q^{2}-3q^{3}+17q^{4}+14q^{5}+15q^{6}+\cdots$
1617.4.a.b	$1617$	$4$	1617.a	1.a	$1$	$1$	$1$	$95.406$	$\Q$	$_{}$	None	None	✓				231.4.a.a	$1$	$1$	$-3$	$3$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{2}+3q^{3}+q^{4}+4q^{5}-9q^{6}+\cdots$
1617.4.a.c	$1617$	$4$	1617.a	1.a	$1$	$1$	$1$	$95.406$	$\Q$	$_{}$	None	None	✓				231.4.a.b	$1$	$1$	$-2$	$-3$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}-4q^{4}-q^{5}+6q^{6}+\cdots$
1617.4.a.d	$1617$	$4$	1617.a	1.a	$1$	$1$	$1$	$95.406$	$\Q$	$_{}$	None	None	✓				33.4.a.b	$1$	$1$	$-1$	$3$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}-7q^{4}+4q^{5}-3q^{6}+\cdots$
1617.4.a.e	$1617$	$4$	1617.a	1.a	$1$	$1$	$1$	$95.406$	$\Q$	$_{}$	None	None	✓				231.4.a.c	$1$	$1$	$2$	$3$	$-11$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}-4q^{4}-11q^{5}+6q^{6}+\cdots$
1617.4.a.f	$1617$	$4$	1617.a	1.a	$1$	$1$	$1$	$95.406$	$\Q$	$_{}$	None	None	✓				231.4.a.d	$1$	$1$	$3$	$-3$	$14$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}-3q^{3}+q^{4}+14q^{5}-9q^{6}+\cdots$
1617.4.a.g	$1617$	$4$	1617.a	1.a	$1$	$1$	$1$	$95.406$	$\Q$	$_{}$	None	None	✓				231.4.a.e	$1$	$1$	$5$	$-3$	$6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+5q^{2}-3q^{3}+17q^{4}+6q^{5}-15q^{6}+\cdots$
1617.4.a.h	$1617$	$4$	1617.a	1.a	$1$	$2$	$2$	$95.406$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				231.4.a.g	$1$	$1$	$-3$	$-6$	$-25$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}-3q^{3}+(-3+3\beta )q^{4}+\cdots$
1617.4.a.i	$1617$	$4$	1617.a	1.a	$1$	$2$	$2$	$95.406$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				231.4.a.f	$1$	$0$	$-3$	$-6$	$19$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}-3q^{3}+(-3+3\beta )q^{4}+\cdots$
1617.4.a.j	$1617$	$4$	1617.a	1.a	$1$	$2$	$2$	$95.406$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓				33.4.a.d	$1$	$0$	$1$	$-6$	$-16$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-3q^{3}+\beta q^{4}+(-10+4\beta )q^{5}+\cdots$
1617.4.a.k	$1617$	$4$	1617.a	1.a	$1$	$2$	$2$	$95.406$	$\Q(\sqrt{97}) $	$_{}$	None	None	✓				33.4.a.c	$1$	$0$	$1$	$6$	$14$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+3q^{3}+(2^{4}+\beta )q^{4}+(6+2\beta )q^{5}+\cdots$
1617.4.a.l	$1617$	$4$	1617.a	1.a	$1$	$2$	$2$	$95.406$	$\Q(\sqrt{37}) $	$_{}$	None	None	✓				231.4.a.i	$1$	$1$	$3$	$-6$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-3q^{3}+(2+3\beta )q^{4}+(1+\cdots)q^{5}+\cdots$
1617.4.a.m	$1617$	$4$	1617.a	1.a	$1$	$2$	$2$	$95.406$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				231.4.a.h	$1$	$0$	$3$	$6$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3q^{3}+(-3+3\beta )q^{4}+\cdots$
1617.4.a.n	$1617$	$4$	1617.a	1.a	$1$	$5$	$5$	$95.406$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓				231.4.a.k	$1$	$1$	$-1$	$15$	$-21$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.