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 86 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
1320.1.b.a	$1320$	$1$	1320.b	1320.b	$2$	$4$	$4$	$0.659$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-66}) $	None		✓			1320.1.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{2}q^{2}-\zeta_{8}^{2}q^{3}-q^{4}-\zeta_{8}q^{5}+\cdots$
1320.1.b.b	$1320$	$1$	1320.b	1320.b	$2$	$4$	$4$	$0.659$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-66}) $	None		✓			1320.1.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{2}q^{3}-q^{4}-\zeta_{8}q^{5}+\cdots$
1320.1.bn.a	$1320$	$1$	1320.bn	1320.an	$4$	$4$	$2$	$0.659$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None		✓			1320.1.bn.a	$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}+\cdots$
1320.1.bn.b	$1320$	$1$	1320.bn	1320.an	$4$	$4$	$2$	$0.659$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None		✓			1320.1.bn.a	$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}+\cdots$
1320.1.cp.a	$1320$	$1$	1320.cp	1320.bp	$10$	$4$	$1$	$0.659$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-30}) $	None		✓			1320.1.cp.a	$4$	$0$	$-1$	$-1$	$-1$	$0$		$1$		$q+\zeta_{10}^{2}q^{2}-\zeta_{10}q^{3}+\zeta_{10}^{4}q^{4}-\zeta_{10}^{3}q^{5}+\cdots$
1320.1.cp.b	$1320$	$1$	1320.cp	1320.bp	$10$	$4$	$1$	$0.659$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-30}) $	None		✓			1320.1.cp.a	$4$	$0$	$-1$	$1$	$1$	$0$		$1$		$q+\zeta_{10}^{2}q^{2}+\zeta_{10}q^{3}+\zeta_{10}^{4}q^{4}+\zeta_{10}^{3}q^{5}+\cdots$
1320.1.cp.c	$1320$	$1$	1320.cp	1320.bp	$10$	$4$	$1$	$0.659$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-30}) $	None		✓			1320.1.cp.a	$4$	$0$	$1$	$-1$	$1$	$0$		$1$		$q-\zeta_{10}^{2}q^{2}-\zeta_{10}q^{3}+\zeta_{10}^{4}q^{4}+\zeta_{10}^{3}q^{5}+\cdots$
1320.1.cp.d	$1320$	$1$	1320.cp	1320.bp	$10$	$4$	$1$	$0.659$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-30}) $	None		✓			1320.1.cp.a	$4$	$0$	$1$	$1$	$-1$	$0$		$1$		$q-\zeta_{10}^{2}q^{2}+\zeta_{10}q^{3}+\zeta_{10}^{4}q^{4}-\zeta_{10}^{3}q^{5}+\cdots$
1320.1.cp.e	$1320$	$1$	1320.cp	1320.bp	$10$	$8$	$2$	$0.659$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-6}) $	None		✓			1320.1.cp.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{9}q^{2}+\zeta_{20}^{7}q^{3}-\zeta_{20}^{8}q^{4}+\cdots$
1320.1.cp.f	$1320$	$1$	1320.cp	1320.bp	$10$	$8$	$2$	$0.659$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-6}) $	None		✓			1320.1.cp.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{9}q^{2}+\zeta_{20}^{7}q^{3}-\zeta_{20}^{8}q^{4}+\cdots$
1320.1.dk.a	$1320$	$1$	1320.dk	1320.ck	$20$	$16$	$2$	$0.659$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-6}) $	None		✓			1320.1.dk.a	$8$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{40}^{17}q^{2}+\zeta_{40}q^{3}-\zeta_{40}^{14}q^{4}+\cdots$
1320.1.dk.b	$1320$	$1$	1320.dk	1320.ck	$20$	$16$	$2$	$0.659$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-6}) $	None		✓			1320.1.dk.a	$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q+\zeta_{40}^{17}q^{2}+\zeta_{40}q^{3}-\zeta_{40}^{14}q^{4}+\cdots$
1320.2.a.a	$1320$	$2$	1320.a	1.a	$1$	$1$	$1$	$10.540$	$\Q$	$_{}$	None	None	✓	✓			1320.2.a.a	$1$	$0$	$0$	$-1$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{7}+q^{9}-q^{11}-4q^{13}+\cdots$
1320.2.a.b	$1320$	$2$	1320.a	1.a	$1$	$1$	$1$	$10.540$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1320.2.a.b	$1$	$1$	$0$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{7}+q^{9}+q^{11}+4q^{13}+\cdots$
1320.2.a.c	$1320$	$2$	1320.a	1.a	$1$	$1$	$1$	$10.540$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1320.2.a.c	$1$	$1$	$0$	$-1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}+q^{9}-q^{11}-4q^{13}+\cdots$
1320.2.a.d	$1320$	$2$	1320.a	1.a	$1$	$1$	$1$	$10.540$	$\Q$	$_{}$	None	None	✓	✓			1320.2.a.d	$1$	$0$	$0$	$-1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+4q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$
1320.2.a.e	$1320$	$2$	1320.a	1.a	$1$	$1$	$1$	$10.540$	$\Q$	$_{}$	None	None	✓	✓			1320.2.a.e	$1$	$1$	$0$	$-1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-4q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$
1320.2.a.f	$1320$	$2$	1320.a	1.a	$1$	$1$	$1$	$10.540$	$\Q$	$_{}$	None	None	✓	✓			1320.2.a.f	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-q^{11}-2q^{13}-q^{15}+\cdots$
1320.2.a.g	$1320$	$2$	1320.a	1.a	$1$	$1$	$1$	$10.540$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1320.2.a.g	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}+q^{11}-6q^{13}-q^{15}+\cdots$
1320.2.a.h	$1320$	$2$	1320.a	1.a	$1$	$1$	$1$	$10.540$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1320.2.a.h	$1$	$0$	$0$	$-1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+4q^{7}+q^{9}+q^{11}+2q^{13}+\cdots$
1320.2.a.i	$1320$	$2$	1320.a	1.a	$1$	$1$	$1$	$10.540$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1320.2.a.i	$1$	$1$	$0$	$1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{7}+q^{9}-q^{11}-4q^{13}+\cdots$
1320.2.a.j	$1320$	$2$	1320.a	1.a	$1$	$1$	$1$	$10.540$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1320.2.a.j	$1$	$0$	$0$	$1$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{7}+q^{9}-q^{11}-q^{15}+\cdots$
1320.2.a.k	$1320$	$2$	1320.a	1.a	$1$	$1$	$1$	$10.540$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1320.2.a.k	$1$	$1$	$0$	$1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{7}+q^{9}+q^{11}-q^{15}+\cdots$
1320.2.a.l	$1320$	$2$	1320.a	1.a	$1$	$1$	$1$	$10.540$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1320.2.a.l	$1$	$0$	$0$	$1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}-q^{15}+\cdots$
1320.2.a.m	$1320$	$2$	1320.a	1.a	$1$	$1$	$1$	$10.540$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1320.2.a.m	$1$	$1$	$0$	$1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-4q^{7}+q^{9}+q^{11}-6q^{13}+\cdots$
1320.2.a.n	$1320$	$2$	1320.a	1.a	$1$	$1$	$1$	$10.540$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1320.2.a.n	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}-q^{11}-2q^{13}+q^{15}+\cdots$
1320.2.a.o	$1320$	$2$	1320.a	1.a	$1$	$2$	$2$	$10.540$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓	✓	1320.2.a.o	$1$	$0$	$0$	$-2$	$-2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+q^{11}+\cdots$
1320.2.a.p	$1320$	$2$	1320.a	1.a	$1$	$2$	$2$	$10.540$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓	✓	1320.2.a.p	$1$	$0$	$0$	$-2$	$2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+\beta q^{7}+q^{9}-q^{11}+(2+\cdots)q^{13}+\cdots$
1320.2.a.q	$1320$	$2$	1320.a	1.a	$1$	$2$	$2$	$10.540$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓	✓	1320.2.a.q	$1$	$0$	$0$	$2$	$2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+\beta q^{7}+q^{9}+q^{11}+(2+\cdots)q^{13}+\cdots$
1320.2.d.a	$1320$	$2$	1320.d	5.b	$2$	$6$	$6$	$10.540$	6.0.350464.1	$_{}$	None	None		✓			1320.2.d.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots$
1320.2.d.b	$1320$	$2$	1320.d	5.b	$2$	$6$	$6$	$10.540$	6.0.350464.1	$_{}$	None	None		✓			1320.2.d.b	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}+(\beta _{1}+\beta _{5})q^{5}+(\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$
1320.2.d.c	$1320$	$2$	1320.d	5.b	$2$	$10$	$10$	$10.540$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		✓			1320.2.d.c	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}-\beta _{6}q^{5}-\beta _{1}q^{7}-q^{9}-q^{11}+\cdots$
1320.2.d.d	$1320$	$2$	1320.d	5.b	$2$	$10$	$10$	$10.540$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		✓			1320.2.d.d	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}-\beta _{1}q^{5}-\beta _{9}q^{7}-q^{9}+q^{11}+\cdots$
1320.2.f.a	$1320$	$2$	1320.f	33.d	$2$	$24$	$24$	$10.540$		$_{}$	None	None		✓			1320.2.f.a	$2$	$0$	$0$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1320.2.f.b	$1320$	$2$	1320.f	33.d	$2$	$24$	$24$	$10.540$		$_{}$	None	None		✓			1320.2.f.a	$2$	$0$	$0$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1320.2.w.a	$1320$	$2$	1320.w	8.b	$2$	$2$	$2$	$10.540$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1320.2.w.a	$2$	$0$	$2$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(i+1)q^{2}-i q^{3}+2 i q^{4}-i q^{5}+\cdots$
1320.2.w.b	$1320$	$2$	1320.w	8.b	$2$	$2$	$2$	$10.540$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1320.2.w.b	$2$	$0$	$2$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(i+1)q^{2}-i q^{3}+2 i q^{4}-i q^{5}+\cdots$
1320.2.w.c	$1320$	$2$	1320.w	8.b	$2$	$12$	$12$	$10.540$	$\Q(\zeta_{28})$	$_{}$	None	None		✓			1320.2.w.c	$2$	$0$	$-2$	$0$	$0$	$4$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{9} q^{2}-\beta_{5} q^{3}-\beta_{4} q^{4}-\beta_{5} q^{5}+\cdots$
1320.2.w.d	$1320$	$2$	1320.w	8.b	$2$	$18$	$18$	$10.540$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		✓			1320.2.w.d	$2$	$0$	$0$	$0$	$0$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{11}q^{3}+\beta _{2}q^{4}-\beta _{11}q^{5}+\cdots$
1320.2.w.e	$1320$	$2$	1320.w	8.b	$2$	$20$	$20$	$10.540$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓			1320.2.w.e	$2$	$0$	$-2$	$0$	$0$	$4$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{11}q^{3}+\beta _{4}q^{4}+\beta _{11}q^{5}+\cdots$
1320.2.w.f	$1320$	$2$	1320.w	8.b	$2$	$26$	$26$	$10.540$		$_{}$	None	None		✓	✓		1320.2.w.f	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1320.2.z.a	$1320$	$2$	1320.z	88.g	$2$	$4$	$4$	$10.540$	$\Q(i, \sqrt{10})$	$_{}$	None	None		✓			1320.2.z.a	$2$	$0$	$-4$	$-4$	$0$	$8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1})q^{2}-q^{3}+2\beta _{1}q^{4}-\beta _{1}q^{5}+\cdots$
1320.2.z.b	$1320$	$2$	1320.z	88.g	$2$	$4$	$4$	$10.540$	$\Q(i, \sqrt{10})$	$_{}$	None	None		✓			1320.2.z.a	$2$	$0$	$4$	$-4$	$0$	$-8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{1})q^{2}-q^{3}-2\beta _{1}q^{4}+\beta _{1}q^{5}+\cdots$
1320.2.z.c	$1320$	$2$	1320.z	88.g	$2$	$40$	$40$	$10.540$		$_{}$	None	None		✓			1320.2.z.c	$4$	$0$	$0$	$-40$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1320.2.z.d	$1320$	$2$	1320.z	88.g	$2$	$48$	$48$	$10.540$		$_{}$	None	None		✓	✓		1320.2.z.d	$4$	$0$	$0$	$48$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1320.2.ba.a	$1320$	$2$	1320.ba	165.d	$2$	$72$	$72$	$10.540$		$_{}$	None	None		✓	✓	✓	1320.2.ba.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1320.2.bu.a	$1320$	$2$	1320.bu	55.e	$4$	$36$	$18$	$10.540$		$_{}$	None	None		✓			1320.2.bu.a	$2$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
1320.2.bu.b	$1320$	$2$	1320.bu	55.e	$4$	$36$	$18$	$10.540$		$_{}$	None	None		✓			1320.2.bu.a	$2$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{4}]$
1320.2.bw.a	$1320$	$2$	1320.bw	11.c	$5$	$4$	$1$	$10.540$	$\Q(\zeta_{10})$	$_{}$	None	None		✓			1320.2.bw.a	$2$	$0$	$0$	$-1$	$1$	$-8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{2}q^{3}+\zeta_{10}q^{5}+(-2+2\zeta_{10}+\cdots)q^{7}+\cdots$
1320.2.bw.b	$1320$	$2$	1320.bw	11.c	$5$	$8$	$2$	$10.540$	8.0.13140625.1	$_{}$	None	None		✓			1320.2.bw.b	$2$	$0$	$0$	$-2$	$-2$	$-5$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{4}q^{3}-\beta _{3}q^{5}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$

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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.