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 114 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
820.1.e.a	$820$	$1$	820.e	820.e	$2$	$1$	$1$	$0.409$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-205}) $	$\Q(\sqrt{41}) $	✓	✓			820.1.e.a	$4$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{9}+q^{10}+\cdots$
820.1.e.b	$820$	$1$	820.e	820.e	$2$	$1$	$1$	$0.409$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-205}) $	$\Q(\sqrt{41}) $	✓	✓			820.1.e.a	$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}+q^{9}-q^{10}+\cdots$
820.1.e.c	$820$	$1$	820.e	820.e	$2$	$8$	$8$	$0.409$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-41}) $	None		✓	✓		820.1.e.c	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+\zeta_{16}^{4}q^{2}+(-\zeta_{16}-\zeta_{16}^{7})q^{3}-q^{4}+\cdots$
820.1.o.a	$820$	$1$	820.o	820.o	$4$	$2$	$1$	$0.409$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓			820.1.o.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-i q^{5}-q^{8}+i q^{9}+\cdots$
820.1.o.b	$820$	$1$	820.o	820.o	$4$	$2$	$1$	$0.409$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-5}) $	None		✓			820.1.o.b	$4$	$0$	$0$	$-2$	$0$	$-2$		$1$		$q+i q^{2}+(i-1)q^{3}-q^{4}+i q^{5}+\cdots$
820.1.o.c	$820$	$1$	820.o	820.o	$4$	$2$	$1$	$0.409$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-5}) $	None		✓			820.1.o.b	$4$	$0$	$0$	$2$	$0$	$2$		$1$		$q-i q^{2}+(-i+1)q^{3}-q^{4}+i q^{5}+\cdots$
820.1.o.d	$820$	$1$	820.o	820.o	$4$	$2$	$1$	$0.409$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓			820.1.o.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}-i q^{5}+q^{8}+i q^{9}+\cdots$
820.1.z.a	$820$	$1$	820.z	820.z	$8$	$4$	$1$	$0.409$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	820.1.z.a	$4$	$0$	$-4$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-\zeta_{8}^{3}q^{5}-q^{8}+\zeta_{8}q^{9}+\cdots$
820.1.ba.a	$820$	$1$	820.ba	820.aa	$8$	$4$	$1$	$0.409$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	820.1.z.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{2}q^{2}-q^{4}+\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{8}+\cdots$
820.1.bd.a	$820$	$1$	820.bd	820.ad	$10$	$4$	$1$	$0.409$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-5}) $	None		✓			820.1.bd.a	$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q+\zeta_{10}^{2}q^{2}+(-\zeta_{10}-\zeta_{10}^{4})q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
820.1.bd.b	$820$	$1$	820.bd	820.ad	$10$	$4$	$1$	$0.409$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-5}) $	None		✓			820.1.bd.a	$4$	$0$	$1$	$0$	$1$	$0$		$1$		$q-\zeta_{10}^{2}q^{2}+(\zeta_{10}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
820.1.bj.a	$820$	$1$	820.bj	820.aj	$10$	$4$	$1$	$0.409$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-5}) $	None		✓			820.1.bj.a	$4$	$0$	$-1$	$-2$	$-1$	$-2$		$1$		$q-\zeta_{10}^{3}q^{2}+(-\zeta_{10}+\zeta_{10}^{4})q^{3}-\zeta_{10}q^{4}+\cdots$
820.1.bj.b	$820$	$1$	820.bj	820.aj	$10$	$4$	$1$	$0.409$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-5}) $	None		✓			820.1.bj.a	$4$	$0$	$1$	$2$	$-1$	$2$		$1$		$q+\zeta_{10}^{3}q^{2}+(\zeta_{10}-\zeta_{10}^{4})q^{3}-\zeta_{10}q^{4}+\cdots$
820.1.bp.a	$820$	$1$	820.bp	820.ap	$20$	$8$	$1$	$0.409$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		✓			820.1.bp.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{6}q^{2}-\zeta_{20}^{2}q^{4}-\zeta_{20}^{3}q^{5}+\cdots$
820.1.bp.b	$820$	$1$	820.bp	820.ap	$20$	$8$	$1$	$0.409$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-5}) $	None		✓			820.1.bp.b	$4$	$0$	$0$	$-2$	$0$	$-2$		$1$		$q+\zeta_{20}q^{2}+(-\zeta_{20}^{2}-\zeta_{20}^{3})q^{3}+\zeta_{20}^{2}q^{4}+\cdots$
820.1.bp.c	$820$	$1$	820.bp	820.ap	$20$	$8$	$1$	$0.409$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-5}) $	None		✓			820.1.bp.b	$4$	$0$	$0$	$2$	$0$	$2$		$1$		$q-\zeta_{20}q^{2}+(\zeta_{20}^{2}+\zeta_{20}^{3})q^{3}+\zeta_{20}^{2}q^{4}+\cdots$
820.1.bp.d	$820$	$1$	820.bp	820.ap	$20$	$8$	$1$	$0.409$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		✓			820.1.bp.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+\zeta_{20}^{6}q^{2}-\zeta_{20}^{2}q^{4}+\zeta_{20}q^{5}-\zeta_{20}^{8}q^{8}+\cdots$
820.1.by.a	$820$	$1$	820.by	820.ay	$40$	$16$	$1$	$0.409$	$\Q(\zeta_{40})$	$D_{40}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	820.1.by.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{40}^{6}q^{2}+\zeta_{40}^{12}q^{4}+\zeta_{40}q^{5}+\cdots$
820.1.bz.a	$820$	$1$	820.bz	820.az	$40$	$16$	$1$	$0.409$	$\Q(\zeta_{40})$	$D_{40}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	820.1.by.a	$4$	$0$	$4$	$0$	$0$	$0$		$1$		$q-\zeta_{40}^{8}q^{2}+\zeta_{40}^{16}q^{4}-\zeta_{40}^{9}q^{5}+\cdots$
820.2.a.a	$820$	$2$	820.a	1.a	$1$	$2$	$2$	$6.548$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓	✓	820.2.a.a	$1$	$1$	$0$	$-2$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-\beta q^{7}-2q^{9}+(-1+4\beta )q^{11}+\cdots$
820.2.a.b	$820$	$2$	820.a	1.a	$1$	$2$	$2$	$6.548$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓	✓	✓	820.2.a.b	$1$	$1$	$0$	$2$	$-2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+(-1-\beta )q^{7}-2q^{9}+(-3+\cdots)q^{11}+\cdots$
820.2.a.c	$820$	$2$	820.a	1.a	$1$	$4$	$4$	$6.548$	$\Q(\sqrt{5}, \sqrt{13})$	$_{}$	None	None	✓	✓	✓	✓	820.2.a.c	$1$	$0$	$0$	$0$	$-4$	$-1$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+(\beta _{1}-\beta _{2})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots$
820.2.a.d	$820$	$2$	820.a	1.a	$1$	$4$	$4$	$6.548$	4.4.13068.1	$_{}$	None	None	✓	✓	✓	✓	820.2.a.d	$1$	$0$	$0$	$0$	$4$	$1$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+q^{5}+\beta _{3}q^{7}+(1-\beta _{1}+\beta _{3})q^{9}+\cdots$
820.2.b.a	$820$	$2$	820.b	41.b	$2$	$6$	$6$	$6.548$	6.0.36433296.1	$_{}$	None	None		✓			820.2.b.a	$2$	$0$	$0$	$0$	$-6$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}-q^{5}-\beta _{4}q^{7}+(-2-\beta _{3}+\cdots)q^{9}+\cdots$
820.2.b.b	$820$	$2$	820.b	41.b	$2$	$8$	$8$	$6.548$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		✓	✓		820.2.b.b	$2$	$0$	$0$	$0$	$8$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{3}+q^{5}-\beta _{4}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots$
820.2.d.a	$820$	$2$	820.d	5.b	$2$	$6$	$6$	$6.548$	6.0.839056.1	$_{}$	None	None		✓			820.2.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+(\beta _{1}-\beta _{4})q^{5}-\beta _{4}q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots$
820.2.d.b	$820$	$2$	820.d	5.b	$2$	$14$	$14$	$6.548$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		✓	✓		820.2.d.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{5}q^{5}+\beta _{11}q^{7}+(-2+\beta _{2}+\cdots)q^{9}+\cdots$
820.2.g.a	$820$	$2$	820.g	205.c	$2$	$4$	$4$	$6.548$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			820.2.g.a	$4$	$0$	$0$	$0$	$8$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{3} q^{3}+(-\beta_1+2)q^{5}-\beta_{3} q^{7}+\cdots$
820.2.g.b	$820$	$2$	820.g	205.c	$2$	$16$	$16$	$6.548$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		820.2.g.b	$4$	$0$	$0$	$0$	$-8$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{3}+(-1-\beta _{8})q^{5}-\beta _{12}q^{7}+\cdots$
820.2.j.a	$820$	$2$	820.j	820.j	$4$	$2$	$1$	$6.548$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			820.2.j.a	$4$	$0$	$-2$	$0$	$2$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i-1)q^{2}+2 i q^{4}+(2 i+1)q^{5}+\cdots$
820.2.j.b	$820$	$2$	820.j	820.j	$4$	$2$	$1$	$6.548$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			820.2.j.b	$4$	$0$	$2$	$0$	$2$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(i+1)q^{2}+2 i q^{4}+(2 i+1)q^{5}+\cdots$
820.2.j.c	$820$	$2$	820.j	820.j	$4$	$240$	$120$	$6.548$		$_{}$	None	None		✓	✓		820.2.j.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
820.2.k.a	$820$	$2$	820.k	20.e	$4$	$4$	$2$	$6.548$	$\Q(i, \sqrt{5})$	$_{}$	None	None		✓			820.2.k.a	$4$	$0$	$-4$	$0$	$-8$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}-2\beta _{1}q^{4}+\cdots$
820.2.k.b	$820$	$2$	820.k	20.e	$4$	$8$	$4$	$6.548$	8.0.$\cdots$.8	$_{}$	None	None		✓			820.2.k.b	$4$	$0$	$-8$	$0$	$8$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}+\cdots$
820.2.k.c	$820$	$2$	820.k	20.e	$4$	$108$	$54$	$6.548$		$_{}$	None	None		✓			820.2.k.c	$4$	$0$	$12$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
820.2.k.d	$820$	$2$	820.k	20.e	$4$	$120$	$60$	$6.548$		$_{}$	None	None		✓	✓		820.2.k.d	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
820.2.n.a	$820$	$2$	820.n	205.j	$4$	$44$	$22$	$6.548$		$_{}$	None	None		✓	✓	✓	820.2.n.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
820.2.p.a	$820$	$2$	820.p	41.c	$4$	$2$	$1$	$6.548$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			820.2.p.a	$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(2 i-2)q^{3}+i q^{5}-5 i q^{9}+(-4 i+4)q^{11}+\cdots$
820.2.p.b	$820$	$2$	820.p	41.c	$4$	$2$	$1$	$6.548$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			820.2.p.b	$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+i q^{5}+(-2 i+2)q^{7}+3 i q^{9}+\cdots$
820.2.p.c	$820$	$2$	820.p	41.c	$4$	$2$	$1$	$6.548$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			820.2.p.c	$2$	$0$	$0$	$2$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i+1)q^{3}-i q^{5}+(-i+1)q^{7}+\cdots$
820.2.p.d	$820$	$2$	820.p	41.c	$4$	$8$	$4$	$6.548$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		✓			820.2.p.d	$2$	$0$	$0$	$2$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{3}+\beta _{2}q^{5}+(-\beta _{3}+\beta _{5})q^{7}+\cdots$
820.2.p.e	$820$	$2$	820.p	41.c	$4$	$14$	$7$	$6.548$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓	✓		820.2.p.e	$2$	$0$	$0$	$-4$	$0$	$-2$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{3}-\beta _{3}q^{5}+\beta _{12}q^{7}+(-\beta _{3}+\cdots)q^{9}+\cdots$
820.2.r.a	$820$	$2$	820.r	820.r	$4$	$2$	$1$	$6.548$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			820.2.r.a	$4$	$0$	$-2$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i-1)q^{2}+2 i q^{4}+(-i+2)q^{5}+\cdots$
820.2.r.b	$820$	$2$	820.r	820.r	$4$	$2$	$1$	$6.548$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			820.2.r.a	$4$	$0$	$-2$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i-1)q^{2}+2 i q^{4}+(-i+2)q^{5}+\cdots$
820.2.r.c	$820$	$2$	820.r	820.r	$4$	$16$	$8$	$6.548$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	$\Q(\sqrt{-41}) $	None		✓			820.2.r.c	$8$	$0$	$-16$	$0$	$0$	$0$		$2^{9}\cdot 5^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+(-1+\beta _{2})q^{2}+\beta _{13}q^{3}-2\beta _{2}q^{4}+\cdots$
820.2.r.d	$820$	$2$	820.r	820.r	$4$	$16$	$8$	$6.548$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	$\Q(\sqrt{-41}) $	None		✓			820.2.r.d	$8$	$0$	$16$	$0$	$0$	$0$		$2^{13}\cdot 5^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+(1+\beta _{1})q^{2}-\beta _{5}q^{3}+2\beta _{1}q^{4}-\beta _{2}q^{5}+\cdots$
820.2.r.e	$820$	$2$	820.r	820.r	$4$	$208$	$104$	$6.548$		$_{}$	None	None		✓	✓		820.2.r.e	$8$	$0$	$0$	$0$	$-16$	$0$			$\mathrm{SU}(2)[C_{4}]$
820.2.s.a	$820$	$2$	820.s	820.s	$4$	$2$	$1$	$6.548$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			820.2.j.b	$4$	$0$	$-2$	$0$	$-2$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(i-1)q^{2}-2 i q^{4}+(2 i-1)q^{5}+\cdots$
820.2.s.b	$820$	$2$	820.s	820.s	$4$	$2$	$1$	$6.548$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		✓			820.2.j.a	$4$	$0$	$2$	$0$	$-2$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i+1)q^{2}-2 i q^{4}+(2 i-1)q^{5}+\cdots$
820.2.s.c	$820$	$2$	820.s	820.s	$4$	$240$	$120$	$6.548$		$_{}$	None	None		✓	✓		820.2.j.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$

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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.