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 (50 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
1380.1.b.a	$1380$	$1$	1380.b	1380.b	$2$	$2$	$2$	$0.689$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-69}) $	$\Q(\sqrt{345}) $		✓			1380.1.b.a	$8$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-iq^{2}-iq^{3}-q^{4}-q^{5}-q^{6}+iq^{7}+\cdots$
1380.1.b.b	$1380$	$1$	1380.b	1380.b	$2$	$2$	$2$	$0.689$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-69}) $	$\Q(\sqrt{115}) $		✓			1380.1.b.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}+iq^{3}-q^{4}-iq^{5}+q^{6}+iq^{8}+\cdots$
1380.1.b.c	$1380$	$1$	1380.b	1380.b	$2$	$2$	$2$	$0.689$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-69}) $	$\Q(\sqrt{115}) $		✓			1380.1.b.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{2}-iq^{3}-q^{4}-iq^{5}+q^{6}-iq^{8}+\cdots$
1380.1.b.d	$1380$	$1$	1380.b	1380.b	$2$	$2$	$2$	$0.689$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-69}) $	$\Q(\sqrt{345}) $		✓			1380.1.b.a	$8$	$0$	$0$	$0$	$2$	$0$		$1$		$q-iq^{2}-iq^{3}-q^{4}+q^{5}-q^{6}-iq^{7}+\cdots$
1380.1.bn.a	$1380$	$1$	1380.bn	1380.an	$22$	$20$	$2$	$0.689$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-5}) $	None		✓			1380.1.bn.a	$8$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+\zeta_{44}^{21}q^{2}+\zeta_{44}^{13}q^{3}-\zeta_{44}^{20}q^{4}+\cdots$
1380.1.bn.b	$1380$	$1$	1380.bn	1380.an	$22$	$20$	$2$	$0.689$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-15}) $	None		✓			1380.1.bn.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{44}^{13}q^{2}+\zeta_{44}^{3}q^{3}-\zeta_{44}^{4}q^{4}+\cdots$
1380.1.bn.c	$1380$	$1$	1380.bn	1380.an	$22$	$20$	$2$	$0.689$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-15}) $	None		✓			1380.1.bn.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{44}^{7}q^{2}+\zeta_{44}^{3}q^{3}+\zeta_{44}^{14}q^{4}+\cdots$
1380.1.bn.d	$1380$	$1$	1380.bn	1380.an	$22$	$20$	$2$	$0.689$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-5}) $	None		✓			1380.1.bn.a	$8$	$0$	$0$	$0$	$2$	$0$		$1$		$q+\zeta_{44}^{21}q^{2}-\zeta_{44}^{15}q^{3}-\zeta_{44}^{20}q^{4}+\cdots$
1380.2.a.a	$1380$	$2$	1380.a	1.a	$1$	$1$	$1$	$11.019$	$\Q$	$_{}$	None	None	✓	✓			1380.2.a.a	$1$	$0$	$0$	$-1$	$-1$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-5q^{7}+q^{9}+4q^{13}+q^{15}+\cdots$
1380.2.a.b	$1380$	$2$	1380.a	1.a	$1$	$1$	$1$	$11.019$	$\Q$	$_{}$	None	None	✓	✓			1380.2.a.b	$1$	$0$	$0$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}-6q^{13}+q^{15}+2q^{17}+\cdots$
1380.2.a.c	$1380$	$2$	1380.a	1.a	$1$	$1$	$1$	$11.019$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1380.2.a.c	$1$	$1$	$0$	$1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}+q^{9}-4q^{13}-q^{15}+\cdots$
1380.2.a.d	$1380$	$2$	1380.a	1.a	$1$	$1$	$1$	$11.019$	$\Q$	$_{}$	None	None	✓	✓			1380.2.a.d	$1$	$0$	$0$	$1$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-4q^{7}+q^{9}+2q^{13}+q^{15}+\cdots$
1380.2.a.e	$1380$	$2$	1380.a	1.a	$1$	$1$	$1$	$11.019$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1380.2.a.e	$1$	$1$	$0$	$1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-3q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
1380.2.a.f	$1380$	$2$	1380.a	1.a	$1$	$2$	$2$	$11.019$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	✓	✓	✓	1380.2.a.f	$1$	$1$	$0$	$-2$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots$
1380.2.a.g	$1380$	$2$	1380.a	1.a	$1$	$2$	$2$	$11.019$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓	✓	1380.2.a.g	$1$	$0$	$0$	$-2$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+\beta q^{7}+q^{9}+2\beta q^{11}+\cdots$
1380.2.a.h	$1380$	$2$	1380.a	1.a	$1$	$2$	$2$	$11.019$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓	✓	✓	1380.2.a.h	$1$	$1$	$0$	$-2$	$2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+(1+2\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
1380.2.a.i	$1380$	$2$	1380.a	1.a	$1$	$2$	$2$	$11.019$	$\Q(\sqrt{15}) $	$_{}$	None	None	✓	✓	✓		1380.2.a.i	$1$	$0$	$0$	$2$	$2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+3q^{7}+q^{9}+(1+\beta )q^{11}+\cdots$
1380.2.a.j	$1380$	$2$	1380.a	1.a	$1$	$3$	$3$	$11.019$	3.3.3144.1	$_{}$	None	None	✓	✓	✓	✓	1380.2.a.j	$1$	$0$	$0$	$3$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+(1-\beta _{1})q^{7}+q^{9}+(1+\beta _{2})q^{11}+\cdots$
1380.2.f.a	$1380$	$2$	1380.f	5.b	$2$	$6$	$6$	$11.019$	6.0.350464.1	$_{}$	None	None		✓			1380.2.f.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+(-\beta _{1}+\beta _{4})q^{5}-\beta _{3}q^{7}+\cdots$
1380.2.f.b	$1380$	$2$	1380.f	5.b	$2$	$14$	$14$	$11.019$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		✓	✓		1380.2.f.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{3}+\beta _{10}q^{5}+\beta _{13}q^{7}-q^{9}+\cdots$
1380.2.i.a	$1380$	$2$	1380.i	69.c	$2$	$16$	$16$	$11.019$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1380.2.i.a	$2$	$0$	$0$	$0$	$-16$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{3}-q^{5}-\beta _{8}q^{7}-\beta _{6}q^{9}-\beta _{9}q^{11}+\cdots$
1380.2.i.b	$1380$	$2$	1380.i	69.c	$2$	$16$	$16$	$11.019$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1380.2.i.a	$2$	$0$	$0$	$0$	$16$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+q^{5}-\beta _{8}q^{7}+\beta _{2}q^{9}+\beta _{9}q^{11}+\cdots$
1380.2.n.a	$1380$	$2$	1380.n	345.h	$2$	$48$	$48$	$11.019$		$_{}$	None	None		✓	✓	✓	1380.2.n.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1380.2.p.a	$1380$	$2$	1380.p	92.b	$2$	$48$	$48$	$11.019$		$_{}$	None	None		✓			1380.2.p.a	$2$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1380.2.p.b	$1380$	$2$	1380.p	92.b	$2$	$48$	$48$	$11.019$		$_{}$	None	None		✓			1380.2.p.a	$2$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1380.2.r.a	$1380$	$2$	1380.r	15.e	$4$	$4$	$2$	$11.019$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1380.2.r.a	$4$	$0$	$0$	$-4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$
1380.2.r.b	$1380$	$2$	1380.r	15.e	$4$	$4$	$2$	$11.019$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1380.2.r.b	$4$	$0$	$0$	$-4$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots$
1380.2.r.c	$1380$	$2$	1380.r	15.e	$4$	$80$	$40$	$11.019$		$_{}$	None	None		✓	✓		1380.2.r.c	$4$	$0$	$0$	$8$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1380.2.t.a	$1380$	$2$	1380.t	115.e	$4$	$48$	$24$	$11.019$		$_{}$	None	None		✓	✓	✓	1380.2.t.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1380.3.c.a	$1380$	$3$	1380.c	15.d	$2$	$88$	$88$	$37.602$		$_{}$	None	None		✓	✓	✓	1380.3.c.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1380.3.d.a	$1380$	$3$	1380.d	23.b	$2$	$32$	$32$	$37.602$		$_{}$	None	None		✓	✓	✓	1380.3.d.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1380.3.k.a	$1380$	$3$	1380.k	115.c	$2$	$48$	$48$	$37.602$		$_{}$	None	None		✓	✓	✓	1380.3.k.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1380.3.l.a	$1380$	$3$	1380.l	3.b	$2$	$60$	$60$	$37.602$		$_{}$	None	None		✓	✓	✓	1380.3.l.a	$2$	$0$	$0$	$-8$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$
1380.3.v.a	$1380$	$3$	1380.v	5.c	$4$	$88$	$44$	$37.602$		$_{}$	None	None		✓	✓	✓	1380.3.v.a	$2$	$0$	$0$	$0$	$-16$	$-16$			$\mathrm{SU}(2)[C_{4}]$
1380.4.a.a	$1380$	$4$	1380.a	1.a	$1$	$1$	$1$	$81.423$	$\Q$	$_{}$	None	None	✓	✓			1380.4.a.a	$1$	$1$	$0$	$-3$	$-5$	$-16$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-5q^{5}-2^{4}q^{7}+9q^{9}+30q^{11}+\cdots$
1380.4.a.b	$1380$	$4$	1380.a	1.a	$1$	$2$	$2$	$81.423$	$\Q(\sqrt{561}) $	$_{}$	None	None	✓	✓			1380.4.a.b	$1$	$1$	$0$	$-6$	$10$	$-17$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+5q^{5}+(-8-\beta )q^{7}+9q^{9}+\cdots$
1380.4.a.c	$1380$	$4$	1380.a	1.a	$1$	$3$	$3$	$81.423$	3.3.72332.1	$_{}$	None	None	✓	✓	✓		1380.4.a.c	$1$	$1$	$0$	$-9$	$15$	$22$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+5q^{5}+(8-2\beta _{1}-\beta _{2})q^{7}+\cdots$
1380.4.a.d	$1380$	$4$	1380.a	1.a	$1$	$4$	$4$	$81.423$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	$_{}$	None	None	✓	✓	✓		1380.4.a.d	$1$	$1$	$0$	$-12$	$-20$	$35$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	$q-3q^{3}-5q^{5}+(9-\beta _{3})q^{7}+9q^{9}+\cdots$
1380.4.a.e	$1380$	$4$	1380.a	1.a	$1$	$5$	$5$	$81.423$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1380.4.a.e	$1$	$0$	$0$	$-15$	$-25$	$-7$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-3q^{3}-5q^{5}+(-1-\beta _{2})q^{7}+9q^{9}+\cdots$
1380.4.a.f	$1380$	$4$	1380.a	1.a	$1$	$5$	$5$	$81.423$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1380.4.a.f	$1$	$0$	$0$	$-15$	$25$	$-25$	$+$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	$q-3q^{3}+5q^{5}+(-5-\beta _{1})q^{7}+9q^{9}+\cdots$
1380.4.a.g	$1380$	$4$	1380.a	1.a	$1$	$5$	$5$	$81.423$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1380.4.a.g	$1$	$1$	$0$	$15$	$-25$	$-5$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+3q^{3}-5q^{5}+(-1-\beta _{1})q^{7}+9q^{9}+\cdots$
1380.4.a.h	$1380$	$4$	1380.a	1.a	$1$	$5$	$5$	$81.423$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1380.4.a.h	$1$	$1$	$0$	$15$	$25$	$-23$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+3q^{3}+5q^{5}+(-5-\beta _{1}-\beta _{3}-\beta _{4})q^{7}+\cdots$
1380.4.a.i	$1380$	$4$	1380.a	1.a	$1$	$7$	$7$	$81.423$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1380.4.a.i	$1$	$0$	$0$	$21$	$-35$	$-7$	$+$	$2^{5}$	$\mathrm{SU}(2)$	$q+3q^{3}-5q^{5}+(-1+\beta _{1})q^{7}+9q^{9}+\cdots$
1380.4.a.j	$1380$	$4$	1380.a	1.a	$1$	$7$	$7$	$81.423$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1380.4.a.j	$1$	$0$	$0$	$21$	$35$	$35$	$+$	$2^{5}$	$\mathrm{SU}(2)$	$q+3q^{3}+5q^{5}+(5-\beta _{1})q^{7}+9q^{9}+\cdots$
1380.4.f.a	$1380$	$4$	1380.f	5.b	$2$	$30$	$30$	$81.423$		$_{}$	None	None		✓			1380.4.f.a	$2$	$0$	$0$	$0$	$12$	$0$			$\mathrm{SU}(2)[C_{2}]$
1380.4.f.b	$1380$	$4$	1380.f	5.b	$2$	$38$	$38$	$81.423$		$_{}$	None	None		✓	✓		1380.4.f.b	$2$	$0$	$0$	$0$	$12$	$0$			$\mathrm{SU}(2)[C_{2}]$
1380.4.i.a	$1380$	$4$	1380.i	69.c	$2$	$48$	$48$	$81.423$		$_{}$	None	None		✓			1380.4.i.a	$2$	$0$	$0$	$0$	$-240$	$0$			$\mathrm{SU}(2)[C_{2}]$
1380.4.i.b	$1380$	$4$	1380.i	69.c	$2$	$48$	$48$	$81.423$		$_{}$	None	None		✓			1380.4.i.a	$2$	$0$	$0$	$0$	$240$	$0$			$\mathrm{SU}(2)[C_{2}]$
1380.5.d.a	$1380$	$5$	1380.d	23.b	$2$	$64$	$64$	$142.651$		$_{}$	None	None		✓	✓	✓	1380.5.d.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1380.5.k.a	$1380$	$5$	1380.k	115.c	$2$	$96$	$96$	$142.651$		$_{}$	None	None		✓	✓	✓	1380.5.k.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.