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 82 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
1760.1.i.a	$1760$	$1$	1760.i	55.d	$2$	$4$	$4$	$0.878$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{55}) $		✓	✓	✓	1760.1.i.a	$8$	$0$	$0$	$0$	$4$	$0$		$2$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+q^{5}-q^{9}-\zeta_{8}^{2}q^{11}+\cdots$
1760.1.o.a	$1760$	$1$	1760.o	440.o	$2$	$1$	$1$	$0.878$	$\Q$	$D_{3}$	$\Q(\sqrt{-110}) $	None	✓				440.1.o.a	$2$	$0$	$0$	$-1$	$-1$	$-1$		$1$		$q-q^{3}-q^{5}-q^{7}-q^{11}+q^{15}+q^{17}+\cdots$
1760.1.o.b	$1760$	$1$	1760.o	440.o	$2$	$1$	$1$	$0.878$	$\Q$	$D_{3}$	$\Q(\sqrt{-110}) $	None	✓				440.1.o.a	$2$	$0$	$0$	$-1$	$-1$	$1$		$1$		$q-q^{3}-q^{5}+q^{7}+q^{11}+q^{15}-q^{17}+\cdots$
1760.1.o.c	$1760$	$1$	1760.o	440.o	$2$	$1$	$1$	$0.878$	$\Q$	$D_{3}$	$\Q(\sqrt{-110}) $	None	✓				440.1.o.a	$2$	$0$	$0$	$1$	$1$	$-1$		$1$		$q+q^{3}+q^{5}-q^{7}+q^{11}+q^{15}+q^{17}+\cdots$
1760.1.o.d	$1760$	$1$	1760.o	440.o	$2$	$1$	$1$	$0.878$	$\Q$	$D_{3}$	$\Q(\sqrt{-110}) $	None	✓				440.1.o.a	$2$	$0$	$0$	$1$	$1$	$1$		$1$		$q+q^{3}+q^{5}+q^{7}-q^{11}+q^{15}-q^{17}+\cdots$
1760.1.o.e	$1760$	$1$	1760.o	440.o	$2$	$4$	$4$	$0.878$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-55}) $	None			✓		440.1.o.e	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q-\zeta_{8}^{2}q^{5}+(\zeta_{8}-\zeta_{8}^{3})q^{7}-q^{9}+\zeta_{8}^{2}q^{11}+\cdots$
1760.1.bw.a	$1760$	$1$	1760.bw	1760.aw	$8$	$16$	$4$	$0.878$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-55}) $	None		✓	✓	✓	1760.1.bw.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{32}^{3}q^{2}+\zeta_{32}^{6}q^{4}+\zeta_{32}^{10}q^{5}+\cdots$
1760.1.cn.a	$1760$	$1$	1760.cn	440.ah	$10$	$4$	$1$	$0.878$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-10}) $	None					440.1.bh.a	$4$	$0$	$0$	$0$	$-1$	$-3$		$1$		$q-\zeta_{10}q^{5}+(-1+\zeta_{10})q^{7}+\zeta_{10}^{4}q^{9}+\cdots$
1760.1.cn.b	$1760$	$1$	1760.cn	440.ah	$10$	$4$	$1$	$0.878$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-10}) $	None					440.1.bh.a	$4$	$0$	$0$	$0$	$1$	$3$		$1$		$q+\zeta_{10}q^{5}+(1-\zeta_{10})q^{7}+\zeta_{10}^{4}q^{9}+\cdots$
1760.2.a.a	$1760$	$2$	1760.a	1.a	$1$	$1$	$1$	$14.054$	$\Q$	$_{}$	None	None	✓	✓			1760.2.a.a	$1$	$1$	$0$	$-2$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}-2q^{13}+\cdots$
1760.2.a.b	$1760$	$2$	1760.a	1.a	$1$	$1$	$1$	$14.054$	$\Q$	$_{}$	None	None	✓	✓			1760.2.a.b	$1$	$1$	$0$	$-2$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}-4q^{7}+q^{9}+q^{11}+4q^{13}+\cdots$
1760.2.a.c	$1760$	$2$	1760.a	1.a	$1$	$1$	$1$	$14.054$	$\Q$	$_{}$	None	None	✓	✓			1760.2.a.c	$1$	$1$	$0$	$-2$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}-q^{11}+4q^{13}+\cdots$
1760.2.a.d	$1760$	$2$	1760.a	1.a	$1$	$1$	$1$	$14.054$	$\Q$	$_{}$	None	None	✓	✓			1760.2.a.d	$1$	$1$	$0$	$-1$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+3q^{7}-2q^{9}-q^{11}-2q^{13}+\cdots$
1760.2.a.e	$1760$	$2$	1760.a	1.a	$1$	$1$	$1$	$14.054$	$\Q$	$_{}$	None	None	✓	✓			1760.2.a.e	$1$	$0$	$0$	$-1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}-2q^{9}-q^{11}-2q^{13}+\cdots$
1760.2.a.f	$1760$	$2$	1760.a	1.a	$1$	$1$	$1$	$14.054$	$\Q$	$_{}$	None	None	✓	✓			1760.2.a.f	$1$	$0$	$0$	$-1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+3q^{7}-2q^{9}+q^{11}-2q^{13}+\cdots$
1760.2.a.g	$1760$	$2$	1760.a	1.a	$1$	$1$	$1$	$14.054$	$\Q$	$_{}$	None	None	✓	✓			1760.2.a.g	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{9}-q^{11}-2q^{13}-2q^{17}+\cdots$
1760.2.a.h	$1760$	$2$	1760.a	1.a	$1$	$1$	$1$	$14.054$	$\Q$	$_{}$	None	None	✓	✓			1760.2.a.g	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{9}+q^{11}-2q^{13}-2q^{17}+\cdots$
1760.2.a.i	$1760$	$2$	1760.a	1.a	$1$	$1$	$1$	$14.054$	$\Q$	$_{}$	None	None	✓	✓			1760.2.a.d	$1$	$0$	$0$	$1$	$-1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-3q^{7}-2q^{9}+q^{11}-2q^{13}+\cdots$
1760.2.a.j	$1760$	$2$	1760.a	1.a	$1$	$1$	$1$	$14.054$	$\Q$	$_{}$	None	None	✓	✓			1760.2.a.f	$1$	$1$	$0$	$1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-3q^{7}-2q^{9}-q^{11}-2q^{13}+\cdots$
1760.2.a.k	$1760$	$2$	1760.a	1.a	$1$	$1$	$1$	$14.054$	$\Q$	$_{}$	None	None	✓	✓			1760.2.a.e	$1$	$1$	$0$	$1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}-2q^{9}+q^{11}-2q^{13}+\cdots$
1760.2.a.l	$1760$	$2$	1760.a	1.a	$1$	$1$	$1$	$14.054$	$\Q$	$_{}$	None	None	✓	✓			1760.2.a.a	$1$	$1$	$0$	$2$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}-2q^{7}+q^{9}-q^{11}-2q^{13}+\cdots$
1760.2.a.m	$1760$	$2$	1760.a	1.a	$1$	$1$	$1$	$14.054$	$\Q$	$_{}$	None	None	✓	✓			1760.2.a.c	$1$	$0$	$0$	$2$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+q^{9}+q^{11}+4q^{13}+\cdots$
1760.2.a.n	$1760$	$2$	1760.a	1.a	$1$	$1$	$1$	$14.054$	$\Q$	$_{}$	None	None	✓	✓			1760.2.a.b	$1$	$0$	$0$	$2$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+4q^{7}+q^{9}-q^{11}+4q^{13}+\cdots$
1760.2.a.o	$1760$	$2$	1760.a	1.a	$1$	$2$	$2$	$14.054$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓		1760.2.a.o	$1$	$1$	$0$	$-2$	$-2$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}-q^{5}-2q^{7}+(3+2\beta )q^{9}+\cdots$
1760.2.a.p	$1760$	$2$	1760.a	1.a	$1$	$2$	$2$	$14.054$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			1760.2.a.o	$1$	$0$	$0$	$2$	$-2$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{5}+2q^{7}+(3+2\beta )q^{9}+\cdots$
1760.2.a.q	$1760$	$2$	1760.a	1.a	$1$	$3$	$3$	$14.054$	3.3.229.1	$_{}$	None	None	✓	✓	✓		1760.2.a.q	$1$	$0$	$0$	$-2$	$-3$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}-q^{5}+(1-\beta _{1})q^{7}+\cdots$
1760.2.a.r	$1760$	$2$	1760.a	1.a	$1$	$3$	$3$	$14.054$	3.3.229.1	$_{}$	None	None	✓	✓			1760.2.a.r	$1$	$0$	$0$	$-1$	$-3$	$7$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-q^{5}+(2-\beta _{1})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
1760.2.a.s	$1760$	$2$	1760.a	1.a	$1$	$3$	$3$	$14.054$	3.3.229.1	$_{}$	None	None	✓	✓	✓		1760.2.a.r	$1$	$1$	$0$	$1$	$-3$	$-7$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}-q^{5}+(-2+\beta _{1})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
1760.2.a.t	$1760$	$2$	1760.a	1.a	$1$	$3$	$3$	$14.054$	3.3.229.1	$_{}$	None	None	✓	✓			1760.2.a.q	$1$	$0$	$0$	$2$	$-3$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}-q^{5}+(-1+\beta _{1})q^{7}+\cdots$
1760.2.a.u	$1760$	$2$	1760.a	1.a	$1$	$5$	$5$	$14.054$	5.5.792644.1	$_{}$	None	None	✓	✓	✓		1760.2.a.u	$1$	$0$	$0$	$0$	$5$	$-2$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+q^{5}-\beta _{4}q^{7}+(2-\beta _{1})q^{9}+\cdots$
1760.2.a.v	$1760$	$2$	1760.a	1.a	$1$	$5$	$5$	$14.054$	5.5.792644.1	$_{}$	None	None	✓	✓	✓		1760.2.a.u	$1$	$0$	$0$	$0$	$5$	$2$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+q^{5}+\beta _{4}q^{7}+(2-\beta _{1})q^{9}+\cdots$
1760.2.b.a	$1760$	$2$	1760.b	5.b	$2$	$2$	$2$	$14.054$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1760.2.b.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{3}+(-i-2)q^{5}+3 i q^{7}+\cdots$
1760.2.b.b	$1760$	$2$	1760.b	5.b	$2$	$2$	$2$	$14.054$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1760.2.b.a	$2$	$1$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{3}+(i-2)q^{5}+3 i q^{7}-6 q^{9}+\cdots$
1760.2.b.c	$1760$	$2$	1760.b	5.b	$2$	$14$	$14$	$14.054$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		✓			1760.2.b.c	$2$	$0$	$0$	$0$	$0$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-\beta _{5}q^{5}+\beta _{7}q^{7}+\beta _{2}q^{9}+\cdots$
1760.2.b.d	$1760$	$2$	1760.b	5.b	$2$	$14$	$14$	$14.054$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		✓			1760.2.b.c	$2$	$0$	$0$	$0$	$0$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{7}q^{7}+\beta _{2}q^{9}+\cdots$
1760.2.b.e	$1760$	$2$	1760.b	5.b	$2$	$14$	$14$	$14.054$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		✓			1760.2.b.e	$2$	$0$	$0$	$0$	$2$	$0$		$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}+\beta _{7}q^{5}+\beta _{11}q^{7}+(-1-\beta _{8}+\cdots)q^{9}+\cdots$
1760.2.b.f	$1760$	$2$	1760.b	5.b	$2$	$14$	$14$	$14.054$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		✓			1760.2.b.e	$2$	$0$	$0$	$0$	$2$	$0$		$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}-\beta _{6}q^{5}+\beta _{11}q^{7}+(-1-\beta _{8}+\cdots)q^{9}+\cdots$
1760.2.c.a	$1760$	$2$	1760.c	440.c	$2$	$4$	$4$	$14.054$	$\Q(\sqrt{-2}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-10}) $	None					440.2.c.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{3}q^{5}+2\beta _{1}q^{7}+3q^{9}+(1+\beta _{2}+\cdots)q^{11}+\cdots$
1760.2.c.b	$1760$	$2$	1760.c	440.c	$2$	$8$	$8$	$14.054$	8.0.$\cdots$.19	$_{}$	$\Q(\sqrt{-55}) $	None					440.2.c.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{5}+\beta _{2}q^{7}+3q^{9}+\beta _{3}q^{11}+\cdots$
1760.2.c.c	$1760$	$2$	1760.c	440.c	$2$	$56$	$56$	$14.054$		$_{}$	None	None			✓		440.2.c.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1760.2.f.a	$1760$	$2$	1760.f	44.c	$2$	$4$	$4$	$14.054$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1760.2.f.a	$4$	$0$	$0$	$0$	$4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{2}-\beta_1)q^{3}+q^{5}+(-\beta_{2}-\beta_1)q^{7}+\cdots$
1760.2.f.b	$1760$	$2$	1760.f	44.c	$2$	$4$	$4$	$14.054$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1760.2.f.b	$4$	$0$	$0$	$0$	$4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{2}-\beta_1)q^{3}+q^{5}-q^{9}+(-\beta_{2}+2\beta_1)q^{11}+\cdots$
1760.2.f.c	$1760$	$2$	1760.f	44.c	$2$	$16$	$16$	$14.054$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1760.2.f.c	$4$	$0$	$0$	$0$	$16$	$0$		$2^{22}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}+q^{5}+\beta _{9}q^{7}+(-2-\beta _{1}+\cdots)q^{9}+\cdots$
1760.2.f.d	$1760$	$2$	1760.f	44.c	$2$	$24$	$24$	$14.054$		$_{}$	None	None		✓	✓		1760.2.f.d	$4$	$0$	$0$	$0$	$-24$	$0$			$\mathrm{SU}(2)[C_{2}]$
1760.2.g.a	$1760$	$2$	1760.g	8.b	$2$	$4$	$4$	$14.054$	$\Q(\zeta_{8})$	$_{}$	None	None					440.2.g.a	$2$	$0$	$0$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{2}+\beta_1)q^{3}-\beta_1 q^{5}+q^{7}-2\beta_{3} q^{9}+\cdots$
1760.2.g.b	$1760$	$2$	1760.g	8.b	$2$	$12$	$12$	$14.054$	12.0.$\cdots$.1	$_{}$	None	None					440.2.g.b	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-\beta _{9}q^{5}+(-\beta _{2}+\beta _{3}-\beta _{10}+\cdots)q^{7}+\cdots$
1760.2.g.c	$1760$	$2$	1760.g	8.b	$2$	$24$	$24$	$14.054$		$_{}$	None	None			✓		440.2.g.c	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1760.2.l.a	$1760$	$2$	1760.l	40.f	$2$	$2$	$2$	$14.054$	$\Q(\sqrt{-1}) $	$_{}$	None	None					440.2.l.a	$2$	$0$	$0$	$-4$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2 q^{3}+(2 i+1)q^{5}+4 i q^{7}+q^{9}+\cdots$
1760.2.l.b	$1760$	$2$	1760.l	40.f	$2$	$2$	$2$	$14.054$	$\Q(\sqrt{-1}) $	$_{}$	None	None					440.2.l.a	$2$	$0$	$0$	$4$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 q^{3}+(2 i-1)q^{5}-4 i q^{7}+q^{9}+\cdots$
1760.2.l.c	$1760$	$2$	1760.l	40.f	$2$	$56$	$56$	$14.054$		$_{}$	None	None			✓		440.2.l.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.