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 78 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
1840.1.g.a	$1840$	$1$	1840.g	115.c	$2$	$1$	$1$	$0.918$	$\Q$	$D_{3}$	$\Q(\sqrt{-115}) $	None	✓				460.1.d.a	$2$	$0$	$0$	$0$	$-1$	$-1$		$1$		$q-q^{5}-q^{7}+q^{9}+q^{17}+q^{23}+q^{25}+\cdots$
1840.1.g.b	$1840$	$1$	1840.g	115.c	$2$	$1$	$1$	$0.918$	$\Q$	$D_{3}$	$\Q(\sqrt{-115}) $	None	✓				460.1.d.a	$2$	$0$	$0$	$0$	$1$	$1$		$1$		$q+q^{5}+q^{7}+q^{9}-q^{17}-q^{23}+q^{25}+\cdots$
1840.1.bq.a	$1840$	$1$	1840.bq	460.n	$22$	$20$	$2$	$0.918$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-5}) $	None		✓	✓	✓	1840.1.bq.a	$8$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(-\zeta_{44}^{7}-\zeta_{44}^{9})q^{3}+\zeta_{44}^{6}q^{5}+\cdots$
1840.2.a.a	$1840$	$2$	1840.a	1.a	$1$	$1$	$1$	$14.692$	$\Q$	$_{}$	None	None	✓				460.2.a.d	$1$	$1$	$0$	$-3$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}-2q^{7}+6q^{9}-3q^{13}+\cdots$
1840.2.a.b	$1840$	$2$	1840.a	1.a	$1$	$1$	$1$	$14.692$	$\Q$	$_{}$	None	None	✓				920.2.a.d	$1$	$1$	$0$	$-1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}-2q^{9}+q^{13}+q^{15}+\cdots$
1840.2.a.c	$1840$	$2$	1840.a	1.a	$1$	$1$	$1$	$14.692$	$\Q$	$_{}$	None	None	✓				460.2.a.c	$1$	$0$	$0$	$-1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+4q^{7}-2q^{9}+6q^{11}+\cdots$
1840.2.a.d	$1840$	$2$	1840.a	1.a	$1$	$1$	$1$	$14.692$	$\Q$	$_{}$	None	None	✓				115.2.a.a	$1$	$0$	$0$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}-3q^{9}-2q^{11}-2q^{13}+\cdots$
1840.2.a.e	$1840$	$2$	1840.a	1.a	$1$	$1$	$1$	$14.692$	$\Q$	$_{}$	None	None	✓				460.2.a.b	$1$	$1$	$0$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}-3q^{9}-6q^{11}+6q^{13}+\cdots$
1840.2.a.f	$1840$	$2$	1840.a	1.a	$1$	$1$	$1$	$14.692$	$\Q$	$_{}$	None	None	✓				920.2.a.c	$1$	$0$	$0$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}-3q^{9}+6q^{11}-2q^{13}+\cdots$
1840.2.a.g	$1840$	$2$	1840.a	1.a	$1$	$1$	$1$	$14.692$	$\Q$	$_{}$	None	None	✓				920.2.a.b	$1$	$1$	$0$	$1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}-2q^{11}-5q^{13}+\cdots$
1840.2.a.h	$1840$	$2$	1840.a	1.a	$1$	$1$	$1$	$14.692$	$\Q$	$_{}$	None	None	✓				460.2.a.a	$1$	$0$	$0$	$1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+2q^{7}-2q^{9}+4q^{11}+\cdots$
1840.2.a.i	$1840$	$2$	1840.a	1.a	$1$	$1$	$1$	$14.692$	$\Q$	$_{}$	None	None	✓				920.2.a.a	$1$	$0$	$0$	$3$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}+2q^{7}+6q^{9}+q^{13}+\cdots$
1840.2.a.j	$1840$	$2$	1840.a	1.a	$1$	$2$	$2$	$14.692$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓				230.2.a.b	$1$	$0$	$0$	$-3$	$2$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+q^{5}+(-2+\beta )q^{7}+\cdots$
1840.2.a.k	$1840$	$2$	1840.a	1.a	$1$	$2$	$2$	$14.692$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				920.2.a.f	$1$	$0$	$0$	$-1$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+q^{5}-2\beta q^{7}+(1+\beta )q^{9}+4q^{11}+\cdots$
1840.2.a.l	$1840$	$2$	1840.a	1.a	$1$	$2$	$2$	$14.692$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				230.2.a.c	$1$	$1$	$0$	$-1$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+q^{5}+(-1+\beta )q^{7}+(-2+\beta )q^{9}+\cdots$
1840.2.a.m	$1840$	$2$	1840.a	1.a	$1$	$2$	$2$	$14.692$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				460.2.a.e	$1$	$1$	$0$	$-1$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+q^{5}+(-1+\beta )q^{7}+(1+\beta )q^{9}+\cdots$
1840.2.a.n	$1840$	$2$	1840.a	1.a	$1$	$2$	$2$	$14.692$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓		✓		230.2.a.a	$1$	$0$	$0$	$1$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+(-1+\beta )q^{7}+(2+\beta )q^{9}+\cdots$
1840.2.a.o	$1840$	$2$	1840.a	1.a	$1$	$2$	$2$	$14.692$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				920.2.a.e	$1$	$0$	$0$	$1$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+(1-\beta )q^{7}+(1+\beta )q^{9}+\cdots$
1840.2.a.p	$1840$	$2$	1840.a	1.a	$1$	$2$	$2$	$14.692$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				115.2.a.b	$1$	$1$	$0$	$2$	$-2$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+(1+\beta )q^{7}-2q^{9}+(1-\beta )q^{11}+\cdots$
1840.2.a.q	$1840$	$2$	1840.a	1.a	$1$	$3$	$3$	$14.692$	3.3.229.1	$_{}$	None	None	✓		✓		920.2.a.i	$1$	$1$	$0$	$-2$	$3$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+q^{5}+(-2+\beta _{2})q^{7}+\cdots$
1840.2.a.r	$1840$	$2$	1840.a	1.a	$1$	$3$	$3$	$14.692$	3.3.1101.1	$_{}$	None	None	✓		✓		230.2.a.d	$1$	$1$	$0$	$-1$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots$
1840.2.a.s	$1840$	$2$	1840.a	1.a	$1$	$3$	$3$	$14.692$	3.3.2597.1	$_{}$	None	None	✓		✓		920.2.a.h	$1$	$0$	$0$	$-1$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+q^{5}+(-1+\beta _{1})q^{7}+(3+\beta _{2})q^{9}+\cdots$
1840.2.a.t	$1840$	$2$	1840.a	1.a	$1$	$3$	$3$	$14.692$	3.3.621.1	$_{}$	None	None	✓		✓		920.2.a.g	$1$	$1$	$0$	$0$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(-1-\beta _{1})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
1840.2.a.u	$1840$	$2$	1840.a	1.a	$1$	$4$	$4$	$14.692$	4.4.15317.1	$_{}$	None	None	✓		✓		115.2.a.c	$1$	$0$	$0$	$2$	$4$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+q^{5}+(1+\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots$
1840.2.a.v	$1840$	$2$	1840.a	1.a	$1$	$5$	$5$	$14.692$	5.5.13955077.1	$_{}$	None	None	✓		✓		920.2.a.j	$1$	$0$	$0$	$0$	$-5$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(\beta _{3}+\beta _{4})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
1840.2.e.a	$1840$	$2$	1840.e	5.b	$2$	$2$	$2$	$14.692$	$\Q(\sqrt{-1}) $	$_{}$	None	None					920.2.e.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{3}+(i+2)q^{5}-3 i q^{7}-q^{9}+\cdots$
1840.2.e.b	$1840$	$2$	1840.e	5.b	$2$	$2$	$2$	$14.692$	$\Q(\sqrt{-1}) $	$_{}$	None	None					115.2.b.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{3}+(i+2)q^{5}-i q^{7}-q^{9}+\cdots$
1840.2.e.c	$1840$	$2$	1840.e	5.b	$2$	$4$	$4$	$14.692$	$\Q(i, \sqrt{5})$	$_{}$	None	None					230.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(1+2\beta _{2})q^{5}+(3\beta _{1}+3\beta _{3})q^{7}+\cdots$
1840.2.e.d	$1840$	$2$	1840.e	5.b	$2$	$8$	$8$	$14.692$	8.0.527896576.2	$_{}$	None	None					115.2.b.b	$2$	$0$	$0$	$0$	$-6$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{2}+\beta _{4})q^{3}+(-1-\beta _{6}+\cdots)q^{5}+\cdots$
1840.2.e.e	$1840$	$2$	1840.e	5.b	$2$	$8$	$8$	$14.692$	8.0.$\cdots$.3	$_{}$	None	None					230.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{2}-\beta _{5})q^{3}+(\beta _{3}+\beta _{6})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
1840.2.e.f	$1840$	$2$	1840.e	5.b	$2$	$12$	$12$	$14.692$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None					460.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{5}+\beta _{6})q^{3}-\beta _{8}q^{5}+(-\beta _{1}-\beta _{6}+\cdots)q^{7}+\cdots$
1840.2.e.g	$1840$	$2$	1840.e	5.b	$2$	$14$	$14$	$14.692$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None					920.2.e.b	$2$	$0$	$0$	$0$	$2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{3}-\beta _{5}q^{5}+(\beta _{7}-\beta _{13})q^{7}+(1+\cdots)q^{9}+\cdots$
1840.2.e.h	$1840$	$2$	1840.e	5.b	$2$	$16$	$16$	$14.692$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None			✓		920.2.e.c	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}-\beta _{10}q^{5}+(-\beta _{2}+\beta _{13})q^{7}+\cdots$
1840.2.i.a	$1840$	$2$	1840.i	92.b	$2$	$16$	$16$	$14.692$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1840.2.i.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{8}q^{5}+(\beta _{3}-\beta _{10})q^{7}+(-2+\cdots)q^{9}+\cdots$
1840.2.i.b	$1840$	$2$	1840.i	92.b	$2$	$16$	$16$	$14.692$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1840.2.i.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{3}+\beta _{2}q^{5}+\beta _{13}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots$
1840.2.i.c	$1840$	$2$	1840.i	92.b	$2$	$16$	$16$	$14.692$	16.0.$\cdots$.1	$_{}$	None	None		✓			1840.2.i.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+\beta _{5}q^{5}+(-\beta _{10}+\beta _{14})q^{7}+\cdots$
1840.2.m.a	$1840$	$2$	1840.m	460.g	$2$	$4$	$4$	$14.692$	$\Q(\sqrt{6}, \sqrt{-14})$	$_{}$	None	None		✓			1840.2.m.a	$4$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\beta _{2}q^{5}-2q^{9}+(2\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots$
1840.2.m.b	$1840$	$2$	1840.m	460.g	$2$	$4$	$4$	$14.692$	$\Q(\sqrt{5}, \sqrt{-23})$	$_{}$	$\Q(\sqrt{-115}) $	None		✓			1840.2.m.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{5}-\beta _{2}q^{7}-3q^{9}+3\beta _{1}q^{17}+\cdots$
1840.2.m.c	$1840$	$2$	1840.m	460.g	$2$	$4$	$4$	$14.692$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-5}) $	None		✓			1840.2.m.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(2\beta _{1}-\beta _{2})q^{3}+\beta _{3}q^{5}+3\beta _{2}q^{7}+\cdots$
1840.2.m.d	$1840$	$2$	1840.m	460.g	$2$	$4$	$4$	$14.692$	$\Q(\sqrt{6}, \sqrt{-14})$	$_{}$	None	None		✓			1840.2.m.a	$4$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta _{2}q^{5}-2q^{9}+(2\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots$
1840.2.m.e	$1840$	$2$	1840.m	460.g	$2$	$8$	$8$	$14.692$	8.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-115}) $	None		✓			1840.2.m.e	$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{5}+\beta _{7}q^{7}-3q^{9}+(-\beta _{1}+\beta _{4}+\cdots)q^{17}+\cdots$
1840.2.m.f	$1840$	$2$	1840.m	460.g	$2$	$8$	$8$	$14.692$	8.0.40960000.1	$_{}$	None	None		✓			1840.2.m.f	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+\beta _{6}q^{5}+2\beta _{5}q^{7}+2q^{9}+\cdots$
1840.2.m.g	$1840$	$2$	1840.m	460.g	$2$	$40$	$40$	$14.692$		$_{}$	None	None		✓	✓		1840.2.m.g	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1840.3.c.a	$1840$	$3$	1840.c	4.b	$2$	$32$	$32$	$50.136$		$_{}$	None	None		✓			1840.3.c.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1840.3.c.b	$1840$	$3$	1840.c	4.b	$2$	$56$	$56$	$50.136$		$_{}$	None	None		✓	✓		1840.3.c.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1840.3.k.a	$1840$	$3$	1840.k	23.b	$2$	$6$	$6$	$50.136$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None					115.3.d.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}-\beta _{3}q^{5}+(\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots$
1840.3.k.b	$1840$	$3$	1840.k	23.b	$2$	$10$	$10$	$50.136$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None					115.3.d.b	$2$	$0$	$0$	$2$	$0$	$0$		$2^{2}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}-\beta _{3}q^{5}+(\beta _{2}+\beta _{3})q^{7}+(-2+\cdots)q^{9}+\cdots$
1840.3.k.c	$1840$	$3$	1840.k	23.b	$2$	$16$	$16$	$50.136$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None					460.3.f.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}-\beta _{4}q^{5}-\beta _{7}q^{7}+(4+\beta _{2}+\cdots)q^{9}+\cdots$
1840.3.k.d	$1840$	$3$	1840.k	23.b	$2$	$16$	$16$	$50.136$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None					230.3.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{5})q^{7}+(5+\cdots)q^{9}+\cdots$
1840.3.k.e	$1840$	$3$	1840.k	23.b	$2$	$48$	$48$	$50.136$		$_{}$	None	None			✓		920.3.k.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.