LMFDB - Newform search results

Refine search

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

				Sort order	Select

Results (1-50 of 68 matches)

Next Download displayed columns for results to

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
1183.1.b.a	$1183$	$1$	1183.b	91.b	$2$	$6$	$6$	$0.590$	6.0.153664.1	$D_{7}$	$\Q(\sqrt{-7}) $	None		✓	✓	✓	1183.1.d.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{5}q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots$
1183.1.d.a	$1183$	$1$	1183.d	7.b	$2$	$3$	$3$	$0.590$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-7}) $	None	✓	✓			1183.1.d.a	$2$	$0$	$-1$	$0$	$0$	$3$		$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{7}+(-1-\beta _{2})q^{8}+\cdots$
1183.1.d.b	$1183$	$1$	1183.d	7.b	$2$	$3$	$3$	$0.590$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-7}) $	None	✓	✓			1183.1.d.a	$2$	$0$	$1$	$0$	$0$	$-3$		$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{7}+(1+\beta _{2})q^{8}+\cdots$
1183.1.n.a	$1183$	$1$	1183.n	91.n	$6$	$6$	$3$	$0.590$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-7}) $	None		✓			1183.1.d.a	$4$	$0$	$-1$	$0$	$0$	$3$		$1$		$q+(-1+\beta _{1}+\beta _{4}+\beta _{5})q^{2}+(-\beta _{3}+\cdots)q^{4}+\cdots$
1183.1.n.b	$1183$	$1$	1183.n	91.n	$6$	$6$	$3$	$0.590$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-7}) $	None		✓			1183.1.d.a	$4$	$0$	$1$	$0$	$0$	$-3$		$1$		$q+(1-\beta _{1}-\beta _{4}-\beta _{5})q^{2}+(-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
1183.1.t.a	$1183$	$1$	1183.t	91.t	$6$	$12$	$6$	$0.590$	12.0.$\cdots$.1	$D_{7}$	$\Q(\sqrt{-7}) $	None		✓	✓	✓	1183.1.d.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\beta _{1}+\beta _{2}-\beta _{6})q^{2}+(-1+\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$
1183.1.x.a	$1183$	$1$	1183.x	91.x	$12$	$8$	$2$	$0.590$	$\Q(\zeta_{24})$	$A_{4}$	None	None		✓	✓	✓	1183.1.z.a	$8$	$0$	$0$	$-4$	$0$	$0$		$1$		$q+\zeta_{24}^{3}q^{2}-\zeta_{24}^{4}q^{3}+\zeta_{24}^{7}q^{5}+\cdots$
1183.1.z.a	$1183$	$1$	1183.z	91.z	$12$	$8$	$2$	$0.590$	$\Q(\zeta_{24})$	$A_{4}$	None	None		✓	✓	✓	1183.1.z.a	$8$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{4}q^{3}+\zeta_{24}^{11}q^{5}+\cdots$
1183.1.bd.a	$1183$	$1$	1183.bd	91.ad	$12$	$8$	$2$	$0.590$	$\Q(\zeta_{24})$	$A_{4}$	None	None		✓	✓	✓	1183.1.z.a	$8$	$0$	$0$	$8$	$0$	$0$		$1$		$q-\zeta_{24}^{11}q^{2}+q^{3}-\zeta_{24}^{7}q^{5}-\zeta_{24}^{11}q^{6}+\cdots$
1183.2.a.a	$1183$	$2$	1183.a	1.a	$1$	$1$	$1$	$9.446$	$\Q$	$_{}$	None	None	✓				91.2.a.b	$1$	$1$	$0$	$-2$	$3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+4q^{12}+\cdots$
1183.2.a.b	$1183$	$2$	1183.a	1.a	$1$	$1$	$1$	$9.446$	$\Q$	$_{}$	None	None	✓				91.2.a.a	$1$	$0$	$2$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+3q^{5}+q^{7}-3q^{9}+\cdots$
1183.2.a.c	$1183$	$2$	1183.a	1.a	$1$	$2$	$2$	$9.446$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				91.2.f.a	$1$	$1$	$-3$	$-3$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots$
1183.2.a.d	$1183$	$2$	1183.a	1.a	$1$	$2$	$2$	$9.446$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				91.2.a.c	$1$	$1$	$0$	$0$	$-6$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+\beta q^{3}+(-3+\beta )q^{5}+2q^{6}+\cdots$
1183.2.a.e	$1183$	$2$	1183.a	1.a	$1$	$2$	$2$	$9.446$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				91.2.f.b	$1$	$1$	$0$	$2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1-\beta )q^{3}+q^{4}+\beta q^{5}+(-3+\cdots)q^{6}+\cdots$
1183.2.a.f	$1183$	$2$	1183.a	1.a	$1$	$2$	$2$	$9.446$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				91.2.f.b	$1$	$0$	$0$	$2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{3}+q^{4}+\beta q^{5}+(3+\cdots)q^{6}+\cdots$
1183.2.a.g	$1183$	$2$	1183.a	1.a	$1$	$2$	$2$	$9.446$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				91.2.f.a	$1$	$0$	$3$	$-3$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots$
1183.2.a.h	$1183$	$2$	1183.a	1.a	$1$	$3$	$3$	$9.446$	3.3.148.1	$_{}$	None	None	✓				91.2.c.a	$1$	$1$	$-2$	$0$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
1183.2.a.i	$1183$	$2$	1183.a	1.a	$1$	$3$	$3$	$9.446$	3.3.316.1	$_{}$	None	None	✓				91.2.a.d	$1$	$0$	$-1$	$-2$	$-2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
1183.2.a.j	$1183$	$2$	1183.a	1.a	$1$	$3$	$3$	$9.446$	3.3.148.1	$_{}$	None	None	✓				91.2.c.a	$1$	$0$	$2$	$0$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
1183.2.a.k	$1183$	$2$	1183.a	1.a	$1$	$4$	$4$	$9.446$	4.4.27004.1	$_{}$	None	None	✓				91.2.f.c	$1$	$1$	$-1$	$1$	$-7$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
1183.2.a.l	$1183$	$2$	1183.a	1.a	$1$	$4$	$4$	$9.446$	4.4.27004.1	$_{}$	None	None	✓				91.2.f.c	$1$	$0$	$1$	$1$	$7$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
1183.2.a.m	$1183$	$2$	1183.a	1.a	$1$	$6$	$6$	$9.446$	6.6.7674048.1	$_{}$	None	None	✓				91.2.q.a	$1$	$1$	$-4$	$0$	$-6$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1183.2.a.n	$1183$	$2$	1183.a	1.a	$1$	$6$	$6$	$9.446$	6.6.1279733.1	$_{}$	None	None	✓	✓			1183.2.a.n	$1$	$1$	$-2$	$-4$	$-2$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots$
1183.2.a.o	$1183$	$2$	1183.a	1.a	$1$	$6$	$6$	$9.446$	6.6.1279733.1	$_{}$	None	None	✓	✓	✓		1183.2.a.n	$1$	$1$	$2$	$-4$	$2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{2}-\beta _{4})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots$
1183.2.a.p	$1183$	$2$	1183.a	1.a	$1$	$6$	$6$	$9.446$	6.6.7674048.1	$_{}$	None	None	✓				91.2.q.a	$1$	$0$	$4$	$0$	$6$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1183.2.a.q	$1183$	$2$	1183.a	1.a	$1$	$12$	$12$	$9.446$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	✓	✓		1183.2.a.q	$1$	$0$	$-3$	$8$	$4$	$-12$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
1183.2.a.r	$1183$	$2$	1183.a	1.a	$1$	$12$	$12$	$9.446$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	✓	✓		1183.2.a.q	$1$	$0$	$3$	$8$	$-4$	$12$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
1183.2.c.a	$1183$	$2$	1183.c	13.b	$2$	$2$	$2$	$9.446$	$\Q(\sqrt{-1}) $	$_{}$	None	None					91.2.a.b	$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2 q^{3}+2 q^{4}-3 i q^{5}-i q^{7}+q^{9}+\cdots$
1183.2.c.b	$1183$	$2$	1183.c	13.b	$2$	$2$	$2$	$9.446$	$\Q(\sqrt{-1}) $	$_{}$	None	None					91.2.a.a	$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{2}-2 q^{4}+3 i q^{5}-i q^{7}+\cdots$
1183.2.c.c	$1183$	$2$	1183.c	13.b	$2$	$4$	$4$	$9.446$	$\Q(i, \sqrt{5})$	$_{}$	None	None					91.2.f.a	$2$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+3\beta _{2}q^{4}+\cdots$
1183.2.c.d	$1183$	$2$	1183.c	13.b	$2$	$4$	$4$	$9.446$	$\Q(\zeta_{8})$	$_{}$	None	None					91.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{2} q^{2}-\beta_{3} q^{3}+(\beta_{2}+3\beta_1)q^{5}+\cdots$
1183.2.c.e	$1183$	$2$	1183.c	13.b	$2$	$4$	$4$	$9.446$	$\Q(\zeta_{12})$	$_{}$	None	None					91.2.f.b	$2$	$0$	$0$	$4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{2} q^{2}+(\beta_{3}+1)q^{3}-q^{4}-\beta_{2} q^{5}+\cdots$
1183.2.c.f	$1183$	$2$	1183.c	13.b	$2$	$6$	$6$	$9.446$	6.0.399424.1	$_{}$	None	None					91.2.a.d	$2$	$0$	$0$	$-4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(-1-\beta _{1}-\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots$
1183.2.c.g	$1183$	$2$	1183.c	13.b	$2$	$8$	$8$	$9.446$	8.0.$\cdots$.1	$_{}$	None	None					91.2.f.c	$2$	$0$	$0$	$2$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
1183.2.c.h	$1183$	$2$	1183.c	13.b	$2$	$12$	$12$	$9.446$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			1183.2.a.n	$2$	$0$	$0$	$-8$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{8}+\beta _{10}-\beta _{11})q^{2}+(-1-\beta _{4}+\cdots)q^{3}+\cdots$
1183.2.c.i	$1183$	$2$	1183.c	13.b	$2$	$12$	$12$	$9.446$	12.0.$\cdots$.1	$_{}$	None	None					91.2.q.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{7})q^{2}-\beta _{2}q^{3}+(-1-\beta _{4}+\cdots)q^{4}+\cdots$
1183.2.c.j	$1183$	$2$	1183.c	13.b	$2$	$24$	$24$	$9.446$		$_{}$	None	None		✓	✓		1183.2.a.q	$2$	$0$	$0$	$16$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1183.2.e.a	$1183$	$2$	1183.e	7.c	$3$	$2$	$1$	$9.446$	$\Q(\sqrt{-3}) $	$_{}$	None	None					91.2.g.a	$2$	$0$	$-1$	$3$	$-3$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
1183.2.e.b	$1183$	$2$	1183.e	7.c	$3$	$2$	$1$	$9.446$	$\Q(\sqrt{-3}) $	$_{}$	None	None					91.2.e.a	$2$	$0$	$1$	$0$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(-2+3\zeta_{6})q^{7}+\cdots$
1183.2.e.c	$1183$	$2$	1183.e	7.c	$3$	$2$	$1$	$9.446$	$\Q(\sqrt{-3}) $	$_{}$	None	None					91.2.g.a	$2$	$0$	$1$	$3$	$3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
1183.2.e.d	$1183$	$2$	1183.e	7.c	$3$	$4$	$2$	$9.446$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None					91.2.e.b	$2$	$0$	$-3$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{1}-\beta _{3})q^{2}+(-2\beta _{1}-2\beta _{2}+\cdots)q^{3}+\cdots$
1183.2.e.e	$1183$	$2$	1183.e	7.c	$3$	$4$	$2$	$9.446$	$\Q(\zeta_{12})$	$_{}$	None	None					91.2.k.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{3}+\cdots$
1183.2.e.f	$1183$	$2$	1183.e	7.c	$3$	$10$	$5$	$9.446$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None					91.2.e.c	$2$	$0$	$4$	$0$	$2$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{7})q^{2}+(-\beta _{4}+\beta _{9})q^{3}+\cdots$
1183.2.e.g	$1183$	$2$	1183.e	7.c	$3$	$12$	$6$	$9.446$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None					91.2.g.b	$2$	$0$	$-2$	$1$	$-1$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{5}-\beta _{11})q^{2}-\beta _{3}q^{3}+(\beta _{6}+\cdots)q^{4}+\cdots$
1183.2.e.h	$1183$	$2$	1183.e	7.c	$3$	$12$	$6$	$9.446$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None					91.2.g.b	$2$	$0$	$2$	$1$	$1$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{5}+\beta _{11})q^{2}-\beta _{3}q^{3}+(\beta _{6}+\cdots)q^{4}+\cdots$
1183.2.e.i	$1183$	$2$	1183.e	7.c	$3$	$16$	$8$	$9.446$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None					91.2.r.a	$4$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{9}q^{2}+(-1-\beta _{4}-\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots$
1183.2.e.j	$1183$	$2$	1183.e	7.c	$3$	$24$	$12$	$9.446$		$_{}$	None	None					91.2.k.b	$4$	$0$	$0$	$-6$	$0$	$0$			$\mathrm{SU}(2)[C_{3}]$
1183.2.e.k	$1183$	$2$	1183.e	7.c	$3$	$48$	$24$	$9.446$		$_{}$	None	None		✓			1183.2.e.k	$2$	$0$	$-1$	$0$	$13$	$-3$			$\mathrm{SU}(2)[C_{3}]$
1183.2.e.l	$1183$	$2$	1183.e	7.c	$3$	$48$	$24$	$9.446$		$_{}$	None	None		✓			1183.2.e.k	$2$	$0$	$1$	$0$	$-13$	$3$			$\mathrm{SU}(2)[C_{3}]$
1183.4.a.a	$1183$	$4$	1183.a	1.a	$1$	$1$	$1$	$69.799$	$\Q$	$_{}$	None	None	✓				91.4.f.a	$1$	$1$	$-5$	$2$	$-19$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-5q^{2}+2q^{3}+17q^{4}-19q^{5}-10q^{6}+\cdots$

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 68 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.