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 83 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
2499.1.e.a	$2499$	$1$	2499.e	51.c	$2$	$1$	$1$	$1.247$	$\Q$	$D_{2}$	$\Q(\sqrt{-51}) $, $\Q(\sqrt{-119}) $	$\Q(\sqrt{21}) $	✓	✓			2499.1.e.a	$4$	$0$	$0$	$-1$	$2$	$0$		$1$		$q-q^{3}+q^{4}+2q^{5}+q^{9}-q^{12}-2q^{15}+\cdots$
2499.1.e.b	$2499$	$1$	2499.e	51.c	$2$	$1$	$1$	$1.247$	$\Q$	$D_{2}$	$\Q(\sqrt{-51}) $, $\Q(\sqrt{-119}) $	$\Q(\sqrt{21}) $	✓	✓			2499.1.e.a	$4$	$0$	$0$	$1$	$-2$	$0$		$1$		$q+q^{3}+q^{4}-2q^{5}+q^{9}+q^{12}-2q^{15}+\cdots$
2499.1.e.c	$2499$	$1$	2499.e	51.c	$2$	$2$	$2$	$1.247$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-51}) $	None	✓	✓			2499.1.e.c	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-q^{3}+q^{4}+q^{9}-\beta q^{11}-q^{12}-\beta q^{13}+\cdots$
2499.1.e.d	$2499$	$1$	2499.e	51.c	$2$	$2$	$2$	$1.247$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-51}) $	None	✓	✓			2499.1.e.c	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+q^{3}+q^{4}+q^{9}-\beta q^{11}+q^{12}+\beta q^{13}+\cdots$
2499.1.e.e	$2499$	$1$	2499.e	51.c	$2$	$4$	$4$	$1.247$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		✓			2499.1.e.e	$4$	$0$	$0$	$-1$	$2$	$0$		$1$		$q+(\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots$
2499.1.e.f	$2499$	$1$	2499.e	51.c	$2$	$4$	$4$	$1.247$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		✓			2499.1.e.e	$4$	$0$	$0$	$1$	$-2$	$0$		$1$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{2}+\zeta_{10}q^{3}+(-1+\cdots)q^{4}+\cdots$
2499.1.q.a	$2499$	$1$	2499.q	357.q	$6$	$2$	$1$	$1.247$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-51}) $, $\Q(\sqrt{-119}) $	$\Q(\sqrt{21}) $		✓			2499.1.e.a	$8$	$0$	$0$	$-1$	$2$	$0$		$1$		$q-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\cdots$
2499.1.q.b	$2499$	$1$	2499.q	357.q	$6$	$2$	$1$	$1.247$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-51}) $, $\Q(\sqrt{-119}) $	$\Q(\sqrt{21}) $		✓			2499.1.e.a	$8$	$0$	$0$	$1$	$-2$	$0$		$1$		$q+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\cdots$
2499.1.q.c	$2499$	$1$	2499.q	357.q	$6$	$4$	$2$	$1.247$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-51}) $	None		✓			2499.1.e.c	$8$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+\beta _{2}q^{3}+\beta _{2}q^{4}+(-1-\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$
2499.1.q.d	$2499$	$1$	2499.q	357.q	$6$	$4$	$2$	$1.247$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-51}) $	None		✓			2499.1.e.c	$8$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\beta _{2}q^{3}+\beta _{2}q^{4}+(-1-\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$
2499.1.q.e	$2499$	$1$	2499.q	357.q	$6$	$8$	$4$	$1.247$	$\Q(\zeta_{15})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		✓			2499.1.e.e	$8$	$0$	$0$	$-1$	$2$	$0$		$1$		$q+(\zeta_{30}^{11}+\zeta_{30}^{14})q^{2}+\zeta_{30}q^{3}+(-\zeta_{30}^{7}+\cdots)q^{4}+\cdots$
2499.1.q.f	$2499$	$1$	2499.q	357.q	$6$	$8$	$4$	$1.247$	$\Q(\zeta_{15})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		✓			2499.1.e.e	$8$	$0$	$0$	$1$	$-2$	$0$		$1$		$q+(-\zeta_{30}^{2}+\zeta_{30}^{8})q^{2}-\zeta_{30}^{7}q^{3}+\cdots$
2499.2.a.a	$2499$	$2$	2499.a	1.a	$1$	$1$	$1$	$19.955$	$\Q$	$_{}$	None	None	✓				357.2.a.a	$1$	$1$	$-2$	$-1$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+3q^{5}+2q^{6}+\cdots$
2499.2.a.b	$2499$	$2$	2499.a	1.a	$1$	$1$	$1$	$19.955$	$\Q$	$_{}$	None	None	✓				357.2.i.c	$1$	$0$	$-1$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+3q^{8}+\cdots$
2499.2.a.c	$2499$	$2$	2499.a	1.a	$1$	$1$	$1$	$19.955$	$\Q$	$_{}$	None	None	✓				357.2.i.c	$1$	$1$	$-1$	$1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots$
2499.2.a.d	$2499$	$2$	2499.a	1.a	$1$	$1$	$1$	$19.955$	$\Q$	$_{}$	None	None	✓				51.2.a.a	$1$	$1$	$0$	$-1$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-3q^{5}+q^{9}-3q^{11}+\cdots$
2499.2.a.e	$2499$	$2$	2499.a	1.a	$1$	$1$	$1$	$19.955$	$\Q$	$_{}$	None	None	✓				357.2.i.b	$1$	$0$	$0$	$-1$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+4q^{5}+q^{9}+4q^{11}+\cdots$
2499.2.a.f	$2499$	$2$	2499.a	1.a	$1$	$1$	$1$	$19.955$	$\Q$	$_{}$	None	None	✓				357.2.i.b	$1$	$1$	$0$	$1$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-4q^{5}+q^{9}+4q^{11}+\cdots$
2499.2.a.g	$2499$	$2$	2499.a	1.a	$1$	$1$	$1$	$19.955$	$\Q$	$_{}$	None	None	✓				357.2.a.c	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}+q^{9}-5q^{11}-2q^{12}+\cdots$
2499.2.a.h	$2499$	$2$	2499.a	1.a	$1$	$1$	$1$	$19.955$	$\Q$	$_{}$	None	None	✓				357.2.a.b	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}+q^{9}+3q^{11}-2q^{12}+\cdots$
2499.2.a.i	$2499$	$2$	2499.a	1.a	$1$	$1$	$1$	$19.955$	$\Q$	$_{}$	None	None	✓				357.2.i.a	$1$	$1$	$1$	$-1$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-3q^{5}-q^{6}-3q^{8}+\cdots$
2499.2.a.j	$2499$	$2$	2499.a	1.a	$1$	$1$	$1$	$19.955$	$\Q$	$_{}$	None	None	✓	✓			2499.2.a.j	$1$	$0$	$1$	$-1$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}-3q^{8}+\cdots$
2499.2.a.k	$2499$	$2$	2499.a	1.a	$1$	$1$	$1$	$19.955$	$\Q$	$_{}$	None	None	✓	✓			2499.2.a.j	$1$	$0$	$1$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+2q^{5}+q^{6}-3q^{8}+\cdots$
2499.2.a.l	$2499$	$2$	2499.a	1.a	$1$	$1$	$1$	$19.955$	$\Q$	$_{}$	None	None	✓				357.2.i.a	$1$	$0$	$1$	$1$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+3q^{5}+q^{6}-3q^{8}+\cdots$
2499.2.a.m	$2499$	$2$	2499.a	1.a	$1$	$1$	$1$	$19.955$	$\Q$	$_{}$	None	None	✓				357.2.a.d	$1$	$1$	$2$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}+q^{9}+\cdots$
2499.2.a.n	$2499$	$2$	2499.a	1.a	$1$	$2$	$2$	$19.955$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				357.2.a.e	$1$	$0$	$-2$	$-2$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-q^{3}+(2-2\beta )q^{4}+(2+\cdots)q^{5}+\cdots$
2499.2.a.o	$2499$	$2$	2499.a	1.a	$1$	$2$	$2$	$19.955$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				51.2.a.b	$1$	$1$	$-1$	$2$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+(-1-\beta )q^{5}+\cdots$
2499.2.a.p	$2499$	$2$	2499.a	1.a	$1$	$2$	$2$	$19.955$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			2499.2.a.p	$1$	$1$	$0$	$-2$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(1+\beta )q^{5}-\beta q^{6}-2\beta q^{8}+\cdots$
2499.2.a.q	$2499$	$2$	2499.a	1.a	$1$	$2$	$2$	$19.955$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			2499.2.a.p	$1$	$1$	$0$	$2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-1-\beta )q^{5}+\beta q^{6}+\cdots$
2499.2.a.r	$2499$	$2$	2499.a	1.a	$1$	$2$	$2$	$19.955$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				357.2.a.f	$1$	$0$	$0$	$2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(1+\beta )q^{5}+\beta q^{6}-2\beta q^{8}+\cdots$
2499.2.a.s	$2499$	$2$	2499.a	1.a	$1$	$3$	$3$	$19.955$	3.3.316.1	$_{}$	None	None	✓				357.2.a.g	$1$	$0$	$1$	$-3$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
2499.2.a.t	$2499$	$2$	2499.a	1.a	$1$	$4$	$4$	$19.955$	4.4.9301.1	$_{}$	None	None	✓				357.2.i.e	$1$	$0$	$-3$	$-4$	$6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
2499.2.a.u	$2499$	$2$	2499.a	1.a	$1$	$4$	$4$	$19.955$	4.4.9301.1	$_{}$	None	None	✓				357.2.i.e	$1$	$1$	$-3$	$4$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
2499.2.a.v	$2499$	$2$	2499.a	1.a	$1$	$4$	$4$	$19.955$	4.4.14013.1	$_{}$	None	None	✓		✓		357.2.i.d	$1$	$1$	$-1$	$-4$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{3})q^{5}+\cdots$
2499.2.a.w	$2499$	$2$	2499.a	1.a	$1$	$4$	$4$	$19.955$	4.4.14013.1	$_{}$	None	None	✓				357.2.i.d	$1$	$0$	$-1$	$4$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots$
2499.2.a.x	$2499$	$2$	2499.a	1.a	$1$	$4$	$4$	$19.955$	$\Q(\zeta_{16})^+$	$_{}$	None	None	✓	✓			2499.2.a.x	$1$	$1$	$0$	$-4$	$4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(1+\beta _{3})q^{5}+\cdots$
2499.2.a.y	$2499$	$2$	2499.a	1.a	$1$	$4$	$4$	$19.955$	$\Q(\zeta_{16})^+$	$_{}$	None	None	✓	✓			2499.2.a.x	$1$	$1$	$0$	$4$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-1-\beta _{3})q^{5}+\cdots$
2499.2.a.z	$2499$	$2$	2499.a	1.a	$1$	$4$	$4$	$19.955$	4.4.7232.1	$_{}$	None	None	✓				357.2.a.h	$1$	$0$	$2$	$4$	$2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+q^{3}+(1-\beta _{2}-\beta _{3})q^{4}-\beta _{1}q^{5}+\cdots$
2499.2.a.ba	$2499$	$2$	2499.a	1.a	$1$	$5$	$5$	$19.955$	5.5.1383597.1	$_{}$	None	None	✓				357.2.i.f	$1$	$0$	$-2$	$-5$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
2499.2.a.bb	$2499$	$2$	2499.a	1.a	$1$	$5$	$5$	$19.955$	5.5.1383597.1	$_{}$	None	None	✓		✓		357.2.i.f	$1$	$1$	$-2$	$5$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
2499.2.a.bc	$2499$	$2$	2499.a	1.a	$1$	$5$	$5$	$19.955$	5.5.885424.1	$_{}$	None	None	✓	✓	✓		2499.2.a.bc	$1$	$0$	$1$	$-5$	$2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}-q^{3}+(2-\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots$
2499.2.a.bd	$2499$	$2$	2499.a	1.a	$1$	$5$	$5$	$19.955$	5.5.885424.1	$_{}$	None	None	✓	✓			2499.2.a.bc	$1$	$0$	$1$	$5$	$-2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+q^{3}+(2-\beta _{3})q^{4}+\beta _{2}q^{5}+\cdots$
2499.2.a.be	$2499$	$2$	2499.a	1.a	$1$	$6$	$6$	$19.955$	6.6.29722117.1	$_{}$	None	None	✓		✓		357.2.i.g	$1$	$1$	$2$	$-6$	$-7$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
2499.2.a.bf	$2499$	$2$	2499.a	1.a	$1$	$6$	$6$	$19.955$	6.6.29722117.1	$_{}$	None	None	✓		✓		357.2.i.g	$1$	$0$	$2$	$6$	$7$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
2499.2.a.bg	$2499$	$2$	2499.a	1.a	$1$	$12$	$12$	$19.955$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	✓	✓		2499.2.a.bg	$1$	$0$	$4$	$-12$	$-4$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots$
2499.2.a.bh	$2499$	$2$	2499.a	1.a	$1$	$12$	$12$	$19.955$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	✓	✓		2499.2.a.bg	$1$	$0$	$4$	$12$	$4$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots$
2499.4.a.a	$2499$	$4$	2499.a	1.a	$1$	$1$	$1$	$147.446$	$\Q$	$_{}$	None	None	✓	✓			2499.4.a.a	$1$	$1$	$-5$	$-3$	$18$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-5q^{2}-3q^{3}+17q^{4}+18q^{5}+15q^{6}+\cdots$
2499.4.a.b	$2499$	$4$	2499.a	1.a	$1$	$1$	$1$	$147.446$	$\Q$	$_{}$	None	None	✓	✓			2499.4.a.a	$1$	$1$	$-5$	$3$	$-18$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-5q^{2}+3q^{3}+17q^{4}-18q^{5}-15q^{6}+\cdots$
2499.4.a.c	$2499$	$4$	2499.a	1.a	$1$	$1$	$1$	$147.446$	$\Q$	$_{}$	None	None	✓				357.4.a.a	$1$	$0$	$-5$	$3$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-5q^{2}+3q^{3}+17q^{4}+q^{5}-15q^{6}+\cdots$
2499.4.a.d	$2499$	$4$	2499.a	1.a	$1$	$1$	$1$	$147.446$	$\Q$	$_{}$	None	None	✓				51.4.a.b	$1$	$0$	$-1$	$-3$	$20$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}-7q^{4}+20q^{5}+3q^{6}+\cdots$

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 83 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.