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 62 matches)

Next Download displayed columns for results to

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	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
2034.2.a.a	$2034$	$2$	2034.a	1.a	$1$	$1$	$1$	$16.242$	$\Q$	None	✓				678.2.a.f	$1$	$0$	$-1$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-4q^{11}+\cdots$
2034.2.a.b	$2034$	$2$	2034.a	1.a	$1$	$1$	$1$	$16.242$	$\Q$	None	✓				678.2.a.c	$1$	$0$	$-1$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{7}-q^{8}+4q^{11}-2q^{13}+\cdots$
2034.2.a.c	$2034$	$2$	2034.a	1.a	$1$	$1$	$1$	$16.242$	$\Q$	None	✓	✓			2034.2.a.c	$1$	$1$	$-1$	$0$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-3q^{7}-q^{8}-q^{10}+\cdots$
2034.2.a.d	$2034$	$2$	2034.a	1.a	$1$	$1$	$1$	$16.242$	$\Q$	None	✓				678.2.a.e	$1$	$0$	$-1$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots$
2034.2.a.e	$2034$	$2$	2034.a	1.a	$1$	$1$	$1$	$16.242$	$\Q$	None	✓				226.2.a.a	$1$	$0$	$-1$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}-q^{8}-4q^{10}+4q^{11}+\cdots$
2034.2.a.f	$2034$	$2$	2034.a	1.a	$1$	$1$	$1$	$16.242$	$\Q$	None	✓				678.2.a.d	$1$	$0$	$-1$	$0$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}+4q^{7}-q^{8}-4q^{10}+\cdots$
2034.2.a.g	$2034$	$2$	2034.a	1.a	$1$	$1$	$1$	$16.242$	$\Q$	None	✓	✓			2034.2.a.c	$1$	$1$	$1$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-3q^{7}+q^{8}-q^{10}+\cdots$
2034.2.a.h	$2034$	$2$	2034.a	1.a	$1$	$1$	$1$	$16.242$	$\Q$	None	✓				678.2.a.a	$1$	$0$	$1$	$0$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots$
2034.2.a.i	$2034$	$2$	2034.a	1.a	$1$	$1$	$1$	$16.242$	$\Q$	None	✓				678.2.a.b	$1$	$1$	$1$	$0$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-3q^{7}+q^{8}+q^{10}+\cdots$
2034.2.a.j	$2034$	$2$	2034.a	1.a	$1$	$2$	$2$	$16.242$	$\Q(\sqrt{61}) $	None	✓		✓		678.2.a.i	$1$	$0$	$-2$	$0$	$-4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}+\beta q^{7}-q^{8}+2q^{10}+\cdots$
2034.2.a.k	$2034$	$2$	2034.a	1.a	$1$	$2$	$2$	$16.242$	$\Q(\sqrt{5}) $	None	✓	✓	✓		2034.2.a.k	$1$	$1$	$-2$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2\beta q^{5}+(-1+\beta )q^{7}+\cdots$
2034.2.a.l	$2034$	$2$	2034.a	1.a	$1$	$2$	$2$	$16.242$	$\Q(\sqrt{3}) $	None	✓				226.2.a.c	$1$	$1$	$2$	$0$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}+(-2+\cdots)q^{11}+\cdots$
2034.2.a.m	$2034$	$2$	2034.a	1.a	$1$	$2$	$2$	$16.242$	$\Q(\sqrt{5}) $	None	✓				678.2.a.h	$1$	$1$	$2$	$0$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+(2-3\beta )q^{7}+q^{8}+\cdots$
2034.2.a.n	$2034$	$2$	2034.a	1.a	$1$	$2$	$2$	$16.242$	$\Q(\sqrt{5}) $	None	✓	✓	✓		2034.2.a.k	$1$	$1$	$2$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2\beta q^{5}+(-1+\beta )q^{7}+\cdots$
2034.2.a.o	$2034$	$2$	2034.a	1.a	$1$	$2$	$2$	$16.242$	$\Q(\sqrt{2}) $	None	✓				226.2.a.b	$1$	$0$	$2$	$0$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(2+\beta )q^{5}+(-2-2\beta )q^{7}+\cdots$
2034.2.a.p	$2034$	$2$	2034.a	1.a	$1$	$2$	$2$	$16.242$	$\Q(\sqrt{2}) $	None	✓				678.2.a.g	$1$	$0$	$2$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(2+\beta )q^{5}+2\beta q^{7}+q^{8}+\cdots$
2034.2.a.q	$2034$	$2$	2034.a	1.a	$1$	$3$	$3$	$16.242$	3.3.469.1	None	✓				678.2.a.j	$1$	$1$	$-3$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots$
2034.2.a.r	$2034$	$2$	2034.a	1.a	$1$	$4$	$4$	$16.242$	$\Q(\zeta_{20})^+$	None	✓		✓		226.2.a.d	$1$	$1$	$-4$	$0$	$-4$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta _{2}+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
2034.2.a.s	$2034$	$2$	2034.a	1.a	$1$	$4$	$4$	$16.242$	4.4.77976.1	None	✓		✓		678.2.a.k	$1$	$0$	$4$	$0$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta _{2}q^{5}+(1-\beta _{3})q^{7}+q^{8}+\cdots$
2034.2.a.t	$2034$	$2$	2034.a	1.a	$1$	$7$	$7$	$16.242$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	2034.2.a.t	$1$	$0$	$-7$	$0$	$-3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta _{1}q^{5}+(1+\beta _{6})q^{7}-q^{8}+\cdots$
2034.2.a.u	$2034$	$2$	2034.a	1.a	$1$	$7$	$7$	$16.242$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	2034.2.a.t	$1$	$0$	$7$	$0$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{1}q^{5}+(1+\beta _{6})q^{7}+q^{8}+\cdots$
2034.2.c.a	$2034$	$2$	2034.c	113.b	$2$	$2$	$2$	$16.242$	$\Q(\sqrt{-1}) $	None					678.2.c.a	$2$	$0$	$-2$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}-q^{8}-4q^{11}+2q^{13}+\cdots$
2034.2.c.b	$2034$	$2$	2034.c	113.b	$2$	$2$	$2$	$16.242$	$\Q(\sqrt{-2}) $	None					226.2.b.c	$2$	$0$	$-2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+4q^{11}+\cdots$
2034.2.c.c	$2034$	$2$	2034.c	113.b	$2$	$2$	$2$	$16.242$	$\Q(\sqrt{-2}) $	None					226.2.b.a	$2$	$1$	$2$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+2\beta q^{5}-4q^{7}+q^{8}+2\beta q^{10}+\cdots$
2034.2.c.d	$2034$	$2$	2034.c	113.b	$2$	$2$	$2$	$16.242$	$\Q(\sqrt{-2}) $	None					226.2.b.b	$2$	$0$	$2$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+\beta q^{5}+2q^{7}+q^{8}+\beta q^{10}+\cdots$
2034.2.c.e	$2034$	$2$	2034.c	113.b	$2$	$4$	$4$	$16.242$	$\Q(\sqrt{-2}, \sqrt{13})$	None					226.2.b.d	$2$	$0$	$-4$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}-\beta _{2}q^{5}+(1-\beta _{3})q^{7}-q^{8}+\cdots$
2034.2.c.f	$2034$	$2$	2034.c	113.b	$2$	$6$	$6$	$16.242$	6.0.199374400.3	None					678.2.c.b	$2$	$0$	$-6$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+(-\beta _{2}-\beta _{4})q^{5}+(-1+\cdots)q^{7}+\cdots$
2034.2.c.g	$2034$	$2$	2034.c	113.b	$2$	$10$	$10$	$16.242$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		✓			2034.2.c.g	$2$	$0$	$-10$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+\beta _{1}q^{5}-\beta _{3}q^{7}-q^{8}+\cdots$
2034.2.c.h	$2034$	$2$	2034.c	113.b	$2$	$10$	$10$	$16.242$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		✓			2034.2.c.g	$2$	$0$	$10$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+\beta _{1}q^{5}-\beta _{3}q^{7}+q^{8}+\cdots$
2034.2.c.i	$2034$	$2$	2034.c	113.b	$2$	$10$	$10$	$16.242$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None					678.2.c.c	$2$	$0$	$10$	$0$	$0$	$4$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+\beta _{1}q^{5}-\beta _{3}q^{7}+q^{8}+\cdots$
2034.2.f.a	$2034$	$2$	2034.f	113.c	$4$	$2$	$1$	$16.242$	$\Q(\sqrt{-1}) $	None					226.2.c.c	$2$	$1$	$-2$	$0$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+q^{4}+(2 i-2)q^{5}-2 q^{7}+\cdots$
2034.2.f.b	$2034$	$2$	2034.f	113.c	$4$	$2$	$1$	$16.242$	$\Q(\sqrt{-1}) $	None					226.2.c.b	$2$	$0$	$-2$	$0$	$6$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+q^{4}+(-3 i+3)q^{5}-4 q^{7}+\cdots$
2034.2.f.c	$2034$	$2$	2034.f	113.c	$4$	$2$	$1$	$16.242$	$\Q(\sqrt{-1}) $	None					226.2.c.a	$2$	$0$	$2$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+q^{4}-4 q^{7}+q^{8}-4 i q^{11}+\cdots$
2034.2.f.d	$2034$	$2$	2034.f	113.c	$4$	$4$	$2$	$16.242$	$\Q(\zeta_{8})$	None					678.2.e.a	$2$	$0$	$4$	$0$	$8$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+q^{4}+(2+\zeta_{8}+2\zeta_{8}^{2})q^{5}+(-1+\cdots)q^{7}+\cdots$
2034.2.f.e	$2034$	$2$	2034.f	113.c	$4$	$6$	$3$	$16.242$	6.0.153664.1	None					226.2.c.d	$2$	$0$	$-6$	$0$	$4$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+q^{4}+(1-\beta _{1}+\beta _{4})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots$
2034.2.f.f	$2034$	$2$	2034.f	113.c	$4$	$8$	$4$	$16.242$	8.0.4057180416.1	None					226.2.c.e	$2$	$0$	$8$	$0$	$0$	$16$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+q^{4}-\beta _{7}q^{5}+2q^{7}+q^{8}-\beta _{7}q^{10}+\cdots$
2034.2.f.g	$2034$	$2$	2034.f	113.c	$4$	$16$	$8$	$16.242$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None					678.2.e.c	$2$	$0$	$-16$	$0$	$-4$	$8$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+q^{4}+\beta _{3}q^{5}+\beta _{1}q^{7}-q^{8}+\cdots$
2034.2.f.h	$2034$	$2$	2034.f	113.c	$4$	$16$	$8$	$16.242$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None					678.2.e.b	$2$	$0$	$16$	$0$	$-8$	$-4$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+q^{4}+(-1+\beta _{15})q^{5}-\beta _{1}q^{7}+\cdots$
2034.2.f.i	$2034$	$2$	2034.f	113.c	$4$	$20$	$10$	$16.242$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓			2034.2.f.i	$2$	$0$	$-20$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+q^{4}+\beta _{8}q^{5}+\beta _{11}q^{7}-q^{8}+\cdots$
2034.2.f.j	$2034$	$2$	2034.f	113.c	$4$	$20$	$10$	$16.242$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓			2034.2.f.i	$2$	$0$	$20$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+q^{4}-\beta _{1}q^{5}+\beta _{11}q^{7}+q^{8}+\cdots$
2034.3.b.a	$2034$	$3$	2034.b	3.b	$2$	$36$	$36$	$55.422$		None		✓			2034.3.b.a	$2$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$
2034.3.b.b	$2034$	$3$	2034.b	3.b	$2$	$36$	$36$	$55.422$		None		✓			2034.3.b.b	$2$	$0$	$0$	$0$	$0$	$24$			$\mathrm{SU}(2)[C_{2}]$
2034.3.d.a	$2034$	$3$	2034.d	339.c	$2$	$36$	$36$	$55.422$		None		✓			2034.3.d.a	$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$
2034.3.d.b	$2034$	$3$	2034.d	339.c	$2$	$40$	$40$	$55.422$		None		✓	✓		2034.3.d.b	$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{2}]$
2034.4.a.a	$2034$	$4$	2034.a	1.a	$1$	$1$	$1$	$120.010$	$\Q$	None	✓				678.4.a.b	$1$	$1$	$-2$	$0$	$-1$	$-33$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}-q^{5}-33q^{7}-8q^{8}+\cdots$
2034.4.a.b	$2034$	$4$	2034.a	1.a	$1$	$1$	$1$	$120.010$	$\Q$	None	✓				678.4.a.a	$1$	$1$	$-2$	$0$	$9$	$11$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+9q^{5}+11q^{7}-8q^{8}+\cdots$
2034.4.a.c	$2034$	$4$	2034.a	1.a	$1$	$2$	$2$	$120.010$	$\Q(\sqrt{2}) $	None	✓				678.4.a.c	$1$	$1$	$-4$	$0$	$10$	$-22$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(5+5\beta )q^{5}+(-11+\cdots)q^{7}+\cdots$
2034.4.a.d	$2034$	$4$	2034.a	1.a	$1$	$5$	$5$	$120.010$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓				226.4.a.a	$1$	$0$	$-10$	$0$	$29$	$-26$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(6-\beta _{2}-\beta _{3}-\beta _{4})q^{5}+\cdots$
2034.4.a.e	$2034$	$4$	2034.a	1.a	$1$	$6$	$6$	$120.010$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓				678.4.a.f	$1$	$0$	$-12$	$0$	$12$	$-16$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(2+\beta _{5})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots$
2034.4.a.f	$2034$	$4$	2034.a	1.a	$1$	$6$	$6$	$120.010$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓				678.4.a.d	$1$	$1$	$12$	$0$	$-12$	$11$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(-2-\beta _{2})q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots$

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 62 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.