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 64 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
1058.2.a.a	$1058$	$2$	1058.a	1.a	$1$	$1$	$1$	$8.448$	$\Q$	None	✓	✓			1058.2.a.a	$1$	$2$	$-1$	$-2$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-3q^{5}+2q^{6}-2q^{7}+\cdots$
1058.2.a.b	$1058$	$2$	1058.a	1.a	$1$	$1$	$1$	$8.448$	$\Q$	None	✓	✓			1058.2.a.a	$1$	$0$	$-1$	$-2$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+3q^{5}+2q^{6}+2q^{7}+\cdots$
1058.2.a.c	$1058$	$2$	1058.a	1.a	$1$	$1$	$1$	$8.448$	$\Q$	None	✓				46.2.a.a	$1$	$0$	$-1$	$0$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{5}+4q^{7}-q^{8}-3q^{9}+\cdots$
1058.2.a.d	$1058$	$2$	1058.a	1.a	$1$	$1$	$1$	$8.448$	$\Q$	None	✓	✓			1058.2.a.d	$1$	$0$	$-1$	$3$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-2q^{5}-3q^{6}+2q^{7}+\cdots$
1058.2.a.e	$1058$	$2$	1058.a	1.a	$1$	$1$	$1$	$8.448$	$\Q$	None	✓	✓			1058.2.a.d	$1$	$0$	$-1$	$3$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}+2q^{5}-3q^{6}-2q^{7}+\cdots$
1058.2.a.f	$1058$	$2$	1058.a	1.a	$1$	$2$	$2$	$8.448$	$\Q(\sqrt{3}) $	None	✓	✓			1058.2.a.f	$2$	$0$	$-2$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2\beta q^{5}-q^{6}+2\beta q^{7}+\cdots$
1058.2.a.g	$1058$	$2$	1058.a	1.a	$1$	$2$	$2$	$8.448$	$\Q(\sqrt{3}) $	None	✓	✓			1058.2.a.g	$2$	$1$	$2$	$-4$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-\beta q^{5}-2q^{6}+2\beta q^{7}+\cdots$
1058.2.a.h	$1058$	$2$	1058.a	1.a	$1$	$2$	$2$	$8.448$	$\Q(\sqrt{2}) $	None	✓	✓			1058.2.a.h	$2$	$0$	$2$	$4$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}+2\beta q^{7}+\cdots$
1058.2.a.i	$1058$	$2$	1058.a	1.a	$1$	$4$	$4$	$8.448$	$\Q(\zeta_{24})^+$	None	✓	✓			1058.2.a.i	$2$	$1$	$-4$	$-4$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{2})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
1058.2.a.j	$1058$	$2$	1058.a	1.a	$1$	$5$	$5$	$8.448$	$\Q(\zeta_{22})^+$	None	✓		✓		46.2.c.b	$1$	$1$	$-5$	$0$	$-2$	$-9$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
1058.2.a.k	$1058$	$2$	1058.a	1.a	$1$	$5$	$5$	$8.448$	$\Q(\zeta_{22})^+$	None	✓		✓		46.2.c.b	$1$	$0$	$-5$	$0$	$2$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
1058.2.a.l	$1058$	$2$	1058.a	1.a	$1$	$5$	$5$	$8.448$	$\Q(\zeta_{22})^+$	None	✓		✓		46.2.c.a	$1$	$1$	$5$	$-2$	$-8$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-\beta _{1}-\beta _{3})q^{3}+q^{4}+(-2+\cdots)q^{5}+\cdots$
1058.2.a.m	$1058$	$2$	1058.a	1.a	$1$	$5$	$5$	$8.448$	$\Q(\zeta_{22})^+$	None	✓				46.2.c.a	$1$	$0$	$5$	$-2$	$8$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-\beta _{1}-\beta _{3})q^{3}+q^{4}+(2+\beta _{2}+\cdots)q^{5}+\cdots$
1058.2.a.n	$1058$	$2$	1058.a	1.a	$1$	$8$	$8$	$8.448$	8.8.$\cdots$.1	None	✓	✓	✓		1058.2.a.n	$2$	$0$	$8$	$4$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{5}q^{3}+q^{4}+(\beta _{2}+\beta _{4})q^{5}+\cdots$
1058.3.b.a	$1058$	$3$	1058.b	23.b	$2$	$8$	$8$	$28.828$	8.0.$\cdots$.2	None		✓			1058.3.b.a	$2$	$0$	$0$	$-8$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-1+\beta _{6})q^{3}+2q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots$
1058.3.b.b	$1058$	$3$	1058.b	23.b	$2$	$8$	$8$	$28.828$	8.0.1358954496.3	None		✓			1058.3.b.b	$2$	$0$	$0$	$8$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{2}-\beta _{6})q^{2}+(1+\beta _{2})q^{3}+2q^{4}+\cdots$
1058.3.b.c	$1058$	$3$	1058.b	23.b	$2$	$12$	$12$	$28.828$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			1058.3.b.c	$2$	$0$	$0$	$8$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(1-\beta _{4})q^{3}+2q^{4}+(\beta _{3}-\beta _{10}+\cdots)q^{5}+\cdots$
1058.3.b.d	$1058$	$3$	1058.b	23.b	$2$	$16$	$16$	$28.828$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			1058.3.b.d	$2$	$0$	$0$	$-8$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{2}-\beta _{4}-\beta _{8})q^{3}+2q^{4}+\cdots$
1058.3.b.e	$1058$	$3$	1058.b	23.b	$2$	$40$	$40$	$28.828$		None			✓		46.3.d.a	$2$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1058.4.a.a	$1058$	$4$	1058.a	1.a	$1$	$1$	$1$	$62.424$	$\Q$	None	✓				46.4.a.a	$1$	$1$	$-2$	$-1$	$10$	$12$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+4q^{4}+10q^{5}+2q^{6}+\cdots$
1058.4.a.b	$1058$	$4$	1058.a	1.a	$1$	$1$	$1$	$62.424$	$\Q$	None	✓				46.4.a.b	$1$	$0$	$2$	$-9$	$20$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-9q^{3}+4q^{4}+20q^{5}-18q^{6}+\cdots$
1058.4.a.c	$1058$	$4$	1058.a	1.a	$1$	$1$	$1$	$62.424$	$\Q$	None	✓	✓			1058.4.a.c	$1$	$0$	$2$	$7$	$-18$	$30$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+7q^{3}+4q^{4}-18q^{5}+14q^{6}+\cdots$
1058.4.a.d	$1058$	$4$	1058.a	1.a	$1$	$1$	$1$	$62.424$	$\Q$	None	✓	✓			1058.4.a.c	$1$	$0$	$2$	$7$	$18$	$-30$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+7q^{3}+4q^{4}+18q^{5}+14q^{6}+\cdots$
1058.4.a.e	$1058$	$4$	1058.a	1.a	$1$	$2$	$2$	$62.424$	$\Q(\sqrt{3}) $	None	✓	✓			1058.4.a.e	$2$	$1$	$-4$	$-10$	$0$	$0$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	$q-2q^{2}-5q^{3}+4q^{4}-\beta q^{5}+10q^{6}+\cdots$
1058.4.a.f	$1058$	$4$	1058.a	1.a	$1$	$2$	$2$	$62.424$	$\Q(\sqrt{41}) $	None	✓				46.4.a.c	$1$	$1$	$-4$	$-1$	$-10$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(1-3\beta )q^{3}+4q^{4}+(-4-2\beta )q^{5}+\cdots$
1058.4.a.g	$1058$	$4$	1058.a	1.a	$1$	$2$	$2$	$62.424$	$\Q(\sqrt{3}) $	None	✓	✓			1058.4.a.g	$1$	$1$	$-4$	$2$	$-12$	$18$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(1+3\beta )q^{3}+4q^{4}+(-6-\beta )q^{5}+\cdots$
1058.4.a.h	$1058$	$4$	1058.a	1.a	$1$	$2$	$2$	$62.424$	$\Q(\sqrt{3}) $	None	✓	✓			1058.4.a.g	$1$	$1$	$-4$	$2$	$12$	$-18$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(1+3\beta )q^{3}+4q^{4}+(6+\beta )q^{5}+\cdots$
1058.4.a.i	$1058$	$4$	1058.a	1.a	$1$	$2$	$2$	$62.424$	$\Q(\sqrt{26}) $	None	✓	✓			1058.4.a.i	$2$	$0$	$4$	$-8$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+2q^{2}-4q^{3}+4q^{4}+\beta q^{5}-8q^{6}+\cdots$
1058.4.a.j	$1058$	$4$	1058.a	1.a	$1$	$2$	$2$	$62.424$	$\Q(\sqrt{73}) $	None	✓				46.4.a.d	$1$	$0$	$4$	$3$	$-10$	$-12$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(1+\beta )q^{3}+4q^{4}+(-6+2\beta )q^{5}+\cdots$
1058.4.a.k	$1058$	$4$	1058.a	1.a	$1$	$3$	$3$	$62.424$	3.3.6584.1	None	✓	✓			1058.4.a.k	$1$	$1$	$-6$	$-2$	$-9$	$30$	$-$	$2$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(-3+\cdots)q^{5}+\cdots$
1058.4.a.l	$1058$	$4$	1058.a	1.a	$1$	$3$	$3$	$62.424$	3.3.6584.1	None	✓	✓			1058.4.a.k	$1$	$1$	$-6$	$-2$	$9$	$-30$	$-$	$2$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(3+2\beta _{1}+\cdots)q^{5}+\cdots$
1058.4.a.m	$1058$	$4$	1058.a	1.a	$1$	$3$	$3$	$62.424$	3.3.123880.1	None	✓	✓			1058.4.a.m	$1$	$0$	$6$	$9$	$-4$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(3+\beta _{1})q^{3}+4q^{4}+(-1+\beta _{2})q^{5}+\cdots$
1058.4.a.n	$1058$	$4$	1058.a	1.a	$1$	$3$	$3$	$62.424$	3.3.123880.1	None	✓	✓			1058.4.a.m	$1$	$0$	$6$	$9$	$4$	$10$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(3+\beta _{1})q^{3}+4q^{4}+(1-\beta _{2})q^{5}+\cdots$
1058.4.a.o	$1058$	$4$	1058.a	1.a	$1$	$4$	$4$	$62.424$	$\Q(\sqrt{2}, \sqrt{13})$	None	✓	✓			1058.4.a.o	$2$	$1$	$8$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+2q^{2}+\beta _{3}q^{3}+4q^{4}+(-5\beta _{1}-6\beta _{2}+\cdots)q^{5}+\cdots$
1058.4.a.p	$1058$	$4$	1058.a	1.a	$1$	$6$	$6$	$62.424$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓			1058.4.a.p	$2$	$0$	$-12$	$12$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-2q^{2}+(2+\beta _{2})q^{3}+4q^{4}+(4\beta _{3}+\beta _{5})q^{5}+\cdots$
1058.4.a.q	$1058$	$4$	1058.a	1.a	$1$	$8$	$8$	$62.424$	8.8.$\cdots$.1	None	✓	✓			1058.4.a.q	$2$	$1$	$16$	$-24$	$0$	$0$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+2q^{2}+(-3+\beta _{1}-\beta _{4})q^{3}+4q^{4}+\cdots$
1058.4.a.r	$1058$	$4$	1058.a	1.a	$1$	$8$	$8$	$62.424$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓			1058.4.a.r	$2$	$0$	$16$	$6$	$0$	$0$	$+$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	$q+2q^{2}+(1-\beta _{3})q^{3}+4q^{4}+(\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots$
1058.4.a.s	$1058$	$4$	1058.a	1.a	$1$	$12$	$12$	$62.424$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓			1058.4.a.s	$2$	$0$	$-24$	$0$	$0$	$0$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-2q^{2}+(-\beta _{1}+\beta _{2})q^{3}+4q^{4}+(\beta _{7}+\cdots)q^{5}+\cdots$
1058.4.a.t	$1058$	$4$	1058.a	1.a	$1$	$15$	$15$	$62.424$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓		✓		46.4.c.b	$1$	$1$	$-30$	$1$	$0$	$-80$	$-$	$23^{4}$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta _{4}q^{3}+4q^{4}-\beta _{7}q^{5}-2\beta _{4}q^{6}+\cdots$
1058.4.a.u	$1058$	$4$	1058.a	1.a	$1$	$15$	$15$	$62.424$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓		✓		46.4.c.b	$1$	$0$	$-30$	$1$	$0$	$80$	$+$	$23^{4}$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta _{4}q^{3}+4q^{4}+\beta _{7}q^{5}-2\beta _{4}q^{6}+\cdots$
1058.4.a.v	$1058$	$4$	1058.a	1.a	$1$	$15$	$15$	$62.424$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓		✓		46.4.c.a	$1$	$1$	$30$	$3$	$-50$	$-84$	$-$	$23^{4}$	$\mathrm{SU}(2)$	$q+2q^{2}+\beta _{1}q^{3}+4q^{4}+(-3+\beta _{10}+\cdots)q^{5}+\cdots$
1058.4.a.w	$1058$	$4$	1058.a	1.a	$1$	$15$	$15$	$62.424$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓		✓		46.4.c.a	$1$	$0$	$30$	$3$	$50$	$84$	$+$	$23^{4}$	$\mathrm{SU}(2)$	$q+2q^{2}+\beta _{1}q^{3}+4q^{4}+(3-\beta _{10})q^{5}+\cdots$
1058.6.a.a	$1058$	$6$	1058.a	1.a	$1$	$1$	$1$	$169.686$	$\Q$	None	✓	✓			1058.6.a.a	$1$	$1$	$4$	$18$	$-23$	$-122$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}+18q^{3}+2^{4}q^{4}-23q^{5}+72q^{6}+\cdots$
1058.6.a.b	$1058$	$6$	1058.a	1.a	$1$	$1$	$1$	$169.686$	$\Q$	None	✓	✓			1058.6.a.a	$1$	$1$	$4$	$18$	$23$	$122$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}+18q^{3}+2^{4}q^{4}+23q^{5}+72q^{6}+\cdots$
1058.6.a.c	$1058$	$6$	1058.a	1.a	$1$	$2$	$2$	$169.686$	$\Q(\sqrt{55}) $	None	✓				46.6.a.a	$1$	$0$	$-8$	$6$	$68$	$-96$	$-$	$2$	$\mathrm{SU}(2)$	$q-4q^{2}+(3+\beta )q^{3}+2^{4}q^{4}+(34+5\beta )q^{5}+\cdots$
1058.6.a.d	$1058$	$6$	1058.a	1.a	$1$	$2$	$2$	$169.686$	$\Q(\sqrt{2}) $	None	✓				46.6.a.b	$1$	$1$	$8$	$-22$	$68$	$312$	$+$	$2$	$\mathrm{SU}(2)$	$q+4q^{2}+(-11+3\beta )q^{3}+2^{4}q^{4}+(34+\cdots)q^{5}+\cdots$
1058.6.a.e	$1058$	$6$	1058.a	1.a	$1$	$3$	$3$	$169.686$	3.3.23196.1	None	✓				46.6.a.c	$1$	$0$	$-12$	$6$	$-32$	$192$	$-$	$2$	$\mathrm{SU}(2)$	$q-4q^{2}+(3+\beta _{1}-2\beta _{2})q^{3}+2^{4}q^{4}+\cdots$
1058.6.a.f	$1058$	$6$	1058.a	1.a	$1$	$3$	$3$	$169.686$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓			1058.6.a.f	$1$	$1$	$12$	$-32$	$-63$	$234$	$+$	$2$	$\mathrm{SU}(2)$	$q+4q^{2}+(-11+\beta _{1})q^{3}+2^{4}q^{4}+(-21+\cdots)q^{5}+\cdots$
1058.6.a.g	$1058$	$6$	1058.a	1.a	$1$	$3$	$3$	$169.686$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓			1058.6.a.f	$1$	$1$	$12$	$-32$	$63$	$-234$	$+$	$2$	$\mathrm{SU}(2)$	$q+4q^{2}+(-11+\beta _{1})q^{3}+2^{4}q^{4}+(21+\cdots)q^{5}+\cdots$
1058.6.a.h	$1058$	$6$	1058.a	1.a	$1$	$3$	$3$	$169.686$	3.3.3149560.1	None	✓				46.6.a.d	$1$	$1$	$12$	$14$	$-82$	$-172$	$+$	$2$	$\mathrm{SU}(2)$	$q+4q^{2}+(5-\beta _{1})q^{3}+2^{4}q^{4}+(-3^{3}+\cdots)q^{5}+\cdots$

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 64 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.