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 (45 matches)

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
1444.1.b.a	$1444$	$1$	1444.b	4.b	$2$	$2$	$2$	$0.721$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-1}) $	None	✓	✓			1444.1.b.a	$2$	$0$	$-2$	$0$	$-1$	$0$		$1$		$q-q^{2}+q^{4}+(-1+\beta )q^{5}-q^{8}+q^{9}+\cdots$
1444.1.b.b	$1444$	$1$	1444.b	4.b	$2$	$2$	$2$	$0.721$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-1}) $	None	✓	✓			1444.1.b.a	$2$	$0$	$2$	$0$	$-1$	$0$		$1$		$q+q^{2}+q^{4}+(-1+\beta )q^{5}+q^{8}+q^{9}+\cdots$
1444.1.c.a	$1444$	$1$	1444.c	19.b	$2$	$2$	$2$	$0.721$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		✓	✓	✓	1444.1.c.a	$2$	$0$	$0$	$0$	$2$	$2$		$1$		$q-\beta q^{3}+q^{5}+q^{7}-q^{9}-q^{11}-\beta q^{15}+\cdots$
1444.1.g.a	$1444$	$1$	1444.g	76.g	$6$	$4$	$2$	$0.721$	$\Q(\sqrt{-3}, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		✓			1444.1.b.a	$4$	$0$	$-2$	$0$	$1$	$0$		$1$		$q+(-1-\beta _{3})q^{2}+\beta _{3}q^{4}+(1-\beta _{1}+\beta _{3})q^{5}+\cdots$
1444.1.g.b	$1444$	$1$	1444.g	76.g	$6$	$4$	$2$	$0.721$	$\Q(\sqrt{-3}, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		✓			1444.1.b.a	$4$	$0$	$2$	$0$	$1$	$0$		$1$		$q+(1+\beta _{3})q^{2}+\beta _{3}q^{4}+(1-\beta _{1}+\beta _{3})q^{5}+\cdots$
1444.1.h.a	$1444$	$1$	1444.h	19.d	$6$	$2$	$1$	$0.721$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-19}) $	None					76.1.c.a	$4$	$0$	$0$	$0$	$1$	$-2$		$1$		$q-\zeta_{6}^{2}q^{5}-q^{7}-\zeta_{6}q^{9}-q^{11}-\zeta_{6}^{2}q^{17}+\cdots$
1444.1.h.b	$1444$	$1$	1444.h	19.d	$6$	$4$	$2$	$0.721$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		✓	✓		1444.1.c.a	$4$	$0$	$0$	$0$	$-2$	$4$		$1$		$q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+q^{7}+\beta _{2}q^{9}+\cdots$
1444.1.j.a	$1444$	$1$	1444.j	19.f	$18$	$6$	$1$	$0.721$	$\Q(\zeta_{18})$	$D_{3}$	$\Q(\sqrt{-19}) $	None					76.1.c.a	$12$	$0$	$0$	$0$	$0$	$3$		$1$		$q-\zeta_{18}^{8}q^{5}+\zeta_{18}^{3}q^{7}+\zeta_{18}^{4}q^{9}+\cdots$
1444.1.j.b	$1444$	$1$	1444.j	19.f	$18$	$12$	$2$	$0.721$	12.0.$\cdots$.1	$S_{4}$	None	None		✓	✓		1444.1.c.a	$12$	$0$	$0$	$0$	$0$	$-6$		$1$		$q+(-\beta _{5}+\beta _{11})q^{3}+(\beta _{2}-\beta _{8})q^{5}+(-1+\cdots)q^{7}+\cdots$
1444.1.l.a	$1444$	$1$	1444.l	76.l	$18$	$12$	$2$	$0.721$	12.0.$\cdots$.1	$D_{5}$	$\Q(\sqrt{-1}) $	None		✓			1444.1.b.a	$12$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\beta _{3}+\beta _{9})q^{2}+(-\beta _{5}+\beta _{11})q^{4}+\cdots$
1444.1.l.b	$1444$	$1$	1444.l	76.l	$18$	$12$	$2$	$0.721$	12.0.$\cdots$.1	$D_{5}$	$\Q(\sqrt{-1}) $	None		✓			1444.1.b.a	$12$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\beta _{3}-\beta _{9})q^{2}+(-\beta _{5}+\beta _{11})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
1444.2.a.a	$1444$	$2$	1444.a	1.a	$1$	$1$	$1$	$11.530$	$\Q$	$_{}$	None	None	✓				76.2.a.a	$1$	$1$	$0$	$-2$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}-3q^{7}+q^{9}+5q^{11}+\cdots$
1444.2.a.b	$1444$	$2$	1444.a	1.a	$1$	$1$	$1$	$11.530$	$\Q$	$_{}$	None	None	✓				76.2.e.a	$1$	$0$	$0$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{9}-4q^{11}-q^{13}+\cdots$
1444.2.a.c	$1444$	$2$	1444.a	1.a	$1$	$1$	$1$	$11.530$	$\Q$	$_{}$	None	None	✓				76.2.e.a	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{9}-4q^{11}+q^{13}+\cdots$
1444.2.a.d	$1444$	$2$	1444.a	1.a	$1$	$2$	$2$	$11.530$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			1444.2.a.d	$1$	$1$	$0$	$-1$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-2\beta q^{5}+(1+2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots$
1444.2.a.e	$1444$	$2$	1444.a	1.a	$1$	$2$	$2$	$11.530$	$\Q(\sqrt{57}) $	$_{}$	$\Q(\sqrt{-19}) $	None	✓	✓			1444.2.a.e	$2$	$0$	$0$	$0$	$1$	$-3$	$-$	$1$	$N(\mathrm{U}(1))$	$q+\beta q^{5}+(-2+\beta )q^{7}-3q^{9}+(2+\beta )q^{11}+\cdots$
1444.2.a.f	$1444$	$2$	1444.a	1.a	$1$	$2$	$2$	$11.530$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			1444.2.a.d	$1$	$1$	$0$	$1$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2\beta q^{5}+(1+2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots$
1444.2.a.g	$1444$	$2$	1444.a	1.a	$1$	$6$	$6$	$11.530$	6.6.20319417.1	$_{}$	None	None	✓		✓		76.2.i.a	$1$	$1$	$0$	$-3$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2}-\beta _{3})q^{3}-\beta _{4}q^{5}+(-1+\cdots)q^{7}+\cdots$
1444.2.a.h	$1444$	$2$	1444.a	1.a	$1$	$6$	$6$	$11.530$	6.6.20319417.1	$_{}$	None	None	✓				76.2.i.a	$1$	$0$	$0$	$3$	$-3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{2}+\beta _{3})q^{3}-\beta _{4}q^{5}+(-1+\cdots)q^{7}+\cdots$
1444.2.a.i	$1444$	$2$	1444.a	1.a	$1$	$8$	$8$	$11.530$	8.8.$\cdots$.1	$_{}$	None	None	✓	✓	✓		1444.2.a.i	$2$	$0$	$0$	$0$	$14$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{3}+\beta _{5})q^{3}+(1+\beta _{1}+\beta _{4})q^{5}+(2+\cdots)q^{7}+\cdots$
1444.2.e.a	$1444$	$2$	1444.e	19.c	$3$	$2$	$1$	$11.530$	$\Q(\sqrt{-3}) $	$_{}$	None	None					76.2.a.a	$2$	$0$	$0$	$-2$	$1$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-3q^{7}+\cdots$
1444.2.e.b	$1444$	$2$	1444.e	19.c	$3$	$2$	$1$	$11.530$	$\Q(\sqrt{-3}) $	$_{}$	None	None					76.2.e.a	$2$	$0$	$0$	$-1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots$
1444.2.e.c	$1444$	$2$	1444.e	19.c	$3$	$2$	$1$	$11.530$	$\Q(\sqrt{-3}) $	$_{}$	None	None					76.2.a.a	$2$	$0$	$0$	$2$	$1$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-3q^{7}+\cdots$
1444.2.e.d	$1444$	$2$	1444.e	19.c	$3$	$4$	$2$	$11.530$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			1444.2.a.d	$2$	$0$	$0$	$-1$	$2$	$8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+2\beta _{1}q^{5}+(1-2\beta _{2})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots$
1444.2.e.e	$1444$	$2$	1444.e	19.c	$3$	$4$	$2$	$11.530$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	$\Q(\sqrt{-19}) $	None		✓			1444.2.a.e	$4$	$0$	$0$	$0$	$-1$	$-6$		$3$	$\mathrm{U}(1)[D_{3}]$	$q+(-1-\beta _{1}+\beta _{3})q^{5}+(-1-\beta _{2})q^{7}+\cdots$
1444.2.e.f	$1444$	$2$	1444.e	19.c	$3$	$4$	$2$	$11.530$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			1444.2.a.d	$2$	$0$	$0$	$1$	$2$	$8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+2\beta _{1}q^{5}+(1-2\beta _{2})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots$
1444.2.e.g	$1444$	$2$	1444.e	19.c	$3$	$12$	$6$	$11.530$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None					76.2.i.a	$2$	$0$	$0$	$-3$	$3$	$-6$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{2}-\beta _{4}+\beta _{8})q^{3}+(1+\beta _{10}+\beta _{11})q^{5}+\cdots$
1444.2.e.h	$1444$	$2$	1444.e	19.c	$3$	$12$	$6$	$11.530$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None					76.2.i.a	$2$	$0$	$0$	$3$	$3$	$-6$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{5}-\beta _{11})q^{3}+\beta _{9}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
1444.2.e.i	$1444$	$2$	1444.e	19.c	$3$	$16$	$8$	$11.530$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		1444.2.a.i	$4$	$0$	$0$	$0$	$-14$	$16$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{5}-\beta _{14})q^{3}+(-\beta _{1}-\beta _{8}+2\beta _{9}+\cdots)q^{5}+\cdots$
1444.3.c.a	$1444$	$3$	1444.c	19.b	$2$	$6$	$6$	$39.346$	6.0.253035008.1	$_{}$	None	None		✓			1444.3.c.a	$2$	$0$	$0$	$0$	$2$	$-10$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(1+\beta _{2}+\beta _{4})q^{5}+(-2-2\beta _{2}+\cdots)q^{7}+\cdots$
1444.3.c.b	$1444$	$3$	1444.c	19.b	$2$	$8$	$8$	$39.346$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None					76.3.h.a	$2$	$0$	$0$	$0$	$2$	$-12$		$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{2}-\beta _{3})q^{3}-\beta _{6}q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots$
1444.3.c.c	$1444$	$3$	1444.c	19.b	$2$	$18$	$18$	$39.346$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None					76.3.j.a	$2$	$0$	$0$	$0$	$6$	$-18$		$2^{9}\cdot 19^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{10}q^{3}+\beta _{6}q^{5}+(-1-\beta _{5})q^{7}+\cdots$
1444.3.c.d	$1444$	$3$	1444.c	19.b	$2$	$24$	$24$	$39.346$		$_{}$	None	None		✓	✓		1444.3.c.d	$2$	$0$	$0$	$0$	$-12$	$40$			$\mathrm{SU}(2)[C_{2}]$
1444.4.a.a	$1444$	$4$	1444.a	1.a	$1$	$1$	$1$	$85.199$	$\Q$	$_{}$	None	None	✓	✓			1444.4.a.a	$1$	$1$	$0$	$-7$	$2$	$-11$	$-$	$1$	$\mathrm{SU}(2)$	$q-7q^{3}+2q^{5}-11q^{7}+22q^{9}+22q^{11}+\cdots$
1444.4.a.b	$1444$	$4$	1444.a	1.a	$1$	$1$	$1$	$85.199$	$\Q$	$_{}$	None	None	✓	✓			1444.4.a.a	$1$	$1$	$0$	$7$	$2$	$-11$	$-$	$1$	$\mathrm{SU}(2)$	$q+7q^{3}+2q^{5}-11q^{7}+22q^{9}+22q^{11}+\cdots$
1444.4.a.c	$1444$	$4$	1444.a	1.a	$1$	$2$	$2$	$85.199$	$\Q(\sqrt{57}) $	$_{}$	$\Q(\sqrt{-19}) $	None	✓	✓			1444.4.a.c	$2$	$1$	$0$	$0$	$-14$	$36$	$-$	$2$	$N(\mathrm{U}(1))$	$q+(-7-2\beta )q^{5}+(18+\beta )q^{7}-3^{3}q^{9}+\cdots$
1444.4.a.d	$1444$	$4$	1444.a	1.a	$1$	$2$	$2$	$85.199$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓				76.4.a.a	$1$	$0$	$0$	$5$	$-5$	$-30$	$+$	$1$	$\mathrm{SU}(2)$	$q+(3-\beta )q^{3}-5\beta q^{5}+(-17+4\beta )q^{7}+\cdots$
1444.4.a.e	$1444$	$4$	1444.a	1.a	$1$	$3$	$3$	$85.199$	3.3.35529.1	$_{}$	None	None	✓				76.4.a.b	$1$	$0$	$0$	$-1$	$9$	$44$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{3}+(3+\beta _{2})q^{5}+(15+\cdots)q^{7}+\cdots$
1444.4.a.f	$1444$	$4$	1444.a	1.a	$1$	$5$	$5$	$85.199$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓				76.4.e.a	$1$	$1$	$0$	$-7$	$4$	$-10$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}+(1+\beta _{3})q^{5}+(-2+\cdots)q^{7}+\cdots$
1444.4.a.g	$1444$	$4$	1444.a	1.a	$1$	$5$	$5$	$85.199$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓				76.4.e.a	$1$	$0$	$0$	$7$	$4$	$-10$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+(1+\beta _{3})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots$
1444.4.a.h	$1444$	$4$	1444.a	1.a	$1$	$10$	$10$	$85.199$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	✓			1444.4.a.h	$1$	$0$	$0$	$-2$	$13$	$-2$	$+$	$2^{8}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(2-2\beta _{3}-\beta _{7})q^{5}+(\beta _{1}-2\beta _{3}+\cdots)q^{7}+\cdots$
1444.4.a.i	$1444$	$4$	1444.a	1.a	$1$	$10$	$10$	$85.199$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	✓			1444.4.a.h	$1$	$0$	$0$	$2$	$13$	$-2$	$+$	$2^{8}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(2-2\beta _{3}-\beta _{7})q^{5}+(\beta _{1}-2\beta _{3}+\cdots)q^{7}+\cdots$
1444.4.a.j	$1444$	$4$	1444.a	1.a	$1$	$15$	$15$	$85.199$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓				76.4.i.a	$1$	$1$	$0$	$0$	$12$	$-6$	$-$	$2^{6}\cdot 3^{2}\cdot 19$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{9})q^{5}-\beta _{11}q^{7}+(9+\cdots)q^{9}+\cdots$
1444.4.a.k	$1444$	$4$	1444.a	1.a	$1$	$15$	$15$	$85.199$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓		✓		76.4.i.a	$1$	$0$	$0$	$0$	$12$	$-6$	$+$	$2^{6}\cdot 3^{2}\cdot 19$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1-\beta _{9})q^{5}-\beta _{11}q^{7}+(9+\cdots)q^{9}+\cdots$
1444.4.a.l	$1444$	$4$	1444.a	1.a	$1$	$16$	$16$	$85.199$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	✓	✓		1444.4.a.l	$2$	$1$	$0$	$0$	$-60$	$-4$	$-$	$2^{8}\cdot 19^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-4+\beta _{9})q^{5}-\beta _{8}q^{7}+(6+\cdots)q^{9}+\cdots$

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 (45 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.