LMFDB - Newform search results

Refine search

Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
		Only for weight 1:

				Sort order	Select

Results (1-50 of 12085 matches)

Next Download displayed columns for results to

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1.12.a.a	$1$	$12$	1.a	1.a	$1$	$1$	$1$	$0.768$	$\Q$	None	✓	$1$	$0$	$-24$	$252$	$4830$	$-16744$	$+$	$1$	$\mathrm{SU}(2)$	$q-24q^{2}+252q^{3}-1472q^{4}+4830q^{5}+\cdots$
2.10.a.a	$2$	$10$	2.a	1.a	$1$	$1$	$1$	$1.030$	$\Q$	None	✓	$1$	$0$	$16$	$-156$	$870$	$-952$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{4}q^{2}-156q^{3}+2^{8}q^{4}+870q^{5}+\cdots$
3.9.b.a	$3$	$9$	3.b	3.b	$2$	$2$	$2$	$1.222$	$\Q(\sqrt{-14}) $	None		$2$	$0$	$0$	$90$	$0$	$-3500$		$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(45-3\beta )q^{3}-248q^{4}-10\beta q^{5}+\cdots$
1.16.a.a	$1$	$16$	1.a	1.a	$1$	$1$	$1$	$1.427$	$\Q$	None	✓	$1$	$0$	$216$	$-3348$	$52110$	$2822456$	$+$	$1$	$\mathrm{SU}(2)$	$q+6^{3}q^{2}-3348q^{3}+13888q^{4}+52110q^{5}+\cdots$
3.10.a.a	$3$	$10$	3.a	1.a	$1$	$1$	$1$	$1.545$	$\Q$	None	✓	$1$	$1$	$-36$	$-81$	$-1314$	$-4480$	$+$	$1$	$\mathrm{SU}(2)$	$q-6^{2}q^{2}-3^{4}q^{3}+28^{2}q^{4}-1314q^{5}+\cdots$
3.10.a.b	$3$	$10$	3.a	1.a	$1$	$1$	$1$	$1.545$	$\Q$	None	✓	$1$	$0$	$18$	$81$	$-1530$	$9128$	$-$	$1$	$\mathrm{SU}(2)$	$q+18q^{2}+3^{4}q^{3}-188q^{4}-1530q^{5}+\cdots$
4.9.b.a	$4$	$9$	4.b	4.b	$2$	$1$	$1$	$1.630$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$16$	$0$	$-1054$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{2}+2^{8}q^{4}-1054q^{5}+2^{12}q^{8}+\cdots$
4.9.b.b	$4$	$9$	4.b	4.b	$2$	$2$	$2$	$1.630$	$\Q(\sqrt{-39}) $	None		$2$	$0$	$-20$	$0$	$1220$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-10-\beta )q^{2}-8\beta q^{3}+(-56+20\beta )q^{4}+\cdots$
3.11.b.a	$3$	$11$	3.b	3.b	$2$	$2$	$2$	$1.906$	$\Q(\sqrt{-5}) $	None		$2$	$0$	$0$	$-54$	$0$	$34468$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(-3^{3}+9\beta )q^{3}+304q^{4}+\cdots$
5.9.c.a	$5$	$9$	5.c	5.c	$4$	$6$	$3$	$2.037$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		$2$	$0$	$-2$	$-72$	$220$	$-2352$		$2^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{2}+(-12-12\beta _{1}-\beta _{2}-\beta _{5})q^{3}+\cdots$
4.10.a.a	$4$	$10$	4.a	1.a	$1$	$1$	$1$	$2.060$	$\Q$	None	✓	$1$	$0$	$0$	$228$	$-666$	$-6328$	$-$	$1$	$\mathrm{SU}(2)$	$q+228q^{3}-666q^{5}-6328q^{7}+32301q^{9}+\cdots$
2.14.a.a	$2$	$14$	2.a	1.a	$1$	$1$	$1$	$2.145$	$\Q$	None	✓	$1$	$1$	$-64$	$-1836$	$3990$	$-433432$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{6}q^{2}-1836q^{3}+2^{12}q^{4}+3990q^{5}+\cdots$
2.14.a.b	$2$	$14$	2.a	1.a	$1$	$1$	$1$	$2.145$	$\Q$	None	✓	$1$	$0$	$64$	$1236$	$-57450$	$64232$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{6}q^{2}+1236q^{3}+2^{12}q^{4}-57450q^{5}+\cdots$
3.12.a.a	$3$	$12$	3.a	1.a	$1$	$1$	$1$	$2.305$	$\Q$	None	✓	$1$	$0$	$78$	$-243$	$-5370$	$-27760$	$+$	$1$	$\mathrm{SU}(2)$	$q+78q^{2}-3^{5}q^{3}+4036q^{4}-5370q^{5}+\cdots$
6.9.b.a	$6$	$9$	6.b	3.b	$2$	$2$	$2$	$2.444$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$-126$	$0$	$5572$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{2}+(-63+9\beta )q^{3}-2^{7}q^{4}+\cdots$
4.11.b.a	$4$	$11$	4.b	4.b	$2$	$4$	$4$	$2.541$	4.0.26777625.2	None		$2$	$0$	$-12$	$0$	$-1560$	$0$		$2^{12}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(-3+\beta _{1})q^{2}+(-2\beta _{1}+\beta _{2})q^{3}+\cdots$
5.10.a.a	$5$	$10$	5.a	1.a	$1$	$1$	$1$	$2.575$	$\Q$	None	✓	$1$	$1$	$-8$	$-114$	$-625$	$4242$	$+$	$1$	$\mathrm{SU}(2)$	$q-8q^{2}-114q^{3}-448q^{4}-5^{4}q^{5}+\cdots$
5.10.a.b	$5$	$10$	5.a	1.a	$1$	$2$	$2$	$2.575$	$\Q(\sqrt{1009}) $	None	✓	$1$	$0$	$-10$	$260$	$1250$	$1700$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-5-\beta )q^{2}+(130+2\beta )q^{3}+(522+\cdots)q^{4}+\cdots$
5.10.b.a	$5$	$10$	5.b	5.b	$2$	$4$	$4$	$2.575$	4.0.49740556.1	None		$2$	$0$	$0$	$0$	$1140$	$0$		$2^{5}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-342+\cdots)q^{4}+\cdots$
3.13.b.a	$3$	$13$	3.b	3.b	$2$	$1$	$1$	$2.742$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$729$	$0$	$-153502$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3^{6}q^{3}+2^{12}q^{4}-153502q^{7}+3^{12}q^{9}+\cdots$
3.13.b.b	$3$	$13$	3.b	3.b	$2$	$2$	$2$	$2.742$	$\Q(\sqrt{-26}) $	None		$2$	$0$	$0$	$-1350$	$0$	$80500$		$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(-675-3\beta )q^{3}-4328q^{4}+\cdots$
7.9.b.a	$7$	$9$	7.b	7.b	$2$	$1$	$1$	$2.852$	$\Q$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$-31$	$0$	$0$	$2401$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-31q^{2}+705q^{4}+7^{4}q^{7}-13919q^{8}+\cdots$
7.9.b.b	$7$	$9$	7.b	7.b	$2$	$4$	$4$	$2.852$	$\mathbb{Q}[x]/(x^{4} + \cdots)$	None		$2$	$0$	$32$	$0$	$0$	$1428$		$2^{4}\cdot 3\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	$q+(8+\beta _{3})q^{2}-\beta _{1}q^{3}+(-8+2^{4}\beta _{3})q^{4}+\cdots$
7.9.d.a	$7$	$9$	7.d	7.d	$6$	$8$	$4$	$2.852$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$-4$	$-84$	$-840$	$-140$		$2^{4}\cdot 3\cdot 7^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(-7+7\beta _{2}+\cdots)q^{3}+\cdots$
2.16.a.a	$2$	$16$	2.a	1.a	$1$	$1$	$1$	$2.854$	$\Q$	None	✓	$1$	$0$	$-128$	$6252$	$90510$	$56$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{7}q^{2}+6252q^{3}+2^{14}q^{4}+90510q^{5}+\cdots$
4.12.a.a	$4$	$12$	4.a	1.a	$1$	$1$	$1$	$3.073$	$\Q$	None	✓	$1$	$1$	$0$	$-516$	$-10530$	$49304$	$-$	$1$	$\mathrm{SU}(2)$	$q-516q^{3}-10530q^{5}+49304q^{7}+\cdots$
6.10.a.a	$6$	$10$	6.a	1.a	$1$	$1$	$1$	$3.090$	$\Q$	None	✓	$1$	$0$	$-16$	$81$	$2694$	$-3544$	$-$	$1$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}+2694q^{5}+\cdots$
5.11.c.a	$5$	$11$	5.c	5.c	$4$	$8$	$4$	$3.177$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$30$	$60$	$-5340$	$-14500$		$2^{8}\cdot 3^{2}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+(4+4\beta _{1}-\beta _{3})q^{2}+(8-8\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
3.14.a.a	$3$	$14$	3.a	1.a	$1$	$1$	$1$	$3.217$	$\Q$	None	✓	$1$	$1$	$-12$	$-729$	$-30210$	$235088$	$+$	$1$	$\mathrm{SU}(2)$	$q-12q^{2}-3^{6}q^{3}-8048q^{4}-30210q^{5}+\cdots$
3.14.a.b	$3$	$14$	3.a	1.a	$1$	$2$	$2$	$3.217$	$\Q(\sqrt{1969}) $	None	✓	$1$	$0$	$-54$	$1458$	$40716$	$-21008$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	$q+(-3^{3}-\beta )q^{2}+3^{6}q^{3}+(10258+54\beta )q^{4}+\cdots$
8.9.d.a	$8$	$9$	8.d	8.d	$2$	$1$	$1$	$3.259$	$\Q$	$\Q(\sqrt{-2}) $	✓	$2$	$0$	$16$	$34$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{2}+34q^{3}+2^{8}q^{4}+544q^{6}+\cdots$
8.9.d.b	$8$	$9$	8.d	8.d	$2$	$6$	$6$	$3.259$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		$2$	$0$	$-14$	$-36$	$0$	$0$		$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+\beta _{1})q^{2}+(-6-\beta _{1}-\beta _{2})q^{3}+\cdots$
7.10.a.a	$7$	$10$	7.a	1.a	$1$	$2$	$2$	$3.605$	$\Q(\sqrt{193}) $	None	✓	$1$	$1$	$-6$	$-86$	$-2238$	$-4802$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-3-\beta )q^{2}+(-43+11\beta )q^{3}+(-310+\cdots)q^{4}+\cdots$
7.10.a.b	$7$	$10$	7.a	1.a	$1$	$3$	$3$	$3.605$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	$1$	$0$	$21$	$84$	$1554$	$7203$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	$q+(7-\beta _{2})q^{2}+(28-\beta _{1}-\beta _{2})q^{3}+(519+\cdots)q^{4}+\cdots$
7.10.c.a	$7$	$10$	7.c	7.c	$3$	$10$	$5$	$3.605$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$-18$	$161$	$1533$	$-1036$		$2^{12}\cdot 3^{3}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{2}-4\beta _{3})q^{2}+(33-\beta _{1}+\cdots)q^{3}+\cdots$
4.13.b.a	$4$	$13$	4.b	4.b	$2$	$1$	$1$	$3.656$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$-64$	$0$	$23506$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2^{6}q^{2}+2^{12}q^{4}+23506q^{5}-2^{18}q^{8}+\cdots$
4.13.b.b	$4$	$13$	4.b	4.b	$2$	$4$	$4$	$3.656$	4.0.8546467905.1	None		$2$	$0$	$108$	$0$	$-18360$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+(3^{3}+\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(-380+\cdots)q^{4}+\cdots$
9.9.b.a	$9$	$9$	9.b	3.b	$2$	$2$	$2$	$3.666$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$0$	$3304$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+238q^{4}+233\beta q^{5}+1652q^{7}+\cdots$
9.9.d.a	$9$	$9$	9.d	9.d	$6$	$14$	$7$	$3.666$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		$2$	$0$	$-3$	$-93$	$438$	$922$		$2^{6}\cdot 3^{21}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{1}q^{2}+(-5-3\beta _{3}+\beta _{4}+\beta _{6})q^{3}+\cdots$
3.15.b.a	$3$	$15$	3.b	3.b	$2$	$4$	$4$	$3.730$	4.0.1929141760.2	None		$2$	$0$	$0$	$2196$	$0$	$825608$		$2^{10}\cdot 3^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(549+3\beta _{1}-\beta _{2})q^{3}+(-9824+\cdots)q^{4}+\cdots$
6.11.b.a	$6$	$11$	6.b	3.b	$2$	$4$	$4$	$3.812$	$\Q(\sqrt{-2}, \sqrt{85})$	None		$2$	$0$	$0$	$84$	$0$	$-45112$		$2^{11}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(21-3\beta _{1}+\beta _{2})q^{3}-2^{9}q^{4}+\cdots$
5.12.a.a	$5$	$12$	5.a	1.a	$1$	$1$	$1$	$3.842$	$\Q$	None	✓	$1$	$1$	$34$	$-792$	$3125$	$-17556$	$-$	$1$	$\mathrm{SU}(2)$	$q+34q^{2}-792q^{3}-892q^{4}+5^{5}q^{5}+\cdots$
5.12.a.b	$5$	$12$	5.a	1.a	$1$	$2$	$2$	$3.842$	$\Q(\sqrt{151}) $	None	✓	$1$	$0$	$-20$	$-220$	$-6250$	$57900$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-10+3\beta )q^{2}+(-110+2^{4}\beta )q^{3}+\cdots$
5.12.b.a	$5$	$12$	5.b	5.b	$2$	$4$	$4$	$3.842$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None		$2$	$0$	$0$	$0$	$-300$	$0$		$2^{5}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-18-\beta _{2})q^{4}+\cdots$
10.9.c.a	$10$	$9$	10.c	5.c	$4$	$4$	$2$	$4.074$	$\Q(i, \sqrt{249})$	None		$2$	$0$	$-32$	$54$	$90$	$-1186$		$2\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-8+8\beta _{1})q^{2}+(13+13\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
10.9.c.b	$10$	$9$	10.c	5.c	$4$	$4$	$2$	$4.074$	$\Q(i, \sqrt{601})$	None		$2$	$0$	$32$	$86$	$-870$	$5726$		$2\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(8+8\beta _{1})q^{2}+(22-21\beta _{1}+\beta _{3})q^{3}+\cdots$
8.10.a.a	$8$	$10$	8.a	1.a	$1$	$1$	$1$	$4.120$	$\Q$	None	✓	$1$	$1$	$0$	$-60$	$-2074$	$-4344$	$+$	$1$	$\mathrm{SU}(2)$	$q-60q^{3}-2074q^{5}-4344q^{7}-16083q^{9}+\cdots$
8.10.a.b	$8$	$10$	8.a	1.a	$1$	$1$	$1$	$4.120$	$\Q$	None	✓	$1$	$0$	$0$	$68$	$1510$	$10248$	$-$	$1$	$\mathrm{SU}(2)$	$q+68q^{3}+1510q^{5}+10248q^{7}-15059q^{9}+\cdots$
8.10.b.a	$8$	$10$	8.b	8.b	$2$	$8$	$8$	$4.120$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$-18$	$0$	$0$	$4800$		$2^{28}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2-\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-54+\cdots)q^{4}+\cdots$
3.16.a.a	$3$	$16$	3.a	1.a	$1$	$1$	$1$	$4.281$	$\Q$	None	✓	$1$	$0$	$-234$	$-2187$	$280710$	$-1373344$	$+$	$1$	$\mathrm{SU}(2)$	$q-234q^{2}-3^{7}q^{3}+21988q^{4}+280710q^{5}+\cdots$

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 12085 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.