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 186 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
95.1.d.a	$95$	$1$	95.d	95.d	$2$	$1$	$1$	$0.047$	$\Q$	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{5}) $	✓	✓			95.1.d.a	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q-q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}+q^{19}+\cdots$
95.1.d.b	$95$	$1$	95.d	95.d	$2$	$2$	$2$	$0.047$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-95}) $	None	✓	✓	✓		95.1.d.b	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\beta q^{2}+\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\cdots$
95.2.a.a	$95$	$2$	95.a	1.a	$1$	$3$	$3$	$0.759$	3.3.148.1	$_{}$	None	None	✓	✓	✓	✓	95.2.a.a	$1$	$0$	$1$	$2$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$
95.2.a.b	$95$	$2$	95.a	1.a	$1$	$4$	$4$	$0.759$	4.4.11344.1	$_{}$	None	None	✓	✓	✓	✓	95.2.a.b	$1$	$0$	$-2$	$2$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots$
95.2.b.a	$95$	$2$	95.b	5.b	$2$	$2$	$2$	$0.759$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			95.2.b.a	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+q^{4}+(2 i-1)q^{5}-2 i q^{7}+\cdots$
95.2.b.b	$95$	$2$	95.b	5.b	$2$	$6$	$6$	$0.759$	6.0.16516096.1	$_{}$	None	None		✓	✓		95.2.b.b	$2$	$0$	$0$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots$
95.2.e.a	$95$	$2$	95.e	19.c	$3$	$2$	$1$	$0.759$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			95.2.e.a	$2$	$0$	$0$	$2$	$1$	$-8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots$
95.2.e.b	$95$	$2$	95.e	19.c	$3$	$6$	$3$	$0.759$	6.0.3518667.1	$_{}$	None	None		✓			95.2.e.b	$2$	$0$	$-1$	$-1$	$3$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3}-\beta _{5})q^{3}+(-3+\cdots)q^{4}+\cdots$
95.2.e.c	$95$	$2$	95.e	19.c	$3$	$8$	$4$	$0.759$	8.0.4601315889.1	$_{}$	None	None		✓	✓		95.2.e.c	$2$	$0$	$-1$	$-3$	$-4$	$-8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{7}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$
95.2.g.a	$95$	$2$	95.g	95.g	$4$	$4$	$2$	$0.759$	$\Q(i, \sqrt{19})$	$_{}$	$\Q(\sqrt{-19}) $	None		✓			95.2.g.a	$4$	$0$	$0$	$0$	$2$	$6$		$1$	$\mathrm{U}(1)[D_{4}]$	$q-2\beta _{2}q^{4}-\beta _{3}q^{5}+(2-\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots$
95.2.g.b	$95$	$2$	95.g	95.g	$4$	$12$	$6$	$0.759$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓		95.2.g.b	$4$	$0$	$0$	$0$	$-4$	$-12$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{7}q^{2}+\beta _{5}q^{3}+(-\beta _{6}-\beta _{8})q^{4}+\cdots$
95.2.i.a	$95$	$2$	95.i	95.i	$6$	$4$	$2$	$0.759$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			95.2.i.a	$4$	$0$	$0$	$0$	$2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta_1 q^{2}+2\beta_{2} q^{4}+(-\beta_{2}-\beta_1+1)q^{5}+\cdots$
95.2.i.b	$95$	$2$	95.i	95.i	$6$	$12$	$6$	$0.759$	12.0.$\cdots$.2	$_{}$	None	None		✓	✓		95.2.i.b	$4$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{5}q^{2}+(\beta _{4}-\beta _{5})q^{3}+(-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
95.2.k.a	$95$	$2$	95.k	19.e	$9$	$18$	$3$	$0.759$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓			95.2.k.a	$2$	$0$	$-3$	$-3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\beta _{4}+\beta _{15})q^{2}+(\beta _{5}+\beta _{6}+\beta _{8}+\cdots)q^{3}+\cdots$
95.2.k.b	$95$	$2$	95.k	19.e	$9$	$18$	$3$	$0.759$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		✓			95.2.k.b	$2$	$0$	$3$	$-3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{14}q^{2}+(-\beta _{4}+\beta _{6}-\beta _{7}-\beta _{15}+\cdots)q^{3}+\cdots$
95.2.l.a	$95$	$2$	95.l	95.l	$12$	$4$	$1$	$0.759$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			95.2.l.a	$4$	$1$	$-6$	$-6$	$-4$	$-8$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-1+\zeta_{12}-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{2}+\cdots$
95.2.l.b	$95$	$2$	95.l	95.l	$12$	$4$	$1$	$0.759$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			95.2.l.b	$4$	$0$	$0$	$-6$	$2$	$8$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-1-\zeta_{12}-\zeta_{12}^{2}+2\zeta_{12}^{3})q^{3}+\cdots$
95.2.l.c	$95$	$2$	95.l	95.l	$12$	$24$	$6$	$0.759$		$_{}$	None	None		✓	✓		95.2.l.c	$4$	$0$	$0$	$6$	$-2$	$-12$			$\mathrm{SU}(2)[C_{12}]$
95.2.p.a	$95$	$2$	95.p	95.p	$18$	$48$	$8$	$0.759$		$_{}$	None	None		✓	✓	✓	95.2.p.a	$4$	$0$	$0$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{18}]$
95.2.r.a	$95$	$2$	95.r	95.r	$36$	$96$	$8$	$0.759$		$_{}$	None	None		✓	✓	✓	95.2.r.a	$4$	$0$	$-12$	$-12$	$-12$	$0$			$\mathrm{SU}(2)[C_{36}]$
95.3.c.a	$95$	$3$	95.c	19.b	$2$	$12$	$12$	$2.589$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓	✓	95.3.c.a	$2$	$0$	$0$	$0$	$0$	$20$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{8}q^{3}+(-1+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots$
95.3.d.a	$95$	$3$	95.d	95.d	$2$	$2$	$2$	$2.589$	$\Q(\sqrt{-19}) $	$_{}$	$\Q(\sqrt{-19}) $	None		✓			95.3.d.a	$4$	$0$	$0$	$0$	$-9$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-4q^{4}+(-4-\beta )q^{5}+(-3+6\beta )q^{7}+\cdots$
95.3.d.b	$95$	$3$	95.d	95.d	$2$	$4$	$4$	$2.589$	4.4.462080.1	$_{}$	$\Q(\sqrt{-95}) $	None	✓	✓			95.3.d.b	$4$	$0$	$0$	$0$	$-20$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(4+\beta _{3})q^{4}+\cdots$
95.3.d.c	$95$	$3$	95.d	95.d	$2$	$4$	$4$	$2.589$	4.4.7600.1	$_{}$	$\Q(\sqrt{-95}) $	None	✓	✓			95.3.d.c	$4$	$0$	$0$	$0$	$20$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(4+3\beta _{3})q^{4}+\cdots$
95.3.d.d	$95$	$3$	95.d	95.d	$2$	$8$	$8$	$2.589$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		✓	✓		95.3.d.d	$4$	$0$	$0$	$0$	$8$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(1+2\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots$
95.3.f.a	$95$	$3$	95.f	5.c	$4$	$36$	$18$	$2.589$		$_{}$	None	None		✓	✓	✓	95.3.f.a	$2$	$0$	$-4$	$-4$	$-6$	$-10$			$\mathrm{SU}(2)[C_{4}]$
95.3.h.a	$95$	$3$	95.h	95.h	$6$	$36$	$18$	$2.589$		$_{}$	None	None		✓	✓	✓	95.3.h.a	$4$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
95.3.j.a	$95$	$3$	95.j	19.d	$6$	$24$	$12$	$2.589$		$_{}$	None	None		✓	✓	✓	95.3.j.a	$2$	$0$	$0$	$12$	$0$	$-20$			$\mathrm{SU}(2)[C_{6}]$
95.3.m.a	$95$	$3$	95.m	95.m	$12$	$72$	$18$	$2.589$		$_{}$	None	None		✓	✓	✓	95.3.m.a	$4$	$0$	$-2$	$-2$	$0$	$-20$			$\mathrm{SU}(2)[C_{12}]$
95.3.n.a	$95$	$3$	95.n	19.f	$18$	$84$	$14$	$2.589$		$_{}$	None	None		✓	✓	✓	95.3.n.a	$2$	$0$	$0$	$-12$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
95.3.o.a	$95$	$3$	95.o	95.o	$18$	$108$	$18$	$2.589$		$_{}$	None	None		✓	✓	✓	95.3.o.a	$4$	$0$	$0$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{18}]$
95.3.q.a	$95$	$3$	95.q	95.q	$36$	$216$	$18$	$2.589$		$_{}$	None	None		✓	✓	✓	95.3.q.a	$4$	$0$	$-12$	$-12$	$-12$	$12$			$\mathrm{SU}(2)[C_{36}]$
95.4.a.a	$95$	$4$	95.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	$_{}$	None	None	✓	✓			95.4.a.a	$1$	$1$	$0$	$4$	$-5$	$-22$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{3}-8q^{4}-5q^{5}-22q^{7}-11q^{9}+\cdots$
95.4.a.b	$95$	$4$	95.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	$_{}$	None	None	✓	✓			95.4.a.b	$1$	$1$	$3$	$-5$	$-5$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}-5q^{3}+q^{4}-5q^{5}-15q^{6}+\cdots$
95.4.a.c	$95$	$4$	95.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	$_{}$	None	None	✓	✓			95.4.a.c	$1$	$0$	$3$	$7$	$5$	$11$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}+7q^{3}+q^{4}+5q^{5}+21q^{6}+\cdots$
95.4.a.d	$95$	$4$	95.a	1.a	$1$	$1$	$1$	$5.605$	$\Q$	$_{}$	None	None	✓	✓			95.4.a.d	$1$	$0$	$5$	$4$	$5$	$-32$	$+$	$1$	$\mathrm{SU}(2)$	$q+5q^{2}+4q^{3}+17q^{4}+5q^{5}+20q^{6}+\cdots$
95.4.a.e	$95$	$4$	95.a	1.a	$1$	$3$	$3$	$5.605$	3.3.1304.1	$_{}$	None	None	✓	✓	✓	✓	95.4.a.e	$1$	$1$	$-3$	$-11$	$15$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{2}+(-4-\beta _{1}-\beta _{2})q^{3}+\cdots$
95.4.a.f	$95$	$4$	95.a	1.a	$1$	$5$	$5$	$5.605$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	✓	✓		95.4.a.f	$1$	$0$	$-3$	$-4$	$25$	$72$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(4+\cdots)q^{4}+\cdots$
95.4.a.g	$95$	$4$	95.a	1.a	$1$	$6$	$6$	$5.605$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	95.4.a.g	$1$	$0$	$-1$	$5$	$-30$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{5})q^{3}+(4+\beta _{2}+\cdots)q^{4}+\cdots$
95.4.b.a	$95$	$4$	95.b	5.b	$2$	$12$	$12$	$5.605$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			95.4.b.a	$2$	$0$	$0$	$0$	$8$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{6})q^{3}+(-3+\beta _{2}+\cdots)q^{4}+\cdots$
95.4.b.b	$95$	$4$	95.b	5.b	$2$	$16$	$16$	$5.605$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓		95.4.b.b	$2$	$0$	$0$	$0$	$-6$	$0$		$2^{2}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{9}q^{3}+(-5+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots$
95.4.e.a	$95$	$4$	95.e	19.c	$3$	$2$	$1$	$5.605$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			95.4.e.a	$2$	$0$	$1$	$5$	$-5$	$44$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(5-5\zeta_{6})q^{3}+7\zeta_{6}q^{4}+\cdots$
95.4.e.b	$95$	$4$	95.e	19.c	$3$	$18$	$9$	$5.605$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓			95.4.e.b	$2$	$0$	$6$	$2$	$-45$	$-90$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{1}+\beta _{4})q^{2}+\beta _{11}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots$
95.4.e.c	$95$	$4$	95.e	19.c	$3$	$20$	$10$	$5.605$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓	✓		95.4.e.c	$2$	$0$	$-3$	$-5$	$50$	$6$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{3})q^{2}-\beta _{2}q^{3}+(4\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
95.4.g.a	$95$	$4$	95.g	95.g	$4$	$4$	$2$	$5.605$	$\Q(i, \sqrt{19})$	$_{}$	$\Q(\sqrt{-19}) $	None		✓			95.4.g.a	$4$	$0$	$0$	$0$	$-28$	$-72$		$2^{2}$	$\mathrm{U}(1)[D_{4}]$	$q-8\beta _{1}q^{4}+(-7+2\beta _{3})q^{5}+(-18+\cdots)q^{7}+\cdots$
95.4.g.b	$95$	$4$	95.g	95.g	$4$	$52$	$26$	$5.605$		$_{}$	None	None		✓	✓		95.4.g.b	$4$	$0$	$0$	$0$	$16$	$64$			$\mathrm{SU}(2)[C_{4}]$
95.4.i.a	$95$	$4$	95.i	95.i	$6$	$56$	$28$	$5.605$		$_{}$	None	None		✓	✓	✓	95.4.i.a	$4$	$0$	$0$	$0$	$-5$	$0$			$\mathrm{SU}(2)[C_{6}]$
95.4.k.a	$95$	$4$	95.k	19.e	$9$	$60$	$10$	$5.605$		$_{}$	None	None		✓			95.4.k.a	$2$	$0$	$-9$	$-3$	$0$	$0$			$\mathrm{SU}(2)[C_{9}]$
95.4.k.b	$95$	$4$	95.k	19.e	$9$	$60$	$10$	$5.605$		$_{}$	None	None		✓			95.4.k.b	$2$	$0$	$9$	$-3$	$0$	$0$			$\mathrm{SU}(2)[C_{9}]$
95.4.l.a	$95$	$4$	95.l	95.l	$12$	$112$	$28$	$5.605$		$_{}$	None	None		✓	✓	✓	95.4.l.a	$4$	$0$	$-6$	$-6$	$6$	$-16$			$\mathrm{SU}(2)[C_{12}]$

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 186 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.