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 143 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
28.2.d.a	$28$	$2$	28.d	28.d	$2$	$2$	$2$	$0.224$	$\Q(\sqrt{-7}) $	$\Q(\sqrt{-7}) $		✓	✓	✓	28.2.d.a	$4$	$0$	$-1$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{2}+(-2+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots$
28.2.e.a	$28$	$2$	28.e	7.c	$3$	$2$	$1$	$0.224$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	28.2.e.a	$2$	$0$	$0$	$-1$	$-3$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{3}+(-3+3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$
28.2.f.a	$28$	$2$	28.f	28.f	$6$	$4$	$2$	$0.224$	$\Q(\zeta_{12})$	None		✓	✓	✓	28.2.f.a	$4$	$0$	$-2$	$0$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\cdots)q^{3}+\cdots$
28.3.b.a	$28$	$3$	28.b	7.b	$2$	$2$	$2$	$0.763$	$\Q(\sqrt{-6}) $	None		✓	✓	✓	28.3.b.a	$2$	$0$	$0$	$0$	$0$	$10$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}-\beta q^{5}+(5-\beta )q^{7}-15q^{9}+\cdots$
28.3.c.a	$28$	$3$	28.c	4.b	$2$	$6$	$6$	$0.763$	6.0.1539727.2	None		✓	✓	✓	28.3.c.a	$2$	$0$	$-1$	$0$	$-4$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-\beta _{3}q^{3}+(-\beta _{1}-\beta _{4})q^{4}+\cdots$
28.3.g.a	$28$	$3$	28.g	28.g	$6$	$12$	$6$	$0.763$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓	✓	28.3.g.a	$4$	$0$	$-2$	$0$	$-2$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{6}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{5}+\beta _{9}+\cdots)q^{4}+\cdots$
28.3.h.a	$28$	$3$	28.h	7.d	$6$	$2$	$1$	$0.763$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	28.3.h.a	$2$	$0$	$0$	$3$	$3$	$-14$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}-7q^{7}-6\zeta_{6}q^{9}+\cdots$
28.4.a.a	$28$	$4$	28.a	1.a	$1$	$1$	$1$	$1.652$	$\Q$	None	✓	✓	✓	✓	28.4.a.a	$1$	$1$	$0$	$-10$	$-8$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q-10q^{3}-8q^{5}-7q^{7}+73q^{9}-40q^{11}+\cdots$
28.4.a.b	$28$	$4$	28.a	1.a	$1$	$1$	$1$	$1.652$	$\Q$	None	✓	✓	✓	✓	28.4.a.b	$1$	$0$	$0$	$4$	$6$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{3}+6q^{5}+7q^{7}-11q^{9}-12q^{11}+\cdots$
28.4.d.a	$28$	$4$	28.d	28.d	$2$	$2$	$2$	$1.652$	$\Q(\sqrt{-7}) $	$\Q(\sqrt{-7}) $		✓			28.4.d.a	$4$	$0$	$5$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(3-\beta )q^{2}+(7-5\beta )q^{4}+(-7+14\beta )q^{7}+\cdots$
28.4.d.b	$28$	$4$	28.d	28.d	$2$	$8$	$8$	$1.652$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓	✓		28.4.d.b	$4$	$0$	$-8$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots$
28.4.e.a	$28$	$4$	28.e	7.c	$3$	$4$	$2$	$1.652$	$\Q(\sqrt{-3}, \sqrt{37})$	None		✓	✓	✓	28.4.e.a	$2$	$0$	$0$	$0$	$14$	$24$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{3}+(7-7\beta _{1}-2\beta _{2}-2\beta _{3})q^{5}+\cdots$
28.4.f.a	$28$	$4$	28.f	28.f	$6$	$20$	$10$	$1.652$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓	✓	28.4.f.a	$4$	$0$	$0$	$0$	$-6$	$0$		$2^{24}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{10}q^{3}-\beta _{14}q^{4}+\cdots$
28.5.b.a	$28$	$5$	28.b	7.b	$2$	$2$	$2$	$2.894$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	28.5.b.a	$2$	$0$	$0$	$0$	$0$	$-14$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}-3\beta q^{5}+(-7\beta-7)q^{7}+\cdots$
28.5.c.a	$28$	$5$	28.c	4.b	$2$	$12$	$12$	$2.894$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓	✓	28.5.c.a	$2$	$0$	$3$	$0$	$24$	$0$		$2^{20}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-3+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots$
28.5.g.a	$28$	$5$	28.g	28.g	$6$	$28$	$14$	$2.894$		None		✓	✓	✓	28.5.g.a	$4$	$0$	$2$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
28.5.h.a	$28$	$5$	28.h	7.d	$6$	$6$	$3$	$2.894$	6.0.11337408.1	None		✓	✓	✓	28.5.h.a	$2$	$0$	$0$	$9$	$-27$	$66$		$2^{2}\cdot 3^{3}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-\beta _{1}+\beta _{3})q^{3}+(-3-3\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
28.6.a.a	$28$	$6$	28.a	1.a	$1$	$1$	$1$	$4.491$	$\Q$	None	✓	✓	✓	✓	28.6.a.a	$1$	$1$	$0$	$-2$	$-96$	$49$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-96q^{5}+7^{2}q^{7}-239q^{9}+\cdots$
28.6.a.b	$28$	$6$	28.a	1.a	$1$	$1$	$1$	$4.491$	$\Q$	None	✓	✓	✓	✓	28.6.a.b	$1$	$0$	$0$	$26$	$16$	$-49$	$-$	$1$	$\mathrm{SU}(2)$	$q+26q^{3}+2^{4}q^{5}-7^{2}q^{7}+433q^{9}+\cdots$
28.6.d.a	$28$	$6$	28.d	28.d	$2$	$2$	$2$	$4.491$	$\Q(\sqrt{-7}) $	$\Q(\sqrt{-7}) $		✓			28.6.d.a	$4$	$0$	$-11$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-5-\beta )q^{2}+(23+11\beta )q^{4}+(7^{2}+\cdots)q^{7}+\cdots$
28.6.d.b	$28$	$6$	28.d	28.d	$2$	$16$	$16$	$4.491$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓		28.6.d.b	$4$	$0$	$8$	$0$	$0$	$0$		$2^{46}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{3})q^{2}-\beta _{2}q^{3}+(-3-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$
28.6.e.a	$28$	$6$	28.e	7.c	$3$	$2$	$1$	$4.491$	$\Q(\sqrt{-3}) $	None		✓			28.6.e.a	$2$	$0$	$0$	$19$	$-19$	$-140$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+19\zeta_{6}q^{3}+(-19+19\zeta_{6})q^{5}+(-133+\cdots)q^{7}+\cdots$
28.6.e.b	$28$	$6$	28.e	7.c	$3$	$4$	$2$	$4.491$	$\Q(\sqrt{-3}, \sqrt{109})$	None		✓	✓		28.6.e.b	$2$	$0$	$0$	$-28$	$-42$	$112$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-14+14\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-21\beta _{1}+\cdots)q^{5}+\cdots$
28.6.f.a	$28$	$6$	28.f	28.f	$6$	$36$	$18$	$4.491$		None		✓	✓	✓	28.6.f.a	$4$	$0$	$0$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{6}]$
28.7.b.a	$28$	$7$	28.b	7.b	$2$	$4$	$4$	$6.442$	4.0.903168.1	None		✓	✓	✓	28.7.b.a	$2$	$0$	$0$	$0$	$0$	$-28$		$2^{7}\cdot 3\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+\beta _{1}q^{5}+(-7-\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots$
28.7.c.a	$28$	$7$	28.c	4.b	$2$	$18$	$18$	$6.442$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		✓	✓	✓	28.7.c.a	$2$	$0$	$-5$	$0$	$-44$	$0$		$2^{48}\cdot 7^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(\beta _{3}-\beta _{4})q^{3}+(10-\beta _{1})q^{4}+\cdots$
28.7.g.a	$28$	$7$	28.g	28.g	$6$	$44$	$22$	$6.442$		None		✓	✓	✓	28.7.g.a	$4$	$0$	$-6$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
28.7.h.a	$28$	$7$	28.h	7.d	$6$	$8$	$4$	$6.442$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓	✓	✓	28.7.h.a	$2$	$0$	$0$	$0$	$168$	$-452$		$2^{8}\cdot 3^{4}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{3}+(28-14\beta _{1}-\beta _{5})q^{5}+(-11^{2}+\cdots)q^{7}+\cdots$
28.8.a.a	$28$	$8$	28.a	1.a	$1$	$2$	$2$	$8.747$	$\Q(\sqrt{3529}) $	None	✓	✓	✓	✓	28.8.a.a	$1$	$0$	$0$	$-14$	$42$	$686$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-7-\beta )q^{3}+(21-3\beta )q^{5}+7^{3}q^{7}+\cdots$
28.8.a.b	$28$	$8$	28.a	1.a	$1$	$2$	$2$	$8.747$	$\Q(\sqrt{1009}) $	None	✓	✓	✓	✓	28.8.a.b	$1$	$1$	$0$	$14$	$-294$	$-686$	$-$	$2$	$\mathrm{SU}(2)$	$q+(7-\beta )q^{3}+(-147+11\beta )q^{5}-7^{3}q^{7}+\cdots$
28.8.d.a	$28$	$8$	28.d	28.d	$2$	$2$	$2$	$8.747$	$\Q(\sqrt{-7}) $	$\Q(\sqrt{-7}) $		✓			28.8.d.a	$4$	$0$	$13$	$0$	$0$	$0$		$7$	$\mathrm{U}(1)[D_{2}]$	$q+(7+\beta )q^{2}+(-37+13\beta )q^{4}+(7^{2}+\cdots)q^{7}+\cdots$
28.8.d.b	$28$	$8$	28.d	28.d	$2$	$24$	$24$	$8.747$		None		✓	✓		28.8.d.b	$4$	$0$	$-8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
28.8.e.a	$28$	$8$	28.e	7.c	$3$	$10$	$5$	$8.747$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		✓	✓	✓	28.8.e.a	$2$	$0$	$0$	$27$	$249$	$332$		$2^{18}\cdot 3^{4}\cdot 7^{5}$	$\mathrm{SU}(2)[C_{3}]$	$q+(5-5\beta _{1}+\beta _{3}-\beta _{5})q^{3}+(7^{2}\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
28.8.f.a	$28$	$8$	28.f	28.f	$6$	$52$	$26$	$8.747$		None		✓	✓	✓	28.8.f.a	$4$	$0$	$-8$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{6}]$
28.9.b.a	$28$	$9$	28.b	7.b	$2$	$6$	$6$	$11.407$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		✓	✓	✓	28.9.b.a	$2$	$0$	$0$	$0$	$0$	$2166$		$2^{12}\cdot 3^{2}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(-3\beta _{1}-\beta _{2})q^{5}+(19^{2}-\beta _{1}+\cdots)q^{7}+\cdots$
28.9.c.a	$28$	$9$	28.c	4.b	$2$	$24$	$24$	$11.407$		None		✓	✓	✓	28.9.c.a	$2$	$0$	$3$	$0$	$-336$	$0$			$\mathrm{SU}(2)[C_{2}]$
28.9.g.a	$28$	$9$	28.g	28.g	$6$	$60$	$30$	$11.407$		None		✓	✓	✓	28.9.g.a	$4$	$0$	$2$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
28.9.h.a	$28$	$9$	28.h	7.d	$6$	$10$	$5$	$11.407$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		✓	✓	✓	28.9.h.a	$2$	$0$	$0$	$-81$	$-837$	$1526$		$2^{12}\cdot 3^{6}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-11+5\beta _{1}+\beta _{3})q^{3}+(-57-55\beta _{1}+\cdots)q^{5}+\cdots$
28.10.a.a	$28$	$10$	28.a	1.a	$1$	$2$	$2$	$14.421$	$\Q(\sqrt{4561}) $	None	✓	✓	✓	✓	28.10.a.a	$1$	$1$	$0$	$-224$	$1596$	$4802$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-112-\beta )q^{3}+(798+9\beta )q^{5}+7^{4}q^{7}+\cdots$
28.10.a.b	$28$	$10$	28.a	1.a	$1$	$2$	$2$	$14.421$	$\Q(\sqrt{11209}) $	None	✓	✓	✓	✓	28.10.a.b	$1$	$0$	$0$	$-70$	$1554$	$-4802$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-35-\beta )q^{3}+(777-19\beta )q^{5}-7^{4}q^{7}+\cdots$
28.10.d.a	$28$	$10$	28.d	28.d	$2$	$2$	$2$	$14.421$	$\Q(\sqrt{-7}) $	$\Q(\sqrt{-7}) $		✓			28.10.d.a	$4$	$0$	$5$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-6+17\beta )q^{2}+(-542+85\beta )q^{4}+\cdots$
28.10.d.b	$28$	$10$	28.d	28.d	$2$	$32$	$32$	$14.421$		None		✓	✓		28.10.d.b	$4$	$0$	$-24$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
28.10.e.a	$28$	$10$	28.e	7.c	$3$	$12$	$6$	$14.421$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓	✓	28.10.e.a	$2$	$0$	$0$	$0$	$-966$	$7696$		$2^{28}\cdot 3^{4}\cdot 7^{7}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{3}+\beta _{4})q^{3}+(-161+161\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
28.10.f.a	$28$	$10$	28.f	28.f	$6$	$68$	$34$	$14.421$		None		✓	✓	✓	28.10.f.a	$4$	$0$	$16$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{6}]$
28.11.b.a	$28$	$11$	28.b	7.b	$2$	$6$	$6$	$17.790$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		✓	✓	✓	28.11.b.a	$2$	$0$	$0$	$0$	$0$	$-15666$		$2^{19}\cdot 3^{2}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-5\beta _{1}-\beta _{2})q^{5}+(-2611+\cdots)q^{7}+\cdots$
28.11.c.a	$28$	$11$	28.c	4.b	$2$	$30$	$30$	$17.790$		None		✓	✓	✓	28.11.c.a	$2$	$0$	$11$	$0$	$3116$	$0$			$\mathrm{SU}(2)[C_{2}]$
28.11.g.a	$28$	$11$	28.g	28.g	$6$	$76$	$38$	$17.790$		None		✓	✓	✓	28.11.g.a	$4$	$0$	$10$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
28.11.h.a	$28$	$11$	28.h	7.d	$6$	$14$	$7$	$17.790$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		✓	✓	✓	28.11.h.a	$2$	$0$	$0$	$-243$	$3333$	$-8810$		$2^{30}\cdot 3^{13}\cdot 7^{10}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-23+12\beta _{1}-\beta _{2})q^{3}+(160+158\beta _{1}+\cdots)q^{5}+\cdots$
28.12.a.a	$28$	$12$	28.a	1.a	$1$	$3$	$3$	$21.514$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	28.12.a.a	$1$	$1$	$0$	$-100$	$4762$	$-50421$	$-$	$2^{5}\cdot 7$	$\mathrm{SU}(2)$	$q+(-33-\beta _{1})q^{3}+(1585+7\beta _{1}-\beta _{2})q^{5}+\cdots$
28.12.a.b	$28$	$12$	28.a	1.a	$1$	$3$	$3$	$21.514$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	28.12.a.b	$1$	$0$	$0$	$1132$	$4986$	$50421$	$+$	$2^{4}\cdot 3\cdot 7$	$\mathrm{SU}(2)$	$q+(377-\beta _{1})q^{3}+(1662+\beta _{2})q^{5}+7^{5}q^{7}+\cdots$

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 143 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.