LMFDB - Newform search results

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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

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Results (1-50 of 256 matches)

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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
72.1.p.a	$72$	$1$	72.p	72.p	$6$	$2$	$1$	$0.036$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		✓	✓	✓	72.1.p.a	$4$	$0$	$-1$	$-1$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots$
72.2.a.a	$72$	$2$	72.a	1.a	$1$	$1$	$1$	$0.575$	$\Q$	$_{}$	None	None	✓		✓	✓	24.2.a.a	$1$	$0$	$0$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{11}-2q^{13}-2q^{17}-4q^{19}+\cdots$
72.2.d.a	$72$	$2$	72.d	8.b	$2$	$2$	$2$	$0.575$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-6}) $	None		✓			72.2.d.a	$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}-2q^{4}+2\beta q^{5}+2q^{7}-2\beta q^{8}+\cdots$
72.2.d.b	$72$	$2$	72.d	8.b	$2$	$2$	$2$	$0.575$	$\Q(\sqrt{-1}) $	$_{}$	None	None					24.2.d.a	$2$	$0$	$2$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(i+1)q^{2}+2 i q^{4}-2 i q^{5}-2 q^{7}+\cdots$
72.2.f.a	$72$	$2$	72.f	24.f	$2$	$4$	$4$	$0.575$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		✓	✓	✓	72.2.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+(-2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
72.2.i.a	$72$	$2$	72.i	9.c	$3$	$2$	$1$	$0.575$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			72.2.i.a	$2$	$0$	$0$	$0$	$1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+3\zeta_{6}q^{7}+\cdots$
72.2.i.b	$72$	$2$	72.i	9.c	$3$	$4$	$2$	$0.575$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		✓	✓		72.2.i.b	$2$	$0$	$0$	$1$	$1$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots$
72.2.l.a	$72$	$2$	72.l	72.l	$6$	$4$	$2$	$0.575$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-2}) $	None		✓			72.2.l.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$
72.2.l.b	$72$	$2$	72.l	72.l	$6$	$16$	$8$	$0.575$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		72.2.l.b	$4$	$0$	$-3$	$-6$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{11}q^{2}+(-\beta _{3}+\beta _{6})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots$
72.2.n.a	$72$	$2$	72.n	72.n	$6$	$4$	$2$	$0.575$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			72.2.n.a	$4$	$0$	$-2$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots$
72.2.n.b	$72$	$2$	72.n	72.n	$6$	$16$	$8$	$0.575$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓		72.2.n.b	$4$	$0$	$1$	$0$	$0$	$6$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{6}q^{2}+(-\beta _{3}-\beta _{10})q^{3}+(\beta _{8}-\beta _{13}+\cdots)q^{4}+\cdots$
72.3.b.a	$72$	$3$	72.b	8.d	$2$	$1$	$1$	$1.962$	$\Q$	$_{}$	$\Q(\sqrt{-2}) $	None	✓				8.3.d.a	$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+4q^{4}+8q^{8}-14q^{11}+2^{4}q^{16}+\cdots$
72.3.b.b	$72$	$3$	72.b	8.d	$2$	$4$	$4$	$1.962$	$\Q(\sqrt{-9 +4 \sqrt{3}})$	$_{}$	None	None					24.3.b.a	$2$	$0$	$-2$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-2+\beta _{1}-\beta _{3})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
72.3.b.c	$72$	$3$	72.b	8.d	$2$	$4$	$4$	$1.962$	$\Q(\sqrt{-6}, \sqrt{10})$	$_{}$	None	None		✓			72.3.b.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}+2\beta _{3})q^{5}+\cdots$
72.3.e.a	$72$	$3$	72.e	3.b	$2$	$2$	$2$	$1.962$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓	✓	✓	72.3.e.a	$2$	$0$	$0$	$0$	$0$	$24$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+5\beta q^{5}+12q^{7}-4\beta q^{11}-8q^{13}+\cdots$
72.3.h.a	$72$	$3$	72.h	24.h	$2$	$8$	$8$	$1.962$	8.0.$\cdots$.2	$_{}$	None	None		✓	✓	✓	72.3.h.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(1+\beta _{5})q^{4}+(-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots$
72.3.j.a	$72$	$3$	72.j	72.j	$6$	$44$	$22$	$1.962$		$_{}$	None	None		✓	✓	✓	72.3.j.a	$4$	$0$	$-3$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{6}]$
72.3.m.a	$72$	$3$	72.m	9.d	$6$	$4$	$2$	$1.962$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		✓			72.3.m.a	$2$	$0$	$0$	$-12$	$6$	$-6$		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q-3q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}-3\beta _{2}+\cdots)q^{7}+\cdots$
72.3.m.b	$72$	$3$	72.m	9.d	$6$	$8$	$4$	$1.962$	8.0.$\cdots$.9	$_{}$	None	None		✓	✓		72.3.m.b	$2$	$0$	$0$	$10$	$-6$	$6$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{2}+\beta _{3})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
72.3.p.a	$72$	$3$	72.p	72.p	$6$	$4$	$2$	$1.962$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-2}) $	None		✓			72.3.p.a	$4$	$0$	$4$	$2$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{6}]$	$q+2\beta _{2}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-4+\cdots)q^{4}+\cdots$
72.3.p.b	$72$	$3$	72.p	72.p	$6$	$40$	$20$	$1.962$		$_{}$	None	None		✓	✓		72.3.p.b	$4$	$0$	$-5$	$-6$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
72.4.a.a	$72$	$4$	72.a	1.a	$1$	$1$	$1$	$4.248$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	72.4.a.a	$1$	$1$	$0$	$0$	$-16$	$-12$	$-$	$1$	$\mathrm{SU}(2)$	$q-2^{4}q^{5}-12q^{7}-2^{6}q^{11}+58q^{13}+\cdots$
72.4.a.b	$72$	$4$	72.a	1.a	$1$	$1$	$1$	$4.248$	$\Q$	$_{}$	None	None	✓		✓	✓	24.4.a.a	$1$	$1$	$0$	$0$	$-14$	$-24$	$-$	$1$	$\mathrm{SU}(2)$	$q-14q^{5}-24q^{7}+28q^{11}-74q^{13}+\cdots$
72.4.a.c	$72$	$4$	72.a	1.a	$1$	$1$	$1$	$4.248$	$\Q$	$_{}$	None	None	✓		✓	✓	8.4.a.a	$1$	$0$	$0$	$0$	$2$	$24$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+24q^{7}+44q^{11}+22q^{13}+\cdots$
72.4.a.d	$72$	$4$	72.a	1.a	$1$	$1$	$1$	$4.248$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	72.4.a.a	$1$	$0$	$0$	$0$	$16$	$-12$	$+$	$1$	$\mathrm{SU}(2)$	$q+2^{4}q^{5}-12q^{7}+2^{6}q^{11}+58q^{13}+\cdots$
72.4.d.a	$72$	$4$	72.d	8.b	$2$	$2$	$2$	$4.248$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-6}) $	None		✓			72.4.d.a	$4$	$0$	$0$	$0$	$0$	$-68$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}-8q^{4}-7\beta q^{5}-34q^{7}-8\beta q^{8}+\cdots$
72.4.d.b	$72$	$4$	72.d	8.b	$2$	$2$	$2$	$4.248$	$\Q(\sqrt{-7}) $	$_{}$	None	None					8.4.b.a	$2$	$0$	$2$	$0$	$0$	$-16$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta )q^{2}+(-6+2\beta )q^{4}+4\beta q^{5}+\cdots$
72.4.d.c	$72$	$4$	72.d	8.b	$2$	$4$	$4$	$4.248$	$\Q(\sqrt{-10}, \sqrt{22})$	$_{}$	None	None		✓			72.4.d.c	$4$	$0$	$0$	$0$	$0$	$40$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(3+\beta _{3})q^{4}+(\beta _{1}+\beta _{2})q^{5}+\cdots$
72.4.d.d	$72$	$4$	72.d	8.b	$2$	$6$	$6$	$4.248$	6.0.8248384.1	$_{}$	None	None			✓		24.4.d.a	$2$	$0$	$-2$	$0$	$0$	$28$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(3+\beta _{5})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
72.4.f.a	$72$	$4$	72.f	24.f	$2$	$12$	$12$	$4.248$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓	✓	72.4.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{15}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(-1+\beta _{6})q^{4}-\beta _{5}q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots$
72.4.i.a	$72$	$4$	72.i	9.c	$3$	$8$	$4$	$4.248$	8.0.5206055409.1	$_{}$	None	None		✓			72.4.i.a	$2$	$0$	$0$	$-3$	$-5$	$3$		$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{5}q^{3}+(2\beta _{1}-\beta _{2}+\beta _{4})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots$
72.4.i.b	$72$	$4$	72.i	9.c	$3$	$10$	$5$	$4.248$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		✓	✓		72.4.i.b	$2$	$0$	$0$	$4$	$-5$	$-3$		$2^{8}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{8})q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots$
72.4.l.a	$72$	$4$	72.l	72.l	$6$	$4$	$2$	$4.248$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-2}) $	None		✓			72.4.l.a	$4$	$0$	$0$	$-10$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+2\beta _{1}q^{2}+(-5+\beta _{1}+5\beta _{2})q^{3}+8\beta _{2}q^{4}+\cdots$
72.4.l.b	$72$	$4$	72.l	72.l	$6$	$64$	$32$	$4.248$		$_{}$	None	None		✓	✓		72.4.l.b	$4$	$0$	$-3$	$6$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
72.4.n.a	$72$	$4$	72.n	72.n	$6$	$68$	$34$	$4.248$		$_{}$	None	None		✓	✓	✓	72.4.n.a	$4$	$0$	$-1$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{6}]$
72.5.b.a	$72$	$5$	72.b	8.d	$2$	$1$	$1$	$7.443$	$\Q$	$_{}$	$\Q(\sqrt{-2}) $	None	✓				8.5.d.a	$2$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-4q^{2}+2^{4}q^{4}-2^{6}q^{8}+46q^{11}+\cdots$
72.5.b.b	$72$	$5$	72.b	8.d	$2$	$2$	$2$	$7.443$	$\Q(\sqrt{-15}) $	$_{}$	None	None					8.5.d.b	$2$	$0$	$2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta )q^{2}+(-14+2\beta )q^{4}-8\beta q^{5}+\cdots$
72.5.b.c	$72$	$5$	72.b	8.d	$2$	$8$	$8$	$7.443$	$\Q(\sqrt{2}, \sqrt{-15}, \sqrt{-39})$	$_{}$	None	None		✓			72.5.b.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{12}\cdot 3^{4}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(3-\beta _{4})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
72.5.b.d	$72$	$5$	72.b	8.d	$2$	$8$	$8$	$7.443$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None					24.5.b.a	$2$	$0$	$6$	$0$	$0$	$0$		$2^{12}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{2}+(1+\beta _{1}+\beta _{5})q^{4}+(3\beta _{1}+\cdots)q^{5}+\cdots$
72.5.e.a	$72$	$5$	72.e	3.b	$2$	$2$	$2$	$7.443$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			72.5.e.a	$2$	$0$	$0$	$0$	$0$	$-120$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+11\beta q^{5}-60q^{7}+44\beta q^{11}-176q^{13}+\cdots$
72.5.e.b	$72$	$5$	72.e	3.b	$2$	$2$	$2$	$7.443$	$\Q(\sqrt{-2}) $	$_{}$	None	None		✓			72.5.e.b	$2$	$0$	$0$	$0$	$0$	$72$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+5\beta q^{5}+6^{2}q^{7}+116\beta q^{11}+304q^{13}+\cdots$
72.5.h.a	$72$	$5$	72.h	24.h	$2$	$16$	$16$	$7.443$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓	✓	✓	72.5.h.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{28}\cdot 3^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2-\beta _{2})q^{4}+\beta _{5}q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots$
72.5.j.a	$72$	$5$	72.j	72.j	$6$	$92$	$46$	$7.443$		$_{}$	None	None		✓	✓	✓	72.5.j.a	$4$	$0$	$-3$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{6}]$
72.5.m.a	$72$	$5$	72.m	9.d	$6$	$24$	$12$	$7.443$		$_{}$	None	None		✓	✓	✓	72.5.m.a	$2$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
72.5.p.a	$72$	$5$	72.p	72.p	$6$	$4$	$2$	$7.443$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-2}) $	None		✓			72.5.p.a	$4$	$0$	$-8$	$14$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{6}]$	$q-4\beta _{2}q^{2}+(\beta _{1}+7\beta _{2}-\beta _{3})q^{3}+(-2^{4}+\cdots)q^{4}+\cdots$
72.5.p.b	$72$	$5$	72.p	72.p	$6$	$88$	$44$	$7.443$		$_{}$	None	None		✓	✓		72.5.p.b	$4$	$0$	$7$	$-18$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
72.6.a.a	$72$	$6$	72.a	1.a	$1$	$1$	$1$	$11.548$	$\Q$	$_{}$	None	None	✓				24.6.a.b	$1$	$0$	$0$	$0$	$-94$	$144$	$-$	$1$	$\mathrm{SU}(2)$	$q-94q^{5}+12^{2}q^{7}+380q^{11}+814q^{13}+\cdots$
72.6.a.b	$72$	$6$	72.a	1.a	$1$	$1$	$1$	$11.548$	$\Q$	$_{}$	None	None	✓				24.6.a.c	$1$	$1$	$0$	$0$	$-38$	$120$	$+$	$1$	$\mathrm{SU}(2)$	$q-38q^{5}+120q^{7}-524q^{11}-962q^{13}+\cdots$
72.6.a.c	$72$	$6$	72.a	1.a	$1$	$1$	$1$	$11.548$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	72.6.a.c	$1$	$1$	$0$	$0$	$-16$	$12$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{4}q^{5}+12q^{7}-448q^{11}-206q^{13}+\cdots$
72.6.a.d	$72$	$6$	72.a	1.a	$1$	$1$	$1$	$11.548$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	72.6.a.c	$1$	$0$	$0$	$0$	$16$	$12$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{4}q^{5}+12q^{7}+448q^{11}-206q^{13}+\cdots$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.