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 59 matches)

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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
1206.2.a.a	$1206$	$2$	1206.a	1.a	$1$	$1$	$1$	$9.630$	$\Q$	None	✓				402.2.a.d	$1$	$0$	$-1$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}+2q^{7}-q^{8}+2q^{10}+\cdots$
1206.2.a.b	$1206$	$2$	1206.a	1.a	$1$	$1$	$1$	$9.630$	$\Q$	None	✓	✓			1206.2.a.b	$1$	$1$	$-1$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
1206.2.a.c	$1206$	$2$	1206.a	1.a	$1$	$1$	$1$	$9.630$	$\Q$	None	✓				402.2.a.c	$1$	$1$	$1$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}-4q^{11}+\cdots$
1206.2.a.d	$1206$	$2$	1206.a	1.a	$1$	$1$	$1$	$9.630$	$\Q$	None	✓				402.2.a.a	$1$	$1$	$1$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-3q^{7}+q^{8}-q^{10}+\cdots$
1206.2.a.e	$1206$	$2$	1206.a	1.a	$1$	$1$	$1$	$9.630$	$\Q$	None	✓	✓			1206.2.a.b	$1$	$0$	$1$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots$
1206.2.a.f	$1206$	$2$	1206.a	1.a	$1$	$1$	$1$	$9.630$	$\Q$	None	✓				402.2.a.b	$1$	$0$	$1$	$0$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}-q^{7}+q^{8}+3q^{10}+\cdots$
1206.2.a.g	$1206$	$2$	1206.a	1.a	$1$	$2$	$2$	$9.630$	$\Q(\sqrt{6}) $	None	✓	✓	✓		1206.2.a.g	$1$	$1$	$-2$	$0$	$-4$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}+(2-\beta )q^{7}-q^{8}+\cdots$
1206.2.a.h	$1206$	$2$	1206.a	1.a	$1$	$2$	$2$	$9.630$	$\Q(\sqrt{41}) $	None	✓				402.2.a.f	$1$	$0$	$-2$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta q^{5}-\beta q^{7}-q^{8}+\beta q^{10}+\cdots$
1206.2.a.i	$1206$	$2$	1206.a	1.a	$1$	$2$	$2$	$9.630$	$\Q(\sqrt{17}) $	None	✓	✓	✓	✓	1206.2.a.i	$1$	$0$	$-2$	$0$	$3$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta )q^{5}+(-3+\beta )q^{7}+\cdots$
1206.2.a.j	$1206$	$2$	1206.a	1.a	$1$	$2$	$2$	$9.630$	$\Q(\sqrt{17}) $	None	✓	✓	✓	✓	1206.2.a.i	$1$	$1$	$2$	$0$	$-3$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta )q^{5}+(-3+\beta )q^{7}+\cdots$
1206.2.a.k	$1206$	$2$	1206.a	1.a	$1$	$2$	$2$	$9.630$	$\Q(\sqrt{3}) $	None	✓				402.2.a.e	$1$	$0$	$2$	$0$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2\beta q^{5}+(3-\beta )q^{7}+q^{8}+\cdots$
1206.2.a.l	$1206$	$2$	1206.a	1.a	$1$	$2$	$2$	$9.630$	$\Q(\sqrt{6}) $	None	✓	✓	✓		1206.2.a.g	$1$	$0$	$2$	$0$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+(2-\beta )q^{7}+q^{8}+\cdots$
1206.2.a.m	$1206$	$2$	1206.a	1.a	$1$	$3$	$3$	$9.630$	3.3.316.1	None	✓		✓	✓	402.2.a.g	$1$	$1$	$-3$	$0$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta _{2})q^{5}+\beta _{1}q^{7}+\cdots$
1206.2.a.n	$1206$	$2$	1206.a	1.a	$1$	$3$	$3$	$9.630$	$\Q(\zeta_{18})^+$	None	✓		✓		134.2.a.b	$1$	$0$	$-3$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1-2\beta _{1}+\beta _{2})q^{5}-2\beta _{2}q^{7}+\cdots$
1206.2.a.o	$1206$	$2$	1206.a	1.a	$1$	$3$	$3$	$9.630$	3.3.473.1	None	✓		✓		134.2.a.a	$1$	$0$	$3$	$0$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{1})q^{5}-2\beta _{1}q^{7}+\cdots$
1206.2.d.a	$1206$	$2$	1206.d	201.d	$2$	$2$	$2$	$9.630$	$\Q(\sqrt{-2}) $	None		✓			1206.2.d.a	$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}-3\beta q^{7}-q^{8}-3\beta q^{13}+\cdots$
1206.2.d.b	$1206$	$2$	1206.d	201.d	$2$	$2$	$2$	$9.630$	$\Q(\sqrt{-2}) $	None		✓			1206.2.d.a	$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+3\beta q^{7}+q^{8}+3\beta q^{13}+\cdots$
1206.2.d.c	$1206$	$2$	1206.d	201.d	$2$	$8$	$8$	$9.630$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓			1206.2.d.c	$2$	$0$	$-8$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+\beta _{2}q^{5}+\beta _{1}q^{7}-q^{8}+\cdots$
1206.2.d.d	$1206$	$2$	1206.d	201.d	$2$	$8$	$8$	$9.630$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓			1206.2.d.c	$2$	$0$	$8$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}-\beta _{2}q^{5}-\beta _{1}q^{7}+q^{8}+\cdots$
1206.2.h.a	$1206$	$2$	1206.h	67.c	$3$	$2$	$1$	$9.630$	$\Q(\sqrt{-3}) $	None					134.2.c.a	$2$	$0$	$1$	$0$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-2q^{5}+4\zeta_{6}q^{7}+\cdots$
1206.2.h.b	$1206$	$2$	1206.h	67.c	$3$	$4$	$2$	$9.630$	$\Q(\sqrt{-3}, \sqrt{5})$	None					134.2.c.c	$2$	$0$	$-2$	$0$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{3})q^{2}+\beta _{3}q^{4}+(-1-2\beta _{2}+\cdots)q^{5}+\cdots$
1206.2.h.c	$1206$	$2$	1206.h	67.c	$3$	$4$	$2$	$9.630$	$\Q(\sqrt{-3}, \sqrt{-7})$	None					134.2.c.b	$2$	$0$	$2$	$0$	$4$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1-\beta _{1})q^{4}+q^{5}-\beta _{3}q^{7}+\cdots$
1206.2.h.d	$1206$	$2$	1206.h	67.c	$3$	$6$	$3$	$9.630$	6.0.18825075.4	None					402.2.e.d	$2$	$0$	$-3$	$0$	$-4$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{1})q^{2}+\beta _{1}q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots$
1206.2.h.e	$1206$	$2$	1206.h	67.c	$3$	$6$	$3$	$9.630$	6.0.309123.1	None					402.2.e.c	$2$	$0$	$-3$	$0$	$4$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{4})q^{2}-\beta _{4}q^{4}+(1+\beta _{1})q^{5}+\cdots$
1206.2.h.f	$1206$	$2$	1206.h	67.c	$3$	$6$	$3$	$9.630$	6.0.48843675.1	None					402.2.e.b	$2$	$0$	$3$	$0$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{4})q^{2}-\beta _{4}q^{4}+\beta _{2}q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots$
1206.2.h.g	$1206$	$2$	1206.h	67.c	$3$	$6$	$3$	$9.630$	6.0.16638075.1	None					402.2.e.a	$2$	$0$	$3$	$0$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{4})q^{2}+\beta _{4}q^{4}+(\beta _{2}+\beta _{3})q^{5}+\cdots$
1206.2.h.h	$1206$	$2$	1206.h	67.c	$3$	$12$	$6$	$9.630$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓			1206.2.h.h	$2$	$0$	$-6$	$0$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{3})q^{2}-\beta _{3}q^{4}-\beta _{9}q^{5}-\beta _{6}q^{7}+\cdots$
1206.2.h.i	$1206$	$2$	1206.h	67.c	$3$	$12$	$6$	$9.630$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓			1206.2.h.h	$2$	$0$	$6$	$0$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+(-1+\beta _{3})q^{4}+\beta _{9}q^{5}+\beta _{1}q^{7}+\cdots$
1206.2.t.a	$1206$	$2$	1206.t	201.f	$6$	$24$	$12$	$9.630$		None		✓			1206.2.t.a	$2$	$0$	$-12$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
1206.2.t.b	$1206$	$2$	1206.t	201.f	$6$	$24$	$12$	$9.630$		None		✓			1206.2.t.a	$2$	$0$	$12$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
1206.3.b.a	$1206$	$3$	1206.b	67.b	$2$	$10$	$10$	$32.861$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None					134.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-2q^{4}+\beta _{5}q^{5}+(\beta _{2}-\beta _{8}+\cdots)q^{7}+\cdots$
1206.3.b.b	$1206$	$3$	1206.b	67.b	$2$	$24$	$24$	$32.861$		None					402.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1206.3.b.c	$1206$	$3$	1206.b	67.b	$2$	$24$	$24$	$32.861$		None		✓			1206.3.b.c	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1206.3.c.a	$1206$	$3$	1206.c	3.b	$2$	$20$	$20$	$32.861$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓			1206.3.c.a	$2$	$0$	$0$	$0$	$0$	$24$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{11}q^{2}-2q^{4}+(\beta _{1}-\beta _{11})q^{5}+(1+\cdots)q^{7}+\cdots$
1206.3.c.b	$1206$	$3$	1206.c	3.b	$2$	$24$	$24$	$32.861$		None		✓	✓		1206.3.c.b	$2$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$
1206.3.i.a	$1206$	$3$	1206.i	201.g	$6$	$44$	$22$	$32.861$		None		✓			1206.3.i.a	$4$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{6}]$
1206.3.i.b	$1206$	$3$	1206.i	201.g	$6$	$44$	$22$	$32.861$		None		✓			1206.3.i.b	$4$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{6}]$
1206.4.a.a	$1206$	$4$	1206.a	1.a	$1$	$1$	$1$	$71.156$	$\Q$	None	✓				134.4.a.a	$1$	$2$	$-2$	$0$	$-6$	$-34$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}-6q^{5}-34q^{7}-8q^{8}+\cdots$
1206.4.a.b	$1206$	$4$	1206.a	1.a	$1$	$1$	$1$	$71.156$	$\Q$	None	✓				402.4.a.a	$1$	$0$	$2$	$0$	$-14$	$20$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}-14q^{5}+20q^{7}+8q^{8}+\cdots$
1206.4.a.c	$1206$	$4$	1206.a	1.a	$1$	$2$	$2$	$71.156$	$\Q(\sqrt{37}) $	None	✓				134.4.a.b	$1$	$1$	$-4$	$0$	$6$	$-21$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(1+4\beta )q^{5}+(-12+\cdots)q^{7}+\cdots$
1206.4.a.d	$1206$	$4$	1206.a	1.a	$1$	$2$	$2$	$71.156$	$\Q(\sqrt{2}) $	None	✓				402.4.a.b	$1$	$0$	$-4$	$0$	$18$	$-26$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(9+\beta )q^{5}+(-13-4\beta )q^{7}+\cdots$
1206.4.a.e	$1206$	$4$	1206.a	1.a	$1$	$3$	$3$	$71.156$	3.3.3132.1	None	✓				402.4.a.e	$1$	$1$	$-6$	$0$	$12$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(4-\beta _{1}+\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots$
1206.4.a.f	$1206$	$4$	1206.a	1.a	$1$	$3$	$3$	$71.156$	3.3.44852.1	None	✓				402.4.a.d	$1$	$1$	$6$	$0$	$3$	$-21$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(2-\beta _{1}+2\beta _{2})q^{5}+\cdots$
1206.4.a.g	$1206$	$4$	1206.a	1.a	$1$	$3$	$3$	$71.156$	3.3.469.1	None	✓				134.4.a.c	$1$	$1$	$6$	$0$	$6$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(2+\beta _{1}+\beta _{2})q^{5}+(2+\cdots)q^{7}+\cdots$
1206.4.a.h	$1206$	$4$	1206.a	1.a	$1$	$3$	$3$	$71.156$	3.3.868440.1	None	✓				402.4.a.c	$1$	$0$	$6$	$0$	$22$	$22$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(7+\beta _{1})q^{5}+(7+\beta _{1}+\cdots)q^{7}+\cdots$
1206.4.a.i	$1206$	$4$	1206.a	1.a	$1$	$4$	$4$	$71.156$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓		✓		402.4.a.g	$1$	$1$	$8$	$0$	$-12$	$-8$	$-$	$3$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(-3-\beta _{1})q^{5}+(-3+\cdots)q^{7}+\cdots$
1206.4.a.j	$1206$	$4$	1206.a	1.a	$1$	$4$	$4$	$71.156$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓				402.4.a.f	$1$	$0$	$8$	$0$	$13$	$-15$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(3-\beta _{2})q^{5}+(-5+2\beta _{1}+\cdots)q^{7}+\cdots$
1206.4.a.k	$1206$	$4$	1206.a	1.a	$1$	$5$	$5$	$71.156$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓				134.4.a.d	$1$	$0$	$-10$	$0$	$-3$	$69$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(\beta _{3}-\beta _{4})q^{5}+(14-\beta _{4})q^{7}+\cdots$
1206.4.a.l	$1206$	$4$	1206.a	1.a	$1$	$6$	$6$	$71.156$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓		✓		402.4.a.i	$1$	$1$	$-12$	$0$	$-27$	$37$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(-4+\beta _{2})q^{5}+(6-\beta _{5})q^{7}+\cdots$
1206.4.a.m	$1206$	$4$	1206.a	1.a	$1$	$6$	$6$	$71.156$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓		✓		402.4.a.h	$1$	$0$	$-12$	$0$	$-3$	$1$	$+$	$2$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(-1+\beta _{1})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$

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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.