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 129 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
169.2.a.a	$169$	$2$	169.a	1.a	$1$	$2$	$2$	$1.349$	$\Q(\sqrt{3}) $	None	✓				13.2.e.a	$2$	$0$	$0$	$4$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+2q^{3}+q^{4}-\beta q^{5}+2\beta q^{6}+\cdots$
169.2.a.b	$169$	$2$	169.a	1.a	$1$	$3$	$3$	$1.349$	$\Q(\zeta_{14})^+$	None	✓	✓	✓	✓	169.2.a.b	$1$	$1$	$-2$	$-2$	$-4$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
169.2.a.c	$169$	$2$	169.a	1.a	$1$	$3$	$3$	$1.349$	$\Q(\zeta_{14})^+$	None	✓	✓	✓		169.2.a.b	$1$	$0$	$2$	$-2$	$4$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots$
169.2.b.a	$169$	$2$	169.b	13.b	$2$	$2$	$2$	$1.349$	$\Q(\sqrt{-3}) $	None					13.2.e.a	$2$	$0$	$0$	$4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{2}+2 q^{3}-q^{4}+\beta q^{5}-2\beta q^{6}+\cdots$
169.2.b.b	$169$	$2$	169.b	13.b	$2$	$6$	$6$	$1.349$	6.0.153664.1	None		✓	✓		169.2.a.b	$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{3}+\beta _{5})q^{2}+(-1+\beta _{4})q^{3}+(1-2\beta _{2}+\cdots)q^{4}+\cdots$
169.2.c.a	$169$	$2$	169.c	13.c	$3$	$4$	$2$	$1.349$	$\Q(\zeta_{12})$	None					13.2.e.a	$4$	$0$	$0$	$-4$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_{2} q^{2}-2\beta_1 q^{3}+(\beta_1-1)q^{4}+\cdots$
169.2.c.b	$169$	$2$	169.c	13.c	$3$	$6$	$3$	$1.349$	6.0.64827.1	None		✓			169.2.a.b	$2$	$0$	$-2$	$2$	$8$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{4}+\beta _{5})q^{2}+(1-\beta _{1}-\beta _{5})q^{3}+\cdots$
169.2.c.c	$169$	$2$	169.c	13.c	$3$	$6$	$3$	$1.349$	6.0.64827.1	None		✓			169.2.a.b	$2$	$0$	$2$	$2$	$-8$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{4})q^{2}+(1-\beta _{4}-\beta _{5})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots$
169.2.e.a	$169$	$2$	169.e	13.e	$6$	$2$	$1$	$1.349$	$\Q(\sqrt{-3}) $	None					13.2.e.a	$2$	$0$	$3$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
169.2.e.b	$169$	$2$	169.e	13.e	$6$	$12$	$6$	$1.349$	12.0.$\cdots$.1	None		✓	✓		169.2.a.b	$4$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}+\beta _{8}+\beta _{10})q^{2}+(1-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots$
169.2.g.a	$169$	$2$	169.g	169.g	$13$	$156$	$13$	$1.349$		None		✓	✓	✓	169.2.g.a	$2$	$0$	$-10$	$-9$	$-7$	$-5$			$\mathrm{SU}(2)[C_{13}]$
169.2.h.a	$169$	$2$	169.h	169.h	$26$	$168$	$14$	$1.349$		None		✓	✓	✓	169.2.h.a	$2$	$0$	$-13$	$-13$	$-13$	$-13$			$\mathrm{SU}(2)[C_{26}]$
169.2.i.a	$169$	$2$	169.i	169.i	$39$	$336$	$14$	$1.349$		None		✓	✓	✓	169.2.i.a	$2$	$0$	$-26$	$-26$	$-26$	$-26$			$\mathrm{SU}(2)[C_{39}]$
169.2.k.a	$169$	$2$	169.k	169.k	$78$	$360$	$15$	$1.349$		None		✓	✓	✓	169.2.k.a	$2$	$0$	$-23$	$-24$	$-26$	$-26$			$\mathrm{SU}(2)[C_{78}]$
169.3.d.a	$169$	$3$	169.d	13.d	$4$	$4$	$2$	$4.605$	$\Q(\zeta_{12})$	None					13.3.f.a	$2$	$0$	$-2$	$4$	$-14$	$4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta_{3} q^{2}+(-\beta_{3}+\beta_{2}-\beta_1+1)q^{3}+\cdots$
169.3.d.b	$169$	$3$	169.d	13.d	$4$	$4$	$2$	$4.605$	$\Q(i, \sqrt{22})$	None		✓			169.3.d.b	$4$	$0$	$0$	$-12$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}-3q^{3}+7\beta _{2}q^{4}-\beta _{1}q^{5}+\cdots$
169.3.d.c	$169$	$3$	169.d	13.d	$4$	$4$	$2$	$4.605$	$\Q(\zeta_{12})$	None					13.3.f.a	$2$	$0$	$2$	$4$	$14$	$-4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta_{2}-\beta_1+1)q^{2}+(-\beta_{3}+\beta_{2}-\beta_1+1)q^{3}+\cdots$
169.3.d.d	$169$	$3$	169.d	13.d	$4$	$4$	$2$	$4.605$	$\Q(i, \sqrt{10})$	None					13.3.d.a	$2$	$0$	$4$	$-4$	$-8$	$12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{1}-\beta _{3})q^{3}+\cdots$
169.3.d.e	$169$	$3$	169.d	13.d	$4$	$24$	$12$	$4.605$		None		✓	✓		169.3.d.e	$4$	$0$	$0$	$12$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
169.3.f.a	$169$	$3$	169.f	13.f	$12$	$4$	$1$	$4.605$	$\Q(\zeta_{12})$	None					13.3.f.a	$2$	$0$	$-4$	$-2$	$14$	$20$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-1-\zeta_{12})q^{2}+(-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots$
169.3.f.b	$169$	$3$	169.f	13.f	$12$	$4$	$1$	$4.605$	$\Q(\zeta_{12})$	None					13.3.f.a	$2$	$0$	$2$	$-2$	$14$	$-16$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(1-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots$
169.3.f.c	$169$	$3$	169.f	13.f	$12$	$4$	$1$	$4.605$	$\Q(\zeta_{12})$	None					13.3.f.a	$2$	$0$	$4$	$-2$	$-14$	$-20$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(1+\zeta_{12})q^{2}+(-\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots$
169.3.f.d	$169$	$3$	169.f	13.f	$12$	$8$	$2$	$4.605$	8.0.3317760000.2	None					13.3.d.a	$4$	$0$	$-4$	$4$	$-16$	$-12$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-1-\beta _{2}-\beta _{3}+\beta _{4}+\beta _{7})q^{2}+(1+\cdots)q^{3}+\cdots$
169.3.f.e	$169$	$3$	169.f	13.f	$12$	$8$	$2$	$4.605$	8.0.$\cdots$.9	None		✓			169.3.d.b	$8$	$0$	$0$	$12$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\beta _{1}q^{2}+3\beta _{4}q^{3}+7\beta _{2}q^{4}+(\beta _{1}-\beta _{5}+\cdots)q^{5}+\cdots$
169.3.f.f	$169$	$3$	169.f	13.f	$12$	$8$	$2$	$4.605$	8.0.3317760000.2	None					13.3.d.a	$4$	$0$	$4$	$4$	$16$	$12$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(1+\beta _{2}-\beta _{3}-\beta _{4}+\beta _{7})q^{2}+(1+\beta _{3}+\cdots)q^{3}+\cdots$
169.3.f.g	$169$	$3$	169.f	13.f	$12$	$48$	$12$	$4.605$		None		✓	✓		169.3.d.e	$8$	$0$	$0$	$-12$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
169.3.j.a	$169$	$3$	169.j	169.j	$52$	$720$	$30$	$4.605$		None		✓	✓	✓	169.3.j.a	$2$	$0$	$-22$	$-22$	$-34$	$-14$			$\mathrm{SU}(2)[C_{52}]$
169.3.l.a	$169$	$3$	169.l	169.l	$156$	$1392$	$29$	$4.605$		None		✓	✓	✓	169.3.l.a	$2$	$0$	$-50$	$-50$	$-38$	$-68$			$\mathrm{SU}(2)[C_{156}]$
169.4.a.a	$169$	$4$	169.a	1.a	$1$	$1$	$1$	$9.971$	$\Q$	None	✓				13.4.c.a	$1$	$0$	$-4$	$2$	$-17$	$-20$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+2q^{3}+8q^{4}-17q^{5}-8q^{6}+\cdots$
169.4.a.b	$169$	$4$	169.a	1.a	$1$	$1$	$1$	$9.971$	$\Q$	None	✓				13.4.b.a	$1$	$1$	$-3$	$-1$	$9$	$-15$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{2}-q^{3}+q^{4}+9q^{5}+3q^{6}-15q^{7}+\cdots$
169.4.a.c	$169$	$4$	169.a	1.a	$1$	$1$	$1$	$9.971$	$\Q$	None	✓				13.4.b.a	$1$	$1$	$3$	$-1$	$-9$	$15$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}-q^{3}+q^{4}-9q^{5}-3q^{6}+15q^{7}+\cdots$
169.4.a.d	$169$	$4$	169.a	1.a	$1$	$1$	$1$	$9.971$	$\Q$	None	✓				13.4.c.a	$1$	$0$	$4$	$2$	$17$	$20$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}+2q^{3}+8q^{4}+17q^{5}+8q^{6}+\cdots$
169.4.a.e	$169$	$4$	169.a	1.a	$1$	$1$	$1$	$9.971$	$\Q$	None	✓				13.4.a.a	$1$	$0$	$5$	$-7$	$7$	$13$	$+$	$1$	$\mathrm{SU}(2)$	$q+5q^{2}-7q^{3}+17q^{4}+7q^{5}-35q^{6}+\cdots$
169.4.a.f	$169$	$4$	169.a	1.a	$1$	$2$	$2$	$9.971$	$\Q(\sqrt{17}) $	None	✓				13.4.c.b	$1$	$0$	$-5$	$5$	$-15$	$15$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta )q^{2}+(1+3\beta )q^{3}+5\beta q^{4}+\cdots$
169.4.a.g	$169$	$4$	169.a	1.a	$1$	$2$	$2$	$9.971$	$\Q(\sqrt{17}) $	None	✓				13.4.a.b	$1$	$0$	$-1$	$5$	$3$	$9$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(4-3\beta )q^{3}+(-4+\beta )q^{4}+\cdots$
169.4.a.h	$169$	$4$	169.a	1.a	$1$	$2$	$2$	$9.971$	$\Q(\sqrt{3}) $	None	✓				13.4.e.a	$2$	$1$	$0$	$-14$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{2}-7q^{3}+4q^{4}+8\beta q^{5}-14\beta q^{6}+\cdots$
169.4.a.i	$169$	$4$	169.a	1.a	$1$	$2$	$2$	$9.971$	$\Q(\sqrt{3}) $	None	✓				13.4.e.b	$2$	$1$	$0$	$4$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+2q^{3}-5q^{4}+\beta q^{5}+2\beta q^{6}+\cdots$
169.4.a.j	$169$	$4$	169.a	1.a	$1$	$2$	$2$	$9.971$	$\Q(\sqrt{17}) $	None	✓				13.4.c.b	$1$	$0$	$5$	$5$	$15$	$-15$	$+$	$1$	$\mathrm{SU}(2)$	$q+(3-\beta )q^{2}+(4-3\beta )q^{3}+(5-5\beta )q^{4}+\cdots$
169.4.a.k	$169$	$4$	169.a	1.a	$1$	$9$	$9$	$9.971$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓		169.4.a.k	$1$	$1$	$-5$	$1$	$-30$	$-38$	$-$	$13^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(5+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
169.4.a.l	$169$	$4$	169.a	1.a	$1$	$9$	$9$	$9.971$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓		169.4.a.k	$1$	$0$	$5$	$1$	$30$	$38$	$+$	$13^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+\beta _{2}q^{3}+(5+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
169.4.b.a	$169$	$4$	169.b	13.b	$2$	$2$	$2$	$9.971$	$\Q(\sqrt{-1}) $	None					13.4.a.a	$2$	$0$	$0$	$-14$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+5 i q^{2}-7 q^{3}-17 q^{4}+7 i q^{5}+\cdots$
169.4.b.b	$169$	$4$	169.b	13.b	$2$	$2$	$2$	$9.971$	$\Q(\sqrt{-3}) $	None					13.4.e.a	$2$	$0$	$0$	$-14$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-2\beta q^{2}-7 q^{3}-4 q^{4}-8\beta q^{5}+\cdots$
169.4.b.c	$169$	$4$	169.b	13.b	$2$	$2$	$2$	$9.971$	$\Q(\sqrt{-1}) $	None					13.4.c.a	$2$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+4 i q^{2}+2 q^{3}-8 q^{4}+17 i q^{5}+\cdots$
169.4.b.d	$169$	$4$	169.b	13.b	$2$	$2$	$2$	$9.971$	$\Q(\sqrt{-3}) $	None					13.4.e.b	$2$	$0$	$0$	$4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{2}+2 q^{3}+5 q^{4}-\beta q^{5}-2\beta q^{6}+\cdots$
169.4.b.e	$169$	$4$	169.b	13.b	$2$	$4$	$4$	$9.971$	$\Q(i, \sqrt{17})$	None					13.4.c.b	$2$	$0$	$0$	$10$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+3\beta _{2})q^{2}+(1+3\beta _{3})q^{3}-5\beta _{3}q^{4}+\cdots$
169.4.b.f	$169$	$4$	169.b	13.b	$2$	$4$	$4$	$9.971$	$\Q(i, \sqrt{17})$	None					13.4.a.b	$2$	$0$	$0$	$10$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(1+3\beta _{3})q^{3}+(3+\beta _{3})q^{4}+\cdots$
169.4.b.g	$169$	$4$	169.b	13.b	$2$	$18$	$18$	$9.971$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		✓	✓		169.4.a.k	$2$	$0$	$0$	$2$	$0$	$0$		$13^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{2}-\beta _{2}q^{3}+(-4+\beta _{1})q^{4}+(-\beta _{9}+\cdots)q^{5}+\cdots$
169.4.c.a	$169$	$4$	169.c	13.c	$3$	$2$	$1$	$9.971$	$\Q(\sqrt{-3}) $	None					13.4.a.a	$2$	$0$	$-5$	$7$	$14$	$-13$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-5+5\zeta_{6})q^{2}+(7-7\zeta_{6})q^{3}-17\zeta_{6}q^{4}+\cdots$
169.4.c.b	$169$	$4$	169.c	13.c	$3$	$2$	$1$	$9.971$	$\Q(\sqrt{-3}) $	None					13.4.b.a	$2$	$0$	$-3$	$1$	$-18$	$-15$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
169.4.c.c	$169$	$4$	169.c	13.c	$3$	$2$	$1$	$9.971$	$\Q(\sqrt{-3}) $	None					13.4.b.a	$2$	$0$	$3$	$1$	$18$	$15$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(3-3\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$

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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.