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 223 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
162.2.a.a	$162$	$2$	162.a	1.a	$1$	$1$	$1$	$1.294$	$\Q$	None	✓	✓	✓	✓	162.2.a.a	$1$	$1$	$-1$	$0$	$-3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}-4q^{7}-q^{8}+3q^{10}+\cdots$
162.2.a.b	$162$	$2$	162.a	1.a	$1$	$1$	$1$	$1.294$	$\Q$	None	✓		✓	✓	18.2.c.a	$1$	$0$	$-1$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{7}-q^{8}+3q^{11}+2q^{13}+\cdots$
162.2.a.c	$162$	$2$	162.a	1.a	$1$	$1$	$1$	$1.294$	$\Q$	None	✓				18.2.c.a	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-3q^{11}+2q^{13}+\cdots$
162.2.a.d	$162$	$2$	162.a	1.a	$1$	$1$	$1$	$1.294$	$\Q$	None	✓	✓			162.2.a.a	$1$	$0$	$1$	$0$	$3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}-4q^{7}+q^{8}+3q^{10}+\cdots$
162.2.c.a	$162$	$2$	162.c	9.c	$3$	$2$	$1$	$1.294$	$\Q(\sqrt{-3})$	None		✓			162.2.a.a	$2$	$0$	$-1$	$0$	$-3$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots$
162.2.c.b	$162$	$2$	162.c	9.c	$3$	$2$	$1$	$1.294$	$\Q(\sqrt{-3})$	None					54.2.a.a	$2$	$0$	$-1$	$0$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots$
162.2.c.c	$162$	$2$	162.c	9.c	$3$	$2$	$1$	$1.294$	$\Q(\sqrt{-3})$	None					54.2.a.a	$2$	$0$	$1$	$0$	$-3$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$
162.2.c.d	$162$	$2$	162.c	9.c	$3$	$2$	$1$	$1.294$	$\Q(\sqrt{-3})$	None		✓			162.2.a.a	$2$	$0$	$1$	$0$	$3$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots$
162.2.e.a	$162$	$2$	162.e	27.e	$9$	$6$	$1$	$1.294$	$\Q(\zeta_{18})$	None					54.2.e.a	$2$	$0$	$0$	$0$	$3$	$3$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}-\zeta_{18}^{5}q^{4}+(\zeta_{18}^{2}+\cdots)q^{5}+\cdots$
162.2.e.b	$162$	$2$	162.e	27.e	$9$	$12$	$2$	$1.294$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None			✓		54.2.e.b	$2$	$0$	$0$	$0$	$3$	$-3$		$3^{3}$	$\mathrm{SU}(2)[C_{9}]$	$q+(\beta _{4}+\beta _{8})q^{2}-\beta _{6}q^{4}+(1-\beta _{2}+\beta _{7}+\cdots)q^{5}+\cdots$
162.2.g.a	$162$	$2$	162.g	81.g	$27$	$72$	$4$	$1.294$		None		✓			162.2.g.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{27}]$
162.2.g.b	$162$	$2$	162.g	81.g	$27$	$90$	$5$	$1.294$		None		✓	✓		162.2.g.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{27}]$
162.3.b.a	$162$	$3$	162.b	3.b	$2$	$4$	$4$	$4.414$	$\Q(\sqrt{-2}, \sqrt{-3})$	None					18.3.d.a	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(-1+\beta _{3})q^{7}+\cdots$
162.3.b.b	$162$	$3$	162.b	3.b	$2$	$4$	$4$	$4.414$	$\Q(\sqrt{-2}, \sqrt{3})$	None		✓			162.3.b.b	$2$	$0$	$0$	$0$	$0$	$8$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-2q^{4}+(\beta _{1}-\beta _{2})q^{5}+(2+2\beta _{3})q^{7}+\cdots$
162.3.d.a	$162$	$3$	162.d	9.d	$6$	$4$	$2$	$4.414$	$\Q(\sqrt{-2}, \sqrt{-3})$	None					54.3.b.a	$4$	$0$	$0$	$0$	$0$	$-10$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(-6\beta _{1}+6\beta _{3})q^{5}+\cdots$
162.3.d.b	$162$	$3$	162.d	9.d	$6$	$4$	$2$	$4.414$	$\Q(\sqrt{-2}, \sqrt{-3})$	None					18.3.b.a	$4$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(3\beta _{1}-3\beta _{3})q^{5}+\cdots$
162.3.d.c	$162$	$3$	162.d	9.d	$6$	$8$	$4$	$4.414$	$\Q(\zeta_{24})$	None		✓	✓		162.3.b.b	$4$	$0$	$0$	$0$	$0$	$-8$		$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta_{5} q^{2}+2\beta_1 q^{4}+(\beta_{7}-\beta_{6}+2\beta_{3})q^{5}+\cdots$
162.3.f.a	$162$	$3$	162.f	27.f	$18$	$36$	$6$	$4.414$		None			✓	✓	54.3.f.a	$2$	$0$	$0$	$0$	$-18$	$0$			$\mathrm{SU}(2)[C_{18}]$
162.3.h.a	$162$	$3$	162.h	81.h	$54$	$324$	$18$	$4.414$		None		✓	✓	✓	162.3.h.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{54}]$
162.4.a.a	$162$	$4$	162.a	1.a	$1$	$1$	$1$	$9.558$	$\Q$	None	✓				18.4.c.a	$1$	$1$	$-2$	$0$	$9$	$-31$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+9q^{5}-31q^{7}-8q^{8}+\cdots$
162.4.a.b	$162$	$4$	162.a	1.a	$1$	$1$	$1$	$9.558$	$\Q$	None	✓	✓			162.4.a.b	$1$	$0$	$-2$	$0$	$21$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+21q^{5}+8q^{7}-8q^{8}+\cdots$
162.4.a.c	$162$	$4$	162.a	1.a	$1$	$1$	$1$	$9.558$	$\Q$	None	✓	✓			162.4.a.b	$1$	$1$	$2$	$0$	$-21$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}-21q^{5}+8q^{7}+8q^{8}+\cdots$
162.4.a.d	$162$	$4$	162.a	1.a	$1$	$1$	$1$	$9.558$	$\Q$	None	✓				18.4.c.a	$1$	$1$	$2$	$0$	$-9$	$-31$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}-9q^{5}-31q^{7}+8q^{8}+\cdots$
162.4.a.e	$162$	$4$	162.a	1.a	$1$	$2$	$2$	$9.558$	$\Q(\sqrt{3})$	None	✓	✓	✓		162.4.a.e	$1$	$1$	$-4$	$0$	$-12$	$16$	$-$	$3$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(-6+\beta )q^{5}+(8-2\beta )q^{7}+\cdots$
162.4.a.f	$162$	$4$	162.a	1.a	$1$	$2$	$2$	$9.558$	$\Q(\sqrt{105})$	None	✓		✓		18.4.c.b	$1$	$0$	$-4$	$0$	$-9$	$19$	$+$	$3$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(-5-\beta )q^{5}+(9-\beta )q^{7}+\cdots$
162.4.a.g	$162$	$4$	162.a	1.a	$1$	$2$	$2$	$9.558$	$\Q(\sqrt{105})$	None	✓				18.4.c.b	$1$	$0$	$4$	$0$	$9$	$19$	$+$	$3$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(4-\beta )q^{5}+(10+\beta )q^{7}+\cdots$
162.4.a.h	$162$	$4$	162.a	1.a	$1$	$2$	$2$	$9.558$	$\Q(\sqrt{3})$	None	✓	✓			162.4.a.e	$1$	$0$	$4$	$0$	$12$	$16$	$+$	$3$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(6+\beta )q^{5}+(8+2\beta )q^{7}+\cdots$
162.4.c.a	$162$	$4$	162.c	9.c	$3$	$2$	$1$	$9.558$	$\Q(\sqrt{-3})$	None					54.4.a.a	$2$	$0$	$-2$	$0$	$-12$	$7$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-12\zeta_{6}q^{5}+\cdots$
162.4.c.b	$162$	$4$	162.c	9.c	$3$	$2$	$1$	$9.558$	$\Q(\sqrt{-3})$	None					54.4.a.b	$2$	$0$	$-2$	$0$	$-3$	$-29$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots$
162.4.c.c	$162$	$4$	162.c	9.c	$3$	$2$	$1$	$9.558$	$\Q(\sqrt{-3})$	None					6.4.a.a	$2$	$0$	$-2$	$0$	$6$	$16$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+6\zeta_{6}q^{5}+\cdots$
162.4.c.d	$162$	$4$	162.c	9.c	$3$	$2$	$1$	$9.558$	$\Q(\sqrt{-3})$	None		✓			162.4.a.b	$2$	$0$	$-2$	$0$	$21$	$-8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+21\zeta_{6}q^{5}+\cdots$
162.4.c.e	$162$	$4$	162.c	9.c	$3$	$2$	$1$	$9.558$	$\Q(\sqrt{-3})$	None		✓			162.4.a.b	$2$	$0$	$2$	$0$	$-21$	$-8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-21\zeta_{6}q^{5}+\cdots$
162.4.c.f	$162$	$4$	162.c	9.c	$3$	$2$	$1$	$9.558$	$\Q(\sqrt{-3})$	None					6.4.a.a	$2$	$0$	$2$	$0$	$-6$	$16$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}-6\zeta_{6}q^{5}+\cdots$
162.4.c.g	$162$	$4$	162.c	9.c	$3$	$2$	$1$	$9.558$	$\Q(\sqrt{-3})$	None					54.4.a.b	$2$	$0$	$2$	$0$	$3$	$-29$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots$
162.4.c.h	$162$	$4$	162.c	9.c	$3$	$2$	$1$	$9.558$	$\Q(\sqrt{-3})$	None					54.4.a.a	$2$	$0$	$2$	$0$	$12$	$7$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+12\zeta_{6}q^{5}+\cdots$
162.4.c.i	$162$	$4$	162.c	9.c	$3$	$4$	$2$	$9.558$	$\Q(\zeta_{12})$	None		✓			162.4.a.e	$2$	$0$	$-4$	$0$	$-12$	$-16$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+(2\beta_1-2)q^{2}-4\beta_1 q^{4}+(\beta_{2}-6\beta_1)q^{5}+\cdots$
162.4.c.j	$162$	$4$	162.c	9.c	$3$	$4$	$2$	$9.558$	$\Q(\zeta_{12})$	None		✓			162.4.a.e	$2$	$0$	$4$	$0$	$12$	$-16$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2\beta_1+2)q^{2}-4\beta_1 q^{4}+(\beta_{2}+6\beta_1)q^{5}+\cdots$
162.4.e.a	$162$	$4$	162.e	27.e	$9$	$24$	$4$	$9.558$		None					54.4.e.a	$2$	$0$	$0$	$0$	$12$	$-33$			$\mathrm{SU}(2)[C_{9}]$
162.4.e.b	$162$	$4$	162.e	27.e	$9$	$30$	$5$	$9.558$		None			✓		54.4.e.b	$2$	$0$	$0$	$0$	$12$	$33$			$\mathrm{SU}(2)[C_{9}]$
162.4.g.a	$162$	$4$	162.g	81.g	$27$	$234$	$13$	$9.558$		None		✓			162.4.g.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{27}]$
162.4.g.b	$162$	$4$	162.g	81.g	$27$	$252$	$14$	$9.558$		None		✓	✓		162.4.g.b	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{27}]$
162.5.b.a	$162$	$5$	162.b	3.b	$2$	$4$	$4$	$16.746$	$\Q(\sqrt{-2}, \sqrt{3})$	None		✓			162.5.b.a	$2$	$0$	$0$	$0$	$0$	$-52$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-2\beta _{1}q^{2}-8q^{4}+(-17\beta _{1}+5\beta _{2}+\cdots)q^{5}+\cdots$
162.5.b.b	$162$	$5$	162.b	3.b	$2$	$4$	$4$	$16.746$	$\Q(\sqrt{-2}, \sqrt{3})$	None		✓			162.5.b.b	$2$	$0$	$0$	$0$	$0$	$-52$		$3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta _{1}q^{2}-8q^{4}+(-8\beta _{1}+\beta _{2})q^{5}+\cdots$
162.5.b.c	$162$	$5$	162.b	3.b	$2$	$8$	$8$	$16.746$	8.0. $\cdots$ .4	None			✓		18.5.d.a	$2$	$0$	$0$	$0$	$0$	$52$		$2^{8}\cdot 3^{16}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-8q^{4}-\beta _{4}q^{5}+(6+\beta _{1})q^{7}+\cdots$
162.5.d.a	$162$	$5$	162.d	9.d	$6$	$4$	$2$	$16.746$	$\Q(\sqrt{-2}, \sqrt{-3})$	None					6.5.b.a	$4$	$0$	$0$	$0$	$0$	$-52$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}+\beta _{3})q^{2}+(8-8\beta _{2})q^{4}+6\beta _{1}q^{5}+\cdots$
162.5.d.b	$162$	$5$	162.d	9.d	$6$	$4$	$2$	$16.746$	$\Q(\sqrt{-2}, \sqrt{-3})$	None					54.5.b.a	$4$	$0$	$0$	$0$	$0$	$146$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{3})q^{2}+(8-8\beta _{2})q^{4}+12\beta _{1}q^{5}+\cdots$
162.5.d.c	$162$	$5$	162.d	9.d	$6$	$8$	$4$	$16.746$	$\Q(\zeta_{24})$	None					54.5.b.b	$4$	$0$	$0$	$0$	$0$	$-68$		$2^{6}\cdot 3^{12}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta_{5} q^{2}+8\beta_{2} q^{4}+(-3\beta_{5}-3\beta_{4}+\cdots+\beta_1)q^{5}+\cdots$
162.5.d.d	$162$	$5$	162.d	9.d	$6$	$8$	$4$	$16.746$	$\Q(\zeta_{24})$	None		✓			162.5.b.a	$4$	$0$	$0$	$0$	$0$	$52$		$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q-2\beta_{3} q^{2}+(-8\beta_1+8)q^{4}+(-5\beta_{6}+22\beta_{5})q^{5}+\cdots$
162.5.d.e	$162$	$5$	162.d	9.d	$6$	$8$	$4$	$16.746$	$\Q(\zeta_{24})$	None		✓			162.5.b.b	$4$	$0$	$0$	$0$	$0$	$52$		$3^{10}$	$\mathrm{SU}(2)[C_{6}]$	$q+(2\beta_{5}+2\beta_{3})q^{2}+(-8\beta_1+8)q^{4}+\cdots$
162.5.f.a	$162$	$5$	162.f	27.f	$18$	$72$	$12$	$16.746$		None			✓	✓	54.5.f.a	$2$	$0$	$0$	$0$	$18$	$0$			$\mathrm{SU}(2)[C_{18}]$

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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.