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 160 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
845.2.a.a	$845$	$2$	845.a	1.a	$1$	$1$	$1$	$6.747$	$\Q$	None	✓				65.2.a.a	$1$	$0$	$1$	$-2$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}-q^{4}+q^{5}-2q^{6}+4q^{7}+\cdots$
845.2.a.b	$845$	$2$	845.a	1.a	$1$	$2$	$2$	$6.747$	$\Q(\sqrt{5}) $	None	✓				65.2.e.a	$1$	$1$	$-1$	$0$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
845.2.a.c	$845$	$2$	845.a	1.a	$1$	$2$	$2$	$6.747$	$\Q(\sqrt{13}) $	None	✓				65.2.e.b	$1$	$1$	$-1$	$2$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots$
845.2.a.d	$845$	$2$	845.a	1.a	$1$	$2$	$2$	$6.747$	$\Q(\sqrt{3}) $	None	✓				65.2.a.c	$1$	$0$	$0$	$2$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{3}+q^{4}+q^{5}+(3+\beta )q^{6}+\cdots$
845.2.a.e	$845$	$2$	845.a	1.a	$1$	$2$	$2$	$6.747$	$\Q(\sqrt{5}) $	None	✓				65.2.e.a	$1$	$0$	$1$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
845.2.a.f	$845$	$2$	845.a	1.a	$1$	$2$	$2$	$6.747$	$\Q(\sqrt{13}) $	None	✓				65.2.e.b	$1$	$0$	$1$	$2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(1+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots$
845.2.a.g	$845$	$2$	845.a	1.a	$1$	$2$	$2$	$6.747$	$\Q(\sqrt{2}) $	None	✓				65.2.a.b	$1$	$1$	$2$	$0$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-\beta q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots$
845.2.a.h	$845$	$2$	845.a	1.a	$1$	$3$	$3$	$6.747$	$\Q(\zeta_{14})^+$	None	✓	✓			845.2.a.h	$1$	$1$	$-1$	$-5$	$3$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots$
845.2.a.i	$845$	$2$	845.a	1.a	$1$	$3$	$3$	$6.747$	3.3.564.1	None	✓				65.2.c.a	$1$	$1$	$-1$	$-2$	$3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{1})q^{3}+(2+\beta _{2})q^{4}+\cdots$
845.2.a.j	$845$	$2$	845.a	1.a	$1$	$3$	$3$	$6.747$	$\Q(\zeta_{14})^+$	None	✓	✓	✓		845.2.a.h	$1$	$1$	$1$	$-5$	$-3$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots$
845.2.a.k	$845$	$2$	845.a	1.a	$1$	$3$	$3$	$6.747$	3.3.564.1	None	✓				65.2.c.a	$1$	$0$	$1$	$-2$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{1})q^{3}+(2+\beta _{2})q^{4}+\cdots$
845.2.a.l	$845$	$2$	845.a	1.a	$1$	$4$	$4$	$6.747$	$\Q(\sqrt{9 +4 \sqrt{3}})$	None	✓		✓		65.2.m.a	$1$	$1$	$-2$	$-2$	$4$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
845.2.a.m	$845$	$2$	845.a	1.a	$1$	$4$	$4$	$6.747$	$\Q(\sqrt{9 +4 \sqrt{3}})$	None	✓				65.2.m.a	$1$	$0$	$2$	$-2$	$-4$	$10$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots$
845.2.a.n	$845$	$2$	845.a	1.a	$1$	$9$	$9$	$6.747$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓		845.2.a.n	$1$	$0$	$-3$	$7$	$-9$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{6})q^{2}+(1-\beta _{4})q^{3}+(2-\beta _{3}+\cdots)q^{4}+\cdots$
845.2.a.o	$845$	$2$	845.a	1.a	$1$	$9$	$9$	$6.747$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓		845.2.a.n	$1$	$0$	$3$	$7$	$9$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{6})q^{2}+(1-\beta _{4})q^{3}+(2-\beta _{3}+\cdots)q^{4}+\cdots$
845.2.b.a	$845$	$2$	845.b	5.b	$2$	$2$	$2$	$6.747$	$\Q(\sqrt{-1}) $	None					65.2.d.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-2 i q^{3}+q^{4}+(i-2)q^{5}+\cdots$
845.2.b.b	$845$	$2$	845.b	5.b	$2$	$2$	$2$	$6.747$	$\Q(\sqrt{-1}) $	None					65.2.d.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+2 i q^{3}+q^{4}+(i+2)q^{5}+\cdots$
845.2.b.c	$845$	$2$	845.b	5.b	$2$	$6$	$6$	$6.747$	6.0.350464.1	None					65.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{3}-\beta _{5})q^{2}+(\beta _{3}+\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots$
845.2.b.d	$845$	$2$	845.b	5.b	$2$	$6$	$6$	$6.747$	6.0.49843600.1	None					65.2.n.a	$2$	$0$	$0$	$0$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{5})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
845.2.b.e	$845$	$2$	845.b	5.b	$2$	$6$	$6$	$6.747$	6.0.49843600.1	None					65.2.n.a	$2$	$0$	$0$	$0$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
845.2.b.f	$845$	$2$	845.b	5.b	$2$	$8$	$8$	$6.747$	$\Q(i, \sqrt{3}, \sqrt{7})$	None					65.2.l.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+\beta _{3}q^{3}+\beta _{4}q^{4}+(-\beta _{2}-\beta _{7})q^{5}+\cdots$
845.2.b.g	$845$	$2$	845.b	5.b	$2$	$18$	$18$	$6.747$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		✓			845.2.b.g	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{15}q^{3}+(-1+\beta _{2})q^{4}+\cdots$
845.2.b.h	$845$	$2$	845.b	5.b	$2$	$18$	$18$	$6.747$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		✓			845.2.b.g	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{15}q^{3}+(-1+\beta _{2})q^{4}+\cdots$
845.2.c.a	$845$	$2$	845.c	13.b	$2$	$2$	$2$	$6.747$	$\Q(\sqrt{-1}) $	None					65.2.a.a	$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-2 q^{3}+q^{4}+i q^{5}-2 i q^{6}+\cdots$
845.2.c.b	$845$	$2$	845.c	13.b	$2$	$4$	$4$	$6.747$	$\Q(\zeta_{8})$	None					65.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta_{2}+\beta_1)q^{2}-\beta_{3} q^{3}+(-2\beta_{3}-1)q^{4}+\cdots$
845.2.c.c	$845$	$2$	845.c	13.b	$2$	$4$	$4$	$6.747$	$\Q(i, \sqrt{5})$	None					65.2.e.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(1+2\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
845.2.c.d	$845$	$2$	845.c	13.b	$2$	$4$	$4$	$6.747$	$\Q(i, \sqrt{13})$	None					65.2.e.b	$2$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+q^{3}+(-2+\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots$
845.2.c.e	$845$	$2$	845.c	13.b	$2$	$4$	$4$	$6.747$	$\Q(\zeta_{12})$	None					65.2.a.c	$2$	$0$	$0$	$4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{2} q^{2}+(-\beta_{3}+1)q^{3}-q^{4}+\beta_1 q^{5}+\cdots$
845.2.c.f	$845$	$2$	845.c	13.b	$2$	$6$	$6$	$6.747$	6.0.153664.1	None		✓			845.2.a.h	$2$	$0$	$0$	$-10$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1-\beta _{2}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots$
845.2.c.g	$845$	$2$	845.c	13.b	$2$	$8$	$8$	$6.747$	8.0.22581504.2	None					65.2.m.a	$2$	$0$	$0$	$-4$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
845.2.c.h	$845$	$2$	845.c	13.b	$2$	$18$	$18$	$6.747$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		✓	✓		845.2.a.n	$2$	$0$	$0$	$14$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{6})q^{2}+(1+\beta _{11})q^{3}+(-2+\cdots)q^{4}+\cdots$
845.2.d.a	$845$	$2$	845.d	65.d	$2$	$6$	$6$	$6.747$	6.0.350464.1	None					65.2.b.a	$2$	$0$	$-6$	$0$	$-2$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1})q^{2}-\beta _{2}q^{3}+(2+\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots$
845.2.d.b	$845$	$2$	845.d	65.d	$2$	$6$	$6$	$6.747$	6.0.350464.1	None					65.2.b.a	$2$	$0$	$6$	$0$	$2$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{2}+\beta _{2}q^{3}+(2+\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots$
845.2.d.c	$845$	$2$	845.d	65.d	$2$	$8$	$8$	$6.747$	$\Q(i, \sqrt{3}, \sqrt{7})$	None					65.2.l.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{2}+\beta _{3}q^{3}-\beta _{4}q^{4}+(\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots$
845.2.d.d	$845$	$2$	845.d	65.d	$2$	$12$	$12$	$6.747$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None					65.2.n.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{3}-\beta _{11})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots$
845.2.d.e	$845$	$2$	845.d	65.d	$2$	$36$	$36$	$6.747$		None		✓	✓		845.2.b.g	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
845.2.e.a	$845$	$2$	845.e	13.c	$3$	$2$	$1$	$6.747$	$\Q(\sqrt{-3}) $	None					65.2.a.a	$2$	$0$	$-1$	$2$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
845.2.e.b	$845$	$2$	845.e	13.c	$3$	$2$	$1$	$6.747$	$\Q(\sqrt{-3}) $	None					65.2.a.a	$2$	$0$	$1$	$2$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
845.2.e.c	$845$	$2$	845.e	13.c	$3$	$4$	$2$	$6.747$	$\Q(\sqrt{2}, \sqrt{-3})$	None					65.2.a.b	$2$	$0$	$-2$	$0$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots$
845.2.e.d	$845$	$2$	845.e	13.c	$3$	$4$	$2$	$6.747$	$\Q(\sqrt{-3}, \sqrt{13})$	None					65.2.e.b	$2$	$0$	$-1$	$-2$	$4$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$
845.2.e.e	$845$	$2$	845.e	13.c	$3$	$4$	$2$	$6.747$	$\Q(\zeta_{12})$	None					65.2.a.c	$2$	$0$	$0$	$-2$	$-4$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_{2} q^{2}+(\beta_{2}-\beta_1)q^{3}+(\beta_1-1)q^{4}+\cdots$
845.2.e.f	$845$	$2$	845.e	13.c	$3$	$4$	$2$	$6.747$	$\Q(\zeta_{12})$	None					65.2.a.c	$2$	$0$	$0$	$-2$	$4$	$4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta_{2} q^{2}+(-\beta_{2}-\beta_1)q^{3}+(\beta_1-1)q^{4}+\cdots$
845.2.e.g	$845$	$2$	845.e	13.c	$3$	$4$	$2$	$6.747$	$\Q(\sqrt{-3}, \sqrt{5})$	None					65.2.e.a	$2$	$0$	$1$	$0$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1+2\beta _{1}-\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
845.2.e.h	$845$	$2$	845.e	13.c	$3$	$4$	$2$	$6.747$	$\Q(\sqrt{2}, \sqrt{-3})$	None					65.2.a.b	$2$	$0$	$2$	$0$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{1}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
845.2.e.i	$845$	$2$	845.e	13.c	$3$	$6$	$3$	$6.747$	6.0.954288.1	None					65.2.c.a	$2$	$0$	$-1$	$2$	$-6$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{4}-\beta _{5})q^{2}+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots$
845.2.e.j	$845$	$2$	845.e	13.c	$3$	$6$	$3$	$6.747$	6.0.64827.1	None		✓			845.2.a.h	$2$	$0$	$-1$	$5$	$-6$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(2-\beta _{4}-2\beta _{5})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
845.2.e.k	$845$	$2$	845.e	13.c	$3$	$6$	$3$	$6.747$	6.0.954288.1	None					65.2.c.a	$2$	$0$	$1$	$2$	$6$	$2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}+\beta _{5})q^{2}+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots$
845.2.e.l	$845$	$2$	845.e	13.c	$3$	$6$	$3$	$6.747$	6.0.64827.1	None		✓			845.2.a.h	$2$	$0$	$1$	$5$	$6$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(2-\beta _{4}-2\beta _{5})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
845.2.e.m	$845$	$2$	845.e	13.c	$3$	$8$	$4$	$6.747$	8.0.22581504.2	None					65.2.m.a	$2$	$0$	$-2$	$2$	$-8$	$-10$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}+\beta _{5})q^{2}+(\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots$
845.2.e.n	$845$	$2$	845.e	13.c	$3$	$8$	$4$	$6.747$	8.0.22581504.2	None					65.2.m.a	$2$	$0$	$2$	$2$	$8$	$10$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{1}-\beta _{5})q^{2}+(\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots$

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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.