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 317 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
882.2.a.a	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	$\Q$	None	✓				126.2.g.a	$1$	$1$	$-1$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+3q^{11}+\cdots$
882.2.a.b	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	$\Q$	None	✓				42.2.a.a	$1$	$1$	$-1$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+4q^{11}+\cdots$
882.2.a.c	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	$\Q$	None	✓				42.2.e.a	$1$	$0$	$-1$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-5q^{11}+\cdots$
882.2.a.d	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	$\Q$	None	✓				42.2.e.a	$1$	$1$	$-1$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-5q^{11}+\cdots$
882.2.a.e	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	$\Q$	None	✓		✓	✓	126.2.g.a	$1$	$0$	$-1$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+3q^{11}+\cdots$
882.2.a.f	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	$\Q$	None	✓				294.2.a.b	$1$	$0$	$1$	$0$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{5}+q^{8}-4q^{10}+4q^{11}+\cdots$
882.2.a.g	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	$\Q$	None	✓		✓	✓	42.2.e.b	$1$	$1$	$1$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\cdots$
882.2.a.h	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	$\Q$	None	✓		✓	✓	126.2.g.a	$1$	$1$	$1$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\cdots$
882.2.a.i	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	$\Q$	None	✓				14.2.a.a	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}+4q^{13}+q^{16}+6q^{17}+\cdots$
882.2.a.j	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	$\Q$	None	✓				126.2.g.a	$1$	$0$	$1$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{11}+\cdots$
882.2.a.k	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	$\Q$	None	✓				42.2.e.b	$1$	$0$	$1$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{11}+\cdots$
882.2.a.l	$882$	$2$	882.a	1.a	$1$	$1$	$1$	$7.043$	$\Q$	None	✓				294.2.a.b	$1$	$0$	$1$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{5}+q^{8}+4q^{10}+4q^{11}+\cdots$
882.2.a.m	$882$	$2$	882.a	1.a	$1$	$2$	$2$	$7.043$	$\Q(\sqrt{2}) $	None	✓	✓	✓		882.2.a.m	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}-4q^{11}+\cdots$
882.2.a.n	$882$	$2$	882.a	1.a	$1$	$2$	$2$	$7.043$	$\Q(\sqrt{2}) $	None	✓		✓		98.2.a.b	$2$	$0$	$-2$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2\beta q^{5}-q^{8}-2\beta q^{10}+\cdots$
882.2.a.o	$882$	$2$	882.a	1.a	$1$	$2$	$2$	$7.043$	$\Q(\sqrt{2}) $	None	✓	✓	✓		882.2.a.m	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+4q^{11}+\cdots$
882.2.d.a	$882$	$2$	882.d	21.c	$2$	$8$	$8$	$7.043$	$\Q(\zeta_{24})$	None					126.2.k.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{24}q^{2}-q^{4}+(-\zeta_{24}^{3}-\zeta_{24}^{4}+\cdots)q^{5}+\cdots$
882.2.d.b	$882$	$2$	882.d	21.c	$2$	$8$	$8$	$7.043$	$\Q(\zeta_{16})$	None		✓			882.2.d.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{16}q^{2}-q^{4}-\zeta_{16}^{5}q^{5}+\zeta_{16}q^{8}+\cdots$
882.2.e.a	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	$\Q(\sqrt{-3}) $	None					126.2.f.b	$2$	$0$	$-2$	$-3$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(-2+2\zeta_{6})q^{5}+\cdots$
882.2.e.b	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	$\Q(\sqrt{-3}) $	None					126.2.f.a	$2$	$0$	$-2$	$-3$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(3-3\zeta_{6})q^{5}+\cdots$
882.2.e.c	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	$\Q(\sqrt{-3}) $	None					126.2.e.a	$2$	$0$	$-2$	$0$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+(3-3\zeta_{6})q^{5}+\cdots$
882.2.e.d	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	$\Q(\sqrt{-3}) $	None					126.2.f.a	$2$	$0$	$-2$	$3$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(-3+3\zeta_{6})q^{5}+\cdots$
882.2.e.e	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	$\Q(\sqrt{-3}) $	None					126.2.f.b	$2$	$0$	$-2$	$3$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(2-\zeta_{6})q^{3}+q^{4}+(2-2\zeta_{6})q^{5}+\cdots$
882.2.e.f	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	$\Q(\sqrt{-3}) $	None		✓			882.2.f.b	$2$	$0$	$2$	$-3$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots$
882.2.e.g	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	$\Q(\sqrt{-3}) $	None					18.2.c.a	$2$	$0$	$2$	$-3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(-2+\zeta_{6})q^{6}+\cdots$
882.2.e.h	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	$\Q(\sqrt{-3}) $	None					126.2.e.b	$2$	$0$	$2$	$0$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+(-3+3\zeta_{6})q^{5}+\cdots$
882.2.e.i	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	$\Q(\sqrt{-3}) $	None					18.2.c.a	$2$	$0$	$2$	$3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(2-\zeta_{6})q^{3}+q^{4}+(2-\zeta_{6})q^{6}+\cdots$
882.2.e.j	$882$	$2$	882.e	63.h	$3$	$2$	$1$	$7.043$	$\Q(\sqrt{-3}) $	None		✓			882.2.f.b	$2$	$0$	$2$	$3$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots$
882.2.e.k	$882$	$2$	882.e	63.h	$3$	$4$	$2$	$7.043$	$\Q(\sqrt{-3}, \sqrt{-11})$	None					126.2.f.d	$2$	$0$	$-4$	$-2$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots$
882.2.e.l	$882$	$2$	882.e	63.h	$3$	$4$	$2$	$7.043$	$\Q(\sqrt{-3}, \sqrt{-11})$	None					126.2.f.d	$2$	$0$	$-4$	$2$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(\beta _{1}-\beta _{3})q^{3}+q^{4}+(1-2\beta _{1}+\cdots)q^{5}+\cdots$
882.2.e.m	$882$	$2$	882.e	63.h	$3$	$4$	$2$	$7.043$	$\Q(\sqrt{-2}, \sqrt{-3})$	None					126.2.f.c	$2$	$0$	$4$	$-2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+q^{4}+\cdots$
882.2.e.n	$882$	$2$	882.e	63.h	$3$	$4$	$2$	$7.043$	$\Q(\sqrt{-2}, \sqrt{-3})$	None					126.2.f.c	$2$	$0$	$4$	$2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
882.2.e.o	$882$	$2$	882.e	63.h	$3$	$6$	$3$	$7.043$	6.0.309123.1	None					126.2.e.c	$2$	$0$	$-6$	$-2$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(\beta _{2}+\beta _{4})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
882.2.e.p	$882$	$2$	882.e	63.h	$3$	$6$	$3$	$7.043$	6.0.309123.1	None					126.2.e.d	$2$	$0$	$6$	$2$	$5$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-\beta _{3}+\beta _{4}+\beta _{5})q^{3}+q^{4}+\cdots$
882.2.e.q	$882$	$2$	882.e	63.h	$3$	$8$	$4$	$7.043$	$\Q(\zeta_{24})$	None		✓			882.2.f.s	$4$	$0$	$-8$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(\zeta_{24}^{3}+\zeta_{24}^{7})q^{3}+q^{4}-\zeta_{24}^{7}q^{5}+\cdots$
882.2.e.r	$882$	$2$	882.e	63.h	$3$	$8$	$4$	$7.043$	8.0.$\cdots$.2	None		✓			882.2.f.r	$4$	$0$	$-8$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}-\beta _{3}q^{3}+q^{4}+(-\beta _{5}-\beta _{6})q^{5}+\cdots$
882.2.e.s	$882$	$2$	882.e	63.h	$3$	$8$	$4$	$7.043$	$\Q(\zeta_{24})$	None		✓			882.2.f.q	$4$	$0$	$8$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-\zeta_{24}^{3}+2\zeta_{24}^{5}+\zeta_{24}^{6}+\cdots)q^{3}+\cdots$
882.2.e.t	$882$	$2$	882.e	63.h	$3$	$8$	$4$	$7.043$	8.0.3317760000.3	None		✓			882.2.f.p	$4$	$0$	$8$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(\beta _{5}-\beta _{6})q^{3}+q^{4}+(2\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
882.2.f.a	$882$	$2$	882.f	9.c	$3$	$2$	$1$	$7.043$	$\Q(\sqrt{-3}) $	None					126.2.e.b	$2$	$1$	$-1$	$-3$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
882.2.f.b	$882$	$2$	882.f	9.c	$3$	$2$	$1$	$7.043$	$\Q(\sqrt{-3}) $	None		✓			882.2.f.b	$2$	$0$	$-1$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
882.2.f.c	$882$	$2$	882.f	9.c	$3$	$2$	$1$	$7.043$	$\Q(\sqrt{-3}) $	None		✓			882.2.f.b	$2$	$0$	$-1$	$0$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
882.2.f.d	$882$	$2$	882.f	9.c	$3$	$2$	$1$	$7.043$	$\Q(\sqrt{-3}) $	None					18.2.c.a	$2$	$0$	$-1$	$3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
882.2.f.e	$882$	$2$	882.f	9.c	$3$	$2$	$1$	$7.043$	$\Q(\sqrt{-3}) $	None					126.2.e.b	$2$	$0$	$-1$	$3$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
882.2.f.f	$882$	$2$	882.f	9.c	$3$	$2$	$1$	$7.043$	$\Q(\sqrt{-3}) $	None					126.2.f.b	$2$	$0$	$1$	$-3$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
882.2.f.g	$882$	$2$	882.f	9.c	$3$	$2$	$1$	$7.043$	$\Q(\sqrt{-3}) $	None					126.2.e.a	$2$	$0$	$1$	$-3$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
882.2.f.h	$882$	$2$	882.f	9.c	$3$	$2$	$1$	$7.043$	$\Q(\sqrt{-3}) $	None					126.2.f.a	$2$	$0$	$1$	$0$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
882.2.f.i	$882$	$2$	882.f	9.c	$3$	$2$	$1$	$7.043$	$\Q(\sqrt{-3}) $	None					126.2.e.a	$2$	$0$	$1$	$3$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
882.2.f.j	$882$	$2$	882.f	9.c	$3$	$4$	$2$	$7.043$	$\Q(\sqrt{-2}, \sqrt{-3})$	None					126.2.f.c	$2$	$0$	$-2$	$-4$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{2})q^{2}+(-1-\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots$
882.2.f.k	$882$	$2$	882.f	9.c	$3$	$4$	$2$	$7.043$	$\Q(\sqrt{-3}, \sqrt{-11})$	None					126.2.f.d	$2$	$0$	$2$	$1$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{2})q^{2}+(\beta _{2}+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots$
882.2.f.l	$882$	$2$	882.f	9.c	$3$	$6$	$3$	$7.043$	6.0.309123.1	None					126.2.e.d	$2$	$0$	$-3$	$-2$	$-5$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{4})q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+\cdots$
882.2.f.m	$882$	$2$	882.f	9.c	$3$	$6$	$3$	$7.043$	6.0.309123.1	None					126.2.e.d	$2$	$0$	$-3$	$2$	$5$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{4})q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+\cdots$

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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.