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 69 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
1666.2.a.a	$1666$	$2$	1666.a	1.a	$1$	$1$	$1$	$13.303$	$\Q$	None	✓				238.2.e.b	$1$	$1$	$-1$	$-3$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}+q^{4}+2q^{5}+3q^{6}-q^{8}+\cdots$
1666.2.a.b	$1666$	$2$	1666.a	1.a	$1$	$1$	$1$	$13.303$	$\Q$	None	✓				238.2.a.b	$1$	$1$	$-1$	$-2$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-4q^{5}+2q^{6}-q^{8}+\cdots$
1666.2.a.c	$1666$	$2$	1666.a	1.a	$1$	$1$	$1$	$13.303$	$\Q$	None	✓				238.2.e.d	$1$	$1$	$-1$	$-2$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+3q^{5}+2q^{6}-q^{8}+\cdots$
1666.2.a.d	$1666$	$2$	1666.a	1.a	$1$	$1$	$1$	$13.303$	$\Q$	None	✓				238.2.e.c	$1$	$1$	$-1$	$-1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots$
1666.2.a.e	$1666$	$2$	1666.a	1.a	$1$	$1$	$1$	$13.303$	$\Q$	None	✓				238.2.a.a	$1$	$1$	$-1$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{8}-3q^{9}-2q^{10}+\cdots$
1666.2.a.f	$1666$	$2$	1666.a	1.a	$1$	$1$	$1$	$13.303$	$\Q$	None	✓				238.2.e.c	$1$	$1$	$-1$	$1$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots$
1666.2.a.g	$1666$	$2$	1666.a	1.a	$1$	$1$	$1$	$13.303$	$\Q$	None	✓				238.2.e.d	$1$	$1$	$-1$	$2$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-3q^{5}-2q^{6}-q^{8}+\cdots$
1666.2.a.h	$1666$	$2$	1666.a	1.a	$1$	$1$	$1$	$13.303$	$\Q$	None	✓				238.2.e.b	$1$	$1$	$-1$	$3$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-2q^{5}-3q^{6}-q^{8}+\cdots$
1666.2.a.i	$1666$	$2$	1666.a	1.a	$1$	$1$	$1$	$13.303$	$\Q$	None	✓				238.2.a.e	$1$	$0$	$1$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots$
1666.2.a.j	$1666$	$2$	1666.a	1.a	$1$	$1$	$1$	$13.303$	$\Q$	None	✓				238.2.a.d	$1$	$1$	$1$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{8}-3q^{9}-2q^{10}+\cdots$
1666.2.a.k	$1666$	$2$	1666.a	1.a	$1$	$1$	$1$	$13.303$	$\Q$	None	✓				238.2.e.a	$1$	$1$	$1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-3q^{9}-q^{10}+\cdots$
1666.2.a.l	$1666$	$2$	1666.a	1.a	$1$	$1$	$1$	$13.303$	$\Q$	None	✓				238.2.e.a	$1$	$1$	$1$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots$
1666.2.a.m	$1666$	$2$	1666.a	1.a	$1$	$1$	$1$	$13.303$	$\Q$	None	✓				34.2.a.a	$1$	$0$	$1$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{8}+q^{9}+\cdots$
1666.2.a.n	$1666$	$2$	1666.a	1.a	$1$	$1$	$1$	$13.303$	$\Q$	None	✓				238.2.a.c	$1$	$0$	$1$	$2$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+4q^{5}+2q^{6}+q^{8}+\cdots$
1666.2.a.o	$1666$	$2$	1666.a	1.a	$1$	$2$	$2$	$13.303$	$\Q(\sqrt{5}) $	None	✓				238.2.a.f	$1$	$0$	$-2$	$-2$	$-2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots$
1666.2.a.p	$1666$	$2$	1666.a	1.a	$1$	$2$	$2$	$13.303$	$\Q(\sqrt{2}) $	None	✓	✓	✓		1666.2.a.p	$1$	$1$	$-2$	$0$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}+(-2+\beta )q^{5}-\beta q^{6}+\cdots$
1666.2.a.q	$1666$	$2$	1666.a	1.a	$1$	$2$	$2$	$13.303$	$\Q(\sqrt{2}) $	None	✓	✓			1666.2.a.p	$1$	$0$	$-2$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}+(2+\beta )q^{5}-\beta q^{6}+\cdots$
1666.2.a.r	$1666$	$2$	1666.a	1.a	$1$	$2$	$2$	$13.303$	$\Q(\sqrt{3}) $	None	✓	✓	✓		1666.2.a.r	$1$	$1$	$2$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots$
1666.2.a.s	$1666$	$2$	1666.a	1.a	$1$	$2$	$2$	$13.303$	$\Q(\sqrt{3}) $	None	✓	✓			1666.2.a.r	$1$	$0$	$2$	$2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+(1-\beta )q^{5}+\cdots$
1666.2.a.t	$1666$	$2$	1666.a	1.a	$1$	$3$	$3$	$13.303$	3.3.404.1	None	✓				238.2.e.e	$1$	$0$	$-3$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}-\beta _{2}q^{5}+\cdots$
1666.2.a.u	$1666$	$2$	1666.a	1.a	$1$	$3$	$3$	$13.303$	3.3.404.1	None	✓		✓		238.2.e.e	$1$	$0$	$-3$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+\beta _{2}q^{5}+\cdots$
1666.2.a.v	$1666$	$2$	1666.a	1.a	$1$	$4$	$4$	$13.303$	$\Q(\sqrt{10 +4 \sqrt{2}})$	None	✓	✓	✓		1666.2.a.v	$1$	$1$	$-4$	$0$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(\beta _{1}-\beta _{3})q^{3}+q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots$
1666.2.a.w	$1666$	$2$	1666.a	1.a	$1$	$4$	$4$	$13.303$	$\Q(\sqrt{10 +4 \sqrt{2}})$	None	✓	✓	✓		1666.2.a.v	$1$	$0$	$-4$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots$
1666.2.a.x	$1666$	$2$	1666.a	1.a	$1$	$4$	$4$	$13.303$	$\Q(\sqrt{10 +4 \sqrt{2}})$	None	✓	✓	✓		1666.2.a.x	$1$	$1$	$4$	$-4$	$-8$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{2}-\beta _{3})q^{3}+q^{4}+(-2+\cdots)q^{5}+\cdots$
1666.2.a.y	$1666$	$2$	1666.a	1.a	$1$	$4$	$4$	$13.303$	$\Q(\sqrt{10 +4 \sqrt{2}})$	None	✓	✓			1666.2.a.x	$1$	$0$	$4$	$4$	$8$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{2}+\beta _{3})q^{3}+q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots$
1666.2.a.z	$1666$	$2$	1666.a	1.a	$1$	$5$	$5$	$13.303$	5.5.23949216.1	None	✓		✓		238.2.e.f	$1$	$0$	$5$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots$
1666.2.a.ba	$1666$	$2$	1666.a	1.a	$1$	$5$	$5$	$13.303$	5.5.23949216.1	None	✓		✓		238.2.e.f	$1$	$0$	$5$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots$
1666.2.b.a	$1666$	$2$	1666.b	17.b	$2$	$2$	$2$	$13.303$	$\Q(\sqrt{-1}) $	None					238.2.j.a	$2$	$1$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+3 i q^{3}+q^{4}-3 i q^{6}-q^{8}+\cdots$
1666.2.b.b	$1666$	$2$	1666.b	17.b	$2$	$2$	$2$	$13.303$	$\Q(\sqrt{-1}) $	None					238.2.j.a	$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+3 i q^{3}+q^{4}-3 i q^{6}-q^{8}+\cdots$
1666.2.b.c	$1666$	$2$	1666.b	17.b	$2$	$2$	$2$	$13.303$	$\Q(\sqrt{-2}) $	None					34.2.b.a	$2$	$0$	$-2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-q^{8}+\cdots$
1666.2.b.d	$1666$	$2$	1666.b	17.b	$2$	$2$	$2$	$13.303$	$\Q(\sqrt{-1}) $	None					238.2.b.a	$2$	$0$	$-2$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}-q^{8}+3q^{9}-2q^{13}+q^{16}+\cdots$
1666.2.b.e	$1666$	$2$	1666.b	17.b	$2$	$2$	$2$	$13.303$	$\Q(\sqrt{-2}) $	None		✓			1666.2.b.e	$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{8}+\cdots$
1666.2.b.f	$1666$	$2$	1666.b	17.b	$2$	$2$	$2$	$13.303$	$\Q(\sqrt{-2}) $	None		✓			1666.2.b.e	$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{8}+\cdots$
1666.2.b.g	$1666$	$2$	1666.b	17.b	$2$	$4$	$4$	$13.303$	$\Q(\sqrt{-2}, \sqrt{15})$	None					238.2.j.b	$2$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{1}q^{5}+\beta _{2}q^{6}+\cdots$
1666.2.b.h	$1666$	$2$	1666.b	17.b	$2$	$4$	$4$	$13.303$	$\Q(\sqrt{-2}, \sqrt{15})$	None		✓			1666.2.b.h	$4$	$0$	$-4$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{5}+\beta _{1}q^{6}+\cdots$
1666.2.b.i	$1666$	$2$	1666.b	17.b	$2$	$4$	$4$	$13.303$	$\Q(\zeta_{8})$	None		✓			1666.2.b.i	$4$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+q^{4}+(\zeta_{8}+\cdots)q^{6}+\cdots$
1666.2.b.j	$1666$	$2$	1666.b	17.b	$2$	$4$	$4$	$13.303$	$\Q(\sqrt{-2}, \sqrt{15})$	None					238.2.j.b	$2$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\beta _{2}q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots$
1666.2.b.k	$1666$	$2$	1666.b	17.b	$2$	$6$	$6$	$13.303$	6.0.84345856.2	None					238.2.j.c	$2$	$0$	$6$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(\beta _{1}-\beta _{4})q^{3}+q^{4}+(-\beta _{1}-\beta _{5})q^{5}+\cdots$
1666.2.b.l	$1666$	$2$	1666.b	17.b	$2$	$6$	$6$	$13.303$	6.0.84345856.2	None					238.2.j.c	$2$	$0$	$6$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(\beta _{1}-\beta _{4})q^{3}+q^{4}+(-\beta _{1}-\beta _{5})q^{5}+\cdots$
1666.2.b.m	$1666$	$2$	1666.b	17.b	$2$	$6$	$6$	$13.303$	6.0.350464.1	None					238.2.b.b	$2$	$0$	$6$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{2}q^{3}+q^{4}+(\beta _{2}-\beta _{3}+\beta _{5})q^{5}+\cdots$
1666.2.b.n	$1666$	$2$	1666.b	17.b	$2$	$8$	$8$	$13.303$	8.0.$\cdots$.5	None		✓			1666.2.b.n	$4$	$0$	$-8$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{3}q^{3}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$
1666.2.b.o	$1666$	$2$	1666.b	17.b	$2$	$8$	$8$	$13.303$	8.0.$\cdots$.3	None		✓			1666.2.b.o	$4$	$0$	$8$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-\beta _{6}q^{3}+q^{4}-\beta _{2}q^{5}-\beta _{6}q^{6}+\cdots$
1666.4.a.a	$1666$	$4$	1666.a	1.a	$1$	$1$	$1$	$98.297$	$\Q$	None	✓				34.4.a.b	$1$	$0$	$-2$	$2$	$-16$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{3}+4q^{4}-2^{4}q^{5}-4q^{6}+\cdots$
1666.4.a.b	$1666$	$4$	1666.a	1.a	$1$	$1$	$1$	$98.297$	$\Q$	None	✓				34.4.a.a	$1$	$1$	$-2$	$2$	$18$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{3}+4q^{4}+18q^{5}-4q^{6}+\cdots$
1666.4.a.c	$1666$	$4$	1666.a	1.a	$1$	$2$	$2$	$98.297$	$\Q(\sqrt{93}) $	None	✓				238.4.a.a	$1$	$1$	$-4$	$5$	$-9$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(3-\beta )q^{3}+4q^{4}+(-4-\beta )q^{5}+\cdots$
1666.4.a.d	$1666$	$4$	1666.a	1.a	$1$	$2$	$2$	$98.297$	$\Q(\sqrt{13}) $	None	✓				34.4.a.c	$1$	$0$	$4$	$-6$	$4$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+2q^{2}+(-3-\beta )q^{3}+4q^{4}+(2+4\beta )q^{5}+\cdots$
1666.4.a.e	$1666$	$4$	1666.a	1.a	$1$	$2$	$2$	$98.297$	$\Q(\sqrt{69}) $	None	✓				238.4.a.b	$1$	$0$	$4$	$11$	$7$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(6-\beta )q^{3}+4q^{4}+(3+\beta )q^{5}+\cdots$
1666.4.a.f	$1666$	$4$	1666.a	1.a	$1$	$3$	$3$	$98.297$	3.3.48173.1	None	✓				238.4.a.d	$1$	$0$	$-6$	$-1$	$5$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}+(2-2\beta _{1}-\beta _{2})q^{5}+\cdots$
1666.4.a.g	$1666$	$4$	1666.a	1.a	$1$	$3$	$3$	$98.297$	3.3.69061.1	None	✓				238.4.a.c	$1$	$0$	$-6$	$5$	$21$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(2-\beta _{1})q^{3}+4q^{4}+(7+\beta _{2})q^{5}+\cdots$
1666.4.a.h	$1666$	$4$	1666.a	1.a	$1$	$3$	$3$	$98.297$	3.3.55029.1	None	✓				238.4.a.f	$1$	$1$	$6$	$-7$	$-19$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-2-\beta _{1})q^{3}+4q^{4}+(-7+\cdots)q^{5}+\cdots$

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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.