LMFDB - Newform search results

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is twist minimal	Is self-dual

$Nk^2$	Coefficient ring index	Coefficient ring gens.	Projective image	Projective image type

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Results (1-50 of 90 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	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	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2366.2.a.a	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	$\Q$	None	✓		182.2.g.c	$1$	$2$	$-1$	$-2$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-3q^{5}+2q^{6}+q^{7}+\cdots$
2366.2.a.b	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	$\Q$	None	✓		182.2.g.d	$1$	$1$	$-1$	$-2$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-q^{7}+\cdots$
2366.2.a.c	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	$\Q$	None	✓		182.2.d.a	$1$	$1$	$-1$	$-1$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots$
2366.2.a.d	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	$\Q$	None	✓		182.2.a.c	$1$	$0$	$-1$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}-3q^{9}+\cdots$
2366.2.a.e	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	$\Q$	None	✓		182.2.a.d	$1$	$1$	$-1$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
2366.2.a.f	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	$\Q$	None	✓		182.2.g.b	$1$	$0$	$-1$	$1$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+q^{7}+\cdots$
2366.2.a.g	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	$\Q$	None	✓		182.2.g.a	$1$	$0$	$-1$	$3$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-3q^{5}-3q^{6}+q^{7}+\cdots$
2366.2.a.h	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	$\Q$	None	✓		182.2.a.e	$1$	$0$	$-1$	$3$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}+4q^{5}-3q^{6}+q^{7}+\cdots$
2366.2.a.i	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	$\Q$	None	✓		182.2.g.d	$1$	$1$	$1$	$-2$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{7}+\cdots$
2366.2.a.j	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	$\Q$	None	✓		14.2.a.a	$1$	$0$	$1$	$-2$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots$
2366.2.a.k	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	$\Q$	None	✓		182.2.g.c	$1$	$0$	$1$	$-2$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}+3q^{5}-2q^{6}-q^{7}+\cdots$
2366.2.a.l	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	$\Q$	None	✓		182.2.d.a	$1$	$1$	$1$	$-1$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-q^{7}+\cdots$
2366.2.a.m	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	$\Q$	None	✓		182.2.a.a	$1$	$1$	$1$	$1$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}+q^{7}+\cdots$
2366.2.a.n	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	$\Q$	None	✓		182.2.g.b	$1$	$0$	$1$	$1$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots$
2366.2.a.o	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	$\Q$	None	✓		182.2.a.b	$1$	$0$	$1$	$3$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+3q^{6}-q^{7}+q^{8}+\cdots$
2366.2.a.p	$2366$	$2$	2366.a	1.a	$1$	$1$	$1$	$18.893$	$\Q$	None	✓		182.2.g.a	$1$	$0$	$1$	$3$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+3q^{5}+3q^{6}-q^{7}+\cdots$
2366.2.a.q	$2366$	$2$	2366.a	1.a	$1$	$2$	$2$	$18.893$	$\Q(\sqrt{3}) $	None	✓		182.2.m.a	$1$	$1$	$-2$	$-2$	$2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots$
2366.2.a.r	$2366$	$2$	2366.a	1.a	$1$	$2$	$2$	$18.893$	$\Q(\sqrt{3}) $	None	✓		182.2.g.e	$1$	$0$	$-2$	$0$	$-4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}+(-2-\beta )q^{5}-\beta q^{6}+\cdots$
2366.2.a.s	$2366$	$2$	2366.a	1.a	$1$	$2$	$2$	$18.893$	$\Q(\sqrt{3}) $	None	✓		182.2.m.a	$1$	$1$	$2$	$-2$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots$
2366.2.a.t	$2366$	$2$	2366.a	1.a	$1$	$2$	$2$	$18.893$	$\Q(\sqrt{3}) $	None	✓		182.2.g.e	$1$	$0$	$2$	$0$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+(2+\beta )q^{5}+\beta q^{6}+\cdots$
2366.2.a.u	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	$\Q(\zeta_{14})^+$	None	✓	✓	2366.2.a.u	$1$	$0$	$-3$	$-5$	$-2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-2-\beta _{2})q^{3}+q^{4}-2\beta _{1}q^{5}+\cdots$
2366.2.a.v	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	$\Q(\zeta_{14})^+$	None	✓	✓	2366.2.a.v	$1$	$0$	$-3$	$-4$	$-2$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
2366.2.a.w	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	$\Q(\zeta_{14})^+$	None	✓	✓	2366.2.a.w	$1$	$0$	$-3$	$0$	$8$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-\beta _{1}-\beta _{2})q^{3}+q^{4}+(3+\beta _{2})q^{5}+\cdots$
2366.2.a.x	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	3.3.1384.1	None	✓		182.2.d.b	$1$	$0$	$-3$	$1$	$-2$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots$
2366.2.a.y	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	$\Q(\zeta_{14})^+$	None	✓	✓	2366.2.a.y	$1$	$1$	$-3$	$2$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\beta _{2})q^{5}+\cdots$
2366.2.a.z	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	$\Q(\zeta_{14})^+$	None	✓	✓	2366.2.a.u	$1$	$1$	$3$	$-5$	$2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-2-\beta _{2})q^{3}+q^{4}+2\beta _{1}q^{5}+\cdots$
2366.2.a.ba	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	$\Q(\zeta_{14})^+$	None	✓	✓	2366.2.a.v	$1$	$1$	$3$	$-4$	$2$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
2366.2.a.bb	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	$\Q(\zeta_{14})^+$	None	✓	✓	2366.2.a.w	$1$	$1$	$3$	$0$	$-8$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-\beta _{1}-\beta _{2})q^{3}+q^{4}+(-3+\cdots)q^{5}+\cdots$
2366.2.a.bc	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	3.3.1384.1	None	✓		182.2.d.b	$1$	$0$	$3$	$1$	$2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{2})q^{5}+\beta _{1}q^{6}+\cdots$
2366.2.a.bd	$2366$	$2$	2366.a	1.a	$1$	$3$	$3$	$18.893$	$\Q(\zeta_{14})^+$	None	✓	✓	2366.2.a.y	$1$	$0$	$3$	$2$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots$
2366.2.a.be	$2366$	$2$	2366.a	1.a	$1$	$6$	$6$	$18.893$	6.6.6052921.1	None	✓	✓	2366.2.a.be	$1$	$1$	$-6$	$1$	$-4$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{4})q^{5}+\cdots$
2366.2.a.bf	$2366$	$2$	2366.a	1.a	$1$	$6$	$6$	$18.893$	6.6.285686784.1	None	✓		182.2.m.b	$1$	$0$	$-6$	$2$	$2$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{1}+\beta _{5})q^{5}+\cdots$
2366.2.a.bg	$2366$	$2$	2366.a	1.a	$1$	$6$	$6$	$18.893$	6.6.6052921.1	None	✓	✓	2366.2.a.be	$1$	$0$	$6$	$1$	$4$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{4})q^{5}+\beta _{1}q^{6}+\cdots$
2366.2.a.bh	$2366$	$2$	2366.a	1.a	$1$	$6$	$6$	$18.893$	6.6.285686784.1	None	✓		182.2.m.b	$1$	$0$	$6$	$2$	$-2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{5})q^{5}+\cdots$
2366.2.d.a	$2366$	$2$	2366.d	13.b	$2$	$2$	$2$	$18.893$	$\Q(\sqrt{-1}) $	None			182.2.g.c	$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-2q^{3}-q^{4}-3iq^{5}+2iq^{6}+\cdots$
2366.2.d.b	$2366$	$2$	2366.d	13.b	$2$	$2$	$2$	$18.893$	$\Q(\sqrt{-1}) $	None			14.2.a.a	$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-2q^{3}-q^{4}+2iq^{6}-iq^{7}+\cdots$
2366.2.d.c	$2366$	$2$	2366.d	13.b	$2$	$2$	$2$	$18.893$	$\Q(\sqrt{-1}) $	None			182.2.g.d	$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-2q^{3}-q^{4}+iq^{5}+2iq^{6}+\cdots$
2366.2.d.d	$2366$	$2$	2366.d	13.b	$2$	$2$	$2$	$18.893$	$\Q(\sqrt{-1}) $	None			182.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-q^{4}-2iq^{5}-iq^{7}+iq^{8}+\cdots$
2366.2.d.e	$2366$	$2$	2366.d	13.b	$2$	$2$	$2$	$18.893$	$\Q(\sqrt{-1}) $	None			182.2.a.d	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{3}-q^{4}+iq^{6}-iq^{7}-iq^{8}+\cdots$
2366.2.d.f	$2366$	$2$	2366.d	13.b	$2$	$2$	$2$	$18.893$	$\Q(\sqrt{-1}) $	None			182.2.g.b	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{3}-q^{4}-3iq^{5}+iq^{6}+\cdots$
2366.2.d.g	$2366$	$2$	2366.d	13.b	$2$	$2$	$2$	$18.893$	$\Q(\sqrt{-1}) $	None			182.2.a.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{3}-q^{4}-4iq^{5}+iq^{6}+\cdots$
2366.2.d.h	$2366$	$2$	2366.d	13.b	$2$	$2$	$2$	$18.893$	$\Q(\sqrt{-1}) $	None			182.2.g.a	$2$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}+3q^{3}-q^{4}-3iq^{5}-3iq^{6}+\cdots$
2366.2.d.i	$2366$	$2$	2366.d	13.b	$2$	$2$	$2$	$18.893$	$\Q(\sqrt{-1}) $	None			182.2.a.b	$2$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}+3q^{3}-q^{4}-3iq^{6}-iq^{7}+\cdots$
2366.2.d.j	$2366$	$2$	2366.d	13.b	$2$	$2$	$2$	$18.893$	$\Q(\sqrt{-1}) $	None			182.2.a.e	$2$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}+3q^{3}-q^{4}+4iq^{5}-3iq^{6}+\cdots$
2366.2.d.k	$2366$	$2$	2366.d	13.b	$2$	$4$	$4$	$18.893$	$\Q(\zeta_{12})$	None			182.2.m.a	$2$	$0$	$0$	$-4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{12}q^{2}+(-1+\zeta_{12}^{3})q^{3}-q^{4}+\cdots$
2366.2.d.l	$2366$	$2$	2366.d	13.b	$2$	$4$	$4$	$18.893$	$\Q(\zeta_{12})$	None			182.2.g.e	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}-q^{4}+(2\zeta_{12}+\cdots)q^{5}+\cdots$
2366.2.d.m	$2366$	$2$	2366.d	13.b	$2$	$6$	$6$	$18.893$	6.0.153664.1	None		✓	2366.2.a.u	$2$	$0$	$0$	$-10$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(-2+\beta _{4})q^{3}-q^{4}-2\beta _{3}q^{5}+\cdots$
2366.2.d.n	$2366$	$2$	2366.d	13.b	$2$	$6$	$6$	$18.893$	6.0.153664.1	None		✓	2366.2.a.v	$2$	$0$	$0$	$-8$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(-1-\beta _{2})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
2366.2.d.o	$2366$	$2$	2366.d	13.b	$2$	$6$	$6$	$18.893$	6.0.153664.1	None		✓	2366.2.a.w	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(-1+\beta _{2}+2\beta _{4})q^{3}-q^{4}+\cdots$
2366.2.d.p	$2366$	$2$	2366.d	13.b	$2$	$6$	$6$	$18.893$	6.0.153664.1	None		✓	2366.2.a.y	$2$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(1-\beta _{4})q^{3}-q^{4}+(2\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$

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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.