LMFDB - Newform search results

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Level	Weight	Analytic conductor	$Nk^2$	Dim.

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

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

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 207 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1170.2.a.a	$1170$	$2$	1170.a	1.a	$1$	$1$	$1$	$9.342$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots$
1170.2.a.b	$1170$	$2$	1170.a	1.a	$1$	$1$	$1$	$9.342$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+q^{13}+\cdots$
1170.2.a.c	$1170$	$2$	1170.a	1.a	$1$	$1$	$1$	$9.342$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots$
1170.2.a.d	$1170$	$2$	1170.a	1.a	$1$	$1$	$1$	$9.342$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots$
1170.2.a.e	$1170$	$2$	1170.a	1.a	$1$	$1$	$1$	$9.342$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots$
1170.2.a.f	$1170$	$2$	1170.a	1.a	$1$	$1$	$1$	$9.342$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots$
1170.2.a.g	$1170$	$2$	1170.a	1.a	$1$	$1$	$1$	$9.342$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots$
1170.2.a.h	$1170$	$2$	1170.a	1.a	$1$	$1$	$1$	$9.342$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots$
1170.2.a.i	$1170$	$2$	1170.a	1.a	$1$	$1$	$1$	$9.342$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots$
1170.2.a.j	$1170$	$2$	1170.a	1.a	$1$	$1$	$1$	$9.342$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots$
1170.2.a.k	$1170$	$2$	1170.a	1.a	$1$	$1$	$1$	$9.342$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots$
1170.2.a.l	$1170$	$2$	1170.a	1.a	$1$	$1$	$1$	$9.342$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots$
1170.2.a.m	$1170$	$2$	1170.a	1.a	$1$	$1$	$1$	$9.342$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-q^{13}+\cdots$
1170.2.a.n	$1170$	$2$	1170.a	1.a	$1$	$1$	$1$	$9.342$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}+q^{10}+\cdots$
1170.2.a.o	$1170$	$2$	1170.a	1.a	$1$	$2$	$2$	$9.342$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$0$	$-2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+\beta q^{7}-q^{8}+q^{10}+\cdots$
1170.2.a.p	$1170$	$2$	1170.a	1.a	$1$	$2$	$2$	$9.342$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$-2$	$0$	$-2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+(1+\beta )q^{7}-q^{8}+\cdots$
1170.2.a.q	$1170$	$2$	1170.a	1.a	$1$	$2$	$2$	$9.342$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$2$	$0$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+(1+\beta )q^{7}+q^{8}+\cdots$
1170.2.b.a	$1170$	$2$	1170.b	13.b	$2$	$2$	$2$	$9.342$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}+iq^{5}-iq^{8}-q^{10}+\cdots$
1170.2.b.b	$1170$	$2$	1170.b	13.b	$2$	$2$	$2$	$9.342$	$\Q(\sqrt{-1}) $	None		$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}-iq^{5}-iq^{8}+q^{10}+\cdots$
1170.2.b.c	$1170$	$2$	1170.b	13.b	$2$	$2$	$2$	$9.342$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-q^{4}+iq^{5}+iq^{8}+q^{10}+\cdots$
1170.2.b.d	$1170$	$2$	1170.b	13.b	$2$	$4$	$4$	$9.342$	$\Q(i, \sqrt{13})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-q^{4}-\beta _{1}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
1170.2.b.e	$1170$	$2$	1170.b	13.b	$2$	$4$	$4$	$9.342$	$\Q(\zeta_{12})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{12}q^{2}-q^{4}-\zeta_{12}q^{5}-\zeta_{12}q^{8}+\cdots$
1170.2.b.f	$1170$	$2$	1170.b	13.b	$2$	$4$	$4$	$9.342$	$\Q(i, \sqrt{17})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{4}-\beta _{1}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
1170.2.b.g	$1170$	$2$	1170.b	13.b	$2$	$8$	$8$	$9.342$	8.0.3057647616.6	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-q^{4}-\beta _{1}q^{5}-\beta _{7}q^{7}+\beta _{1}q^{8}+\cdots$
1170.2.e.a	$1170$	$2$	1170.e	5.b	$2$	$2$	$2$	$9.342$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-q^{4}+(-2-i)q^{5}+2iq^{7}+\cdots$
1170.2.e.b	$1170$	$2$	1170.e	5.b	$2$	$2$	$2$	$9.342$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-q^{4}+(-2+i)q^{5}+4iq^{7}+\cdots$
1170.2.e.c	$1170$	$2$	1170.e	5.b	$2$	$2$	$2$	$9.342$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}+(-2-i)q^{5}+4iq^{7}+\cdots$
1170.2.e.d	$1170$	$2$	1170.e	5.b	$2$	$2$	$2$	$9.342$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-q^{4}+(2+i)q^{5}+iq^{8}+(1+\cdots)q^{10}+\cdots$
1170.2.e.e	$1170$	$2$	1170.e	5.b	$2$	$4$	$4$	$9.342$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
1170.2.e.f	$1170$	$2$	1170.e	5.b	$2$	$6$	$6$	$9.342$	6.0.3534400.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}-q^{4}+(-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots$
1170.2.e.g	$1170$	$2$	1170.e	5.b	$2$	$6$	$6$	$9.342$	6.0.350464.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}-q^{4}+(-\beta _{2}+\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
1170.2.e.h	$1170$	$2$	1170.e	5.b	$2$	$6$	$6$	$9.342$	6.0.350464.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-q^{4}+(\beta _{2}-\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
1170.2.f.a	$1170$	$2$	1170.f	65.d	$2$	$4$	$4$	$9.342$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		$2$	$0$	$-4$	$0$	$3$	$-2$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+(1+\beta _{1})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
1170.2.f.b	$1170$	$2$	1170.f	65.d	$2$	$4$	$4$	$9.342$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		$2$	$0$	$4$	$0$	$-3$	$2$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+(-1-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
1170.2.f.c	$1170$	$2$	1170.f	65.d	$2$	$6$	$6$	$9.342$	6.0.350464.1	None		$2$	$0$	$-6$	$0$	$-2$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots$
1170.2.f.d	$1170$	$2$	1170.f	65.d	$2$	$6$	$6$	$9.342$	6.0.350464.1	None		$2$	$0$	$6$	$0$	$2$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+(\beta _{1}-\beta _{3})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots$
1170.2.f.e	$1170$	$2$	1170.f	65.d	$2$	$8$	$8$	$9.342$	8.0.$\cdots$.15	None		$4$	$0$	$-8$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+\beta _{5}q^{5}-\beta _{4}q^{7}-q^{8}+\cdots$
1170.2.f.f	$1170$	$2$	1170.f	65.d	$2$	$8$	$8$	$9.342$	8.0.$\cdots$.15	None		$4$	$0$	$8$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}-\beta _{5}q^{5}-\beta _{4}q^{7}+q^{8}+\cdots$
1170.2.i.a	$1170$	$2$	1170.i	13.c	$3$	$2$	$1$	$9.342$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+2\zeta_{6}q^{7}+\cdots$
1170.2.i.b	$1170$	$2$	1170.i	13.c	$3$	$2$	$1$	$9.342$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+4\zeta_{6}q^{7}+\cdots$
1170.2.i.c	$1170$	$2$	1170.i	13.c	$3$	$2$	$1$	$9.342$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$2$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}-3\zeta_{6}q^{7}+\cdots$
1170.2.i.d	$1170$	$2$	1170.i	13.c	$3$	$2$	$1$	$9.342$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}-2\zeta_{6}q^{7}+\cdots$
1170.2.i.e	$1170$	$2$	1170.i	13.c	$3$	$2$	$1$	$9.342$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+q^{8}+\cdots$
1170.2.i.f	$1170$	$2$	1170.i	13.c	$3$	$2$	$1$	$9.342$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+\zeta_{6}q^{7}+\cdots$
1170.2.i.g	$1170$	$2$	1170.i	13.c	$3$	$2$	$1$	$9.342$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$2$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+5\zeta_{6}q^{7}+\cdots$
1170.2.i.h	$1170$	$2$	1170.i	13.c	$3$	$2$	$1$	$9.342$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}-q^{8}+(-1+\cdots)q^{10}+\cdots$
1170.2.i.i	$1170$	$2$	1170.i	13.c	$3$	$2$	$1$	$9.342$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$-2$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+3\zeta_{6}q^{7}+\cdots$
1170.2.i.j	$1170$	$2$	1170.i	13.c	$3$	$2$	$1$	$9.342$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$-2$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+3\zeta_{6}q^{7}+\cdots$
1170.2.i.k	$1170$	$2$	1170.i	13.c	$3$	$2$	$1$	$9.342$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}-2\zeta_{6}q^{7}+\cdots$
1170.2.i.l	$1170$	$2$	1170.i	13.c	$3$	$2$	$1$	$9.342$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+4\zeta_{6}q^{7}+\cdots$

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