Newform search results

Note: Search results may be incomplete due to uncomputed quantities: Analytic rank (80 objects)

Results (1-50 of 567 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
122.2.b.a	$122$	$2$	122.b	61.b	$2$	$2$	$2$	$0.974$	\(\Q(\sqrt{-1}) \)	None		✓	122.2.b.a	$2$	$1$	\(0\)	\(-4\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-2q^{3}-q^{4}-3q^{5}-2iq^{6}+\cdots\)
258.2.d.a	$258$	$2$	258.d	129.d	$2$	$2$	$2$	$2.060$	\(\Q(\sqrt{-3}) \)	None		✓	258.2.d.a	$2$	$1$	\(-2\)	\(0\)	\(-6\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\zeta_{6}q^{3}+q^{4}-3q^{5}+\zeta_{6}q^{6}+\cdots\)
265.2.d.a	$265$	$2$	265.d	265.d	$2$	$4$	$4$	$2.116$	4.0.4400.1	None		✓	265.2.d.a	$2$	$1$	\(-2\)	\(-6\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{2})q^{2}+(-2+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
312.2.m.a	$312$	$2$	312.m	104.e	$2$	$2$	$2$	$2.491$	\(\Q(\sqrt{-1}) \)	None		✓	312.2.m.a	$2$	$1$	\(-2\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+i)q^{2}-iq^{3}-2iq^{4}-2q^{5}+\cdots\)
321.2.d.a	$321$	$2$	321.d	321.d	$2$	$4$	$4$	$2.563$	\(\Q(\sqrt{-2}, \sqrt{13})\)	None		✓	321.2.d.a	$2$	$1$	\(-2\)	\(-4\)	\(-12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+(-1+\beta _{2})q^{3}+(1+\beta _{3})q^{4}+\cdots\)
348.2.h.a	$348$	$2$	348.h	29.b	$2$	$2$	$2$	$2.779$	\(\Q(\sqrt{-1}) \)	None		✓	348.2.h.a	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-2q^{5}-3q^{7}-q^{9}-3iq^{11}+\cdots\)
360.2.k.a	$360$	$2$	360.k	8.b	$2$	$2$	$2$	$2.875$	\(\Q(\sqrt{-1}) \)	None		✓	360.2.k.a	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+i)q^{2}-2iq^{4}+iq^{5}-4q^{7}+\cdots\)
362.2.b.a	$362$	$2$	362.b	181.b	$2$	$2$	$2$	$2.891$	\(\Q(\sqrt{-1}) \)	None		✓	362.2.b.a	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{3}-q^{4}-iq^{6}-iq^{8}-2q^{9}+\cdots\)
369.2.d.a	$369$	$2$	369.d	41.b	$2$	$2$	$2$	$2.946$	\(\Q(\sqrt{-5}) \)	None		✓	369.2.d.a	$2$	$1$	\(-4\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{2}+2q^{4}-2q^{5}+2\beta q^{7}+4q^{10}+\cdots\)
372.2.c.a	$372$	$2$	372.c	12.b	$2$	$4$	$4$	$2.970$	\(\Q(\zeta_{8})\)	None		✓	372.2.c.a	$2$	$1$	\(-4\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\zeta_{8}^{2})q^{2}+(-1-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
390.2.e.a	$390$	$2$	390.e	5.b	$2$	$2$	$2$	$3.114$	\(\Q(\sqrt{-1}) \)	None		✓	390.2.e.a	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}+(-2-i)q^{5}+\cdots\)
399.2.c.a	$399$	$2$	399.c	133.c	$2$	$2$	$2$	$3.186$	\(\Q(\sqrt{-3}) \)	None		✓	399.2.c.a	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{2}-q^{3}-q^{4}+2\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots\)
408.2.f.a	$408$	$2$	408.f	8.b	$2$	$2$	$2$	$3.258$	\(\Q(\sqrt{-1}) \)	None		✓	408.2.f.a	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+i)q^{2}-iq^{3}-2iq^{4}+4iq^{5}+\cdots\)
408.2.h.a	$408$	$2$	408.h	408.h	$2$	$2$	$2$	$3.258$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		✓	408.2.h.a	$4$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}+(-1+\beta )q^{3}-2q^{4}+(-2+\cdots)q^{6}+\cdots\)
408.2.j.a	$408$	$2$	408.j	24.f	$2$	$4$	$4$	$3.258$	\(\Q(\zeta_{8})\)	None		✓	408.2.j.a	$2$	$1$	\(-4\)	\(-4\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{8}^{2})q^{2}+(-1-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
416.2.f.a	$416$	$2$	416.f	13.b	$2$	$2$	$2$	$3.322$	\(\Q(\sqrt{-1}) \)	None		✓	416.2.f.a	$2$	$1$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{3}+3iq^{5}-iq^{7}+6q^{9}+4iq^{11}+\cdots\)
423.2.c.a	$423$	$2$	423.c	141.c	$2$	$4$	$4$	$3.378$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None		✓	423.2.c.a	$2$	$1$	\(0\)	\(0\)	\(-12\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{3})q^{4}-3q^{5}+(-2+\cdots)q^{7}+\cdots\)
435.2.f.b	$435$	$2$	435.f	145.d	$2$	$2$	$2$	$3.473$	\(\Q(\sqrt{-1}) \)	None		✓	435.2.f.b	$2$	$1$	\(-2\)	\(-2\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-q^{3}-q^{4}+(-1+i)q^{5}+q^{6}+\cdots\)
440.2.l.a	$440$	$2$	440.l	40.f	$2$	$2$	$2$	$3.513$	\(\Q(\sqrt{-1}) \)	None		✓	440.2.l.a	$2$	$1$	\(-2\)	\(-4\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+i)q^{2}-2q^{3}-2iq^{4}+(-1+\cdots)q^{5}+\cdots\)
448.2.f.a	$448$	$2$	448.f	28.d	$2$	$2$	$2$	$3.577$	\(\Q(\sqrt{-3}) \)	None			112.2.f.a	$2$	$1$	\(0\)	\(-4\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{3}-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+q^{9}+\cdots\)
464.2.e.a	$464$	$2$	464.e	29.b	$2$	$2$	$2$	$3.705$	\(\Q(\sqrt{-5}) \)	None			29.2.b.a	$2$	$1$	\(0\)	\(0\)	\(-6\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-3q^{5}-2q^{7}-2q^{9}-\beta q^{11}+\cdots\)
470.2.c.b	$470$	$2$	470.c	5.b	$2$	$2$	$2$	$3.753$	\(\Q(\sqrt{-1}) \)	None		✓	470.2.c.b	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-3iq^{3}-q^{4}+(-2-i)q^{5}+\cdots\)
480.2.f.a	$480$	$2$	480.f	5.b	$2$	$2$	$2$	$3.833$	\(\Q(\sqrt{-1}) \)	None		✓	480.2.f.a	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(-2+i)q^{5}-2iq^{7}-q^{9}+\cdots\)
532.2.f.a	$532$	$2$	532.f	28.d	$2$	$4$	$4$	$4.248$	\(\Q(i, \sqrt{5})\)	None		✓	532.2.f.a	$2$	$1$	\(-4\)	\(-6\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{3})q^{2}+(-1+\beta _{2})q^{3}-2\beta _{3}q^{4}+\cdots\)
552.2.j.a	$552$	$2$	552.j	24.f	$2$	$2$	$2$	$4.408$	\(\Q(\sqrt{-2}) \)	None		✓	552.2.j.a	$2$	$1$	\(0\)	\(-2\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(-1+\beta )q^{3}-2q^{4}-4q^{5}+\cdots\)
560.2.g.a	$560$	$2$	560.g	5.b	$2$	$2$	$2$	$4.472$	\(\Q(\sqrt{-1}) \)	None			140.2.e.a	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+(-2-i)q^{5}-iq^{7}-6q^{9}+\cdots\)
568.2.c.b	$568$	$2$	568.c	8.b	$2$	$2$	$2$	$4.536$	\(\Q(\sqrt{-1}) \)	None		✓	568.2.c.b	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+i)q^{2}-3iq^{3}-2iq^{4}+(3+\cdots)q^{6}+\cdots\)
585.2.h.b	$585$	$2$	585.h	65.d	$2$	$2$	$2$	$4.671$	\(\Q(\sqrt{-1}) \)	None			65.2.d.a	$2$	$1$	\(-2\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-q^{4}+(-1-i)q^{5}+3q^{8}+(1+\cdots)q^{10}+\cdots\)
592.2.g.a	$592$	$2$	592.g	37.b	$2$	$2$	$2$	$4.727$	\(\Q(\sqrt{-3}) \)	None			148.2.d.a	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\zeta_{6}q^{5}-q^{7}-2q^{9}-3q^{11}+\cdots\)
616.2.l.b	$616$	$2$	616.l	88.g	$2$	$2$	$2$	$4.919$	\(\Q(\sqrt{-2}) \)	None		✓	616.2.l.a	$2$	$1$	\(0\)	\(-4\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}-2q^{3}-2q^{4}-2\beta q^{5}+2\beta q^{6}+\cdots\)
616.2.o.a	$616$	$2$	616.o	616.o	$2$	$2$	$2$	$4.919$	\(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{-7}) \)		✓	616.2.o.a	$4$	$1$	\(-1\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{2}+(-2+\beta )q^{4}+(1-2\beta )q^{7}+\cdots\)
624.2.n.a	$624$	$2$	624.n	156.h	$2$	$2$	$2$	$4.983$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		✓	624.2.n.a	$4$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{6}q^{3}-4q^{7}-3q^{9}+(1+2\zeta_{6})q^{13}+\cdots\)
630.2.g.b	$630$	$2$	630.g	5.b	$2$	$2$	$2$	$5.031$	\(\Q(\sqrt{-1}) \)	None		✓	630.2.g.b	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(-1+2i)q^{5}-iq^{7}+\cdots\)
637.2.c.a	$637$	$2$	637.c	13.b	$2$	$2$	$2$	$5.086$	\(\Q(\sqrt{-1}) \)	None		✓	637.2.c.a	$2$	$1$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-2q^{3}-2q^{4}+iq^{5}-4iq^{6}+\cdots\)
640.2.f.a	$640$	$2$	640.f	40.f	$2$	$2$	$2$	$5.110$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓	640.2.f.a	$4$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1+i)q^{5}-3q^{9}-6q^{13}-4iq^{17}+\cdots\)
648.2.d.b	$648$	$2$	648.d	8.b	$2$	$2$	$2$	$5.174$	\(\Q(\sqrt{-7}) \)	None		✓	648.2.d.b	$2$	$1$	\(-1\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}+(-2+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots\)
688.2.g.a	$688$	$2$	688.g	172.d	$2$	$2$	$2$	$5.494$	\(\Q(\sqrt{-3}) \)	None		✓	688.2.g.a	$2$	$1$	\(0\)	\(-4\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{3}-2\zeta_{6}q^{5}-2q^{7}+q^{9}-\zeta_{6}q^{11}+\cdots\)
689.2.c.a	$689$	$2$	689.c	13.b	$2$	$2$	$2$	$5.502$	\(\Q(\sqrt{-3}) \)	None		✓	689.2.c.a	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-2\zeta_{6})q^{2}-q^{3}-q^{4}+(-2+4\zeta_{6})q^{5}+\cdots\)
700.2.c.b	$700$	$2$	700.c	140.c	$2$	$4$	$4$	$5.590$	\(\Q(\zeta_{12})\)	None			140.2.g.a	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{12}^{3})q^{2}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
704.2.e.a	$704$	$2$	704.e	44.c	$2$	$2$	$2$	$5.621$	\(\Q(\sqrt{-11}) \)	\(\Q(\sqrt{-11}) \)			176.2.e.a	$4$	$1$	\(0\)	\(0\)	\(-6\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{3}-3q^{5}-8q^{9}+\beta q^{11}+3\beta q^{15}+\cdots\)
720.2.f.a	$720$	$2$	720.f	5.b	$2$	$2$	$2$	$5.749$	\(\Q(\sqrt{-1}) \)	None			360.2.f.b	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+i)q^{5}+4iq^{7}-4q^{11}-4iq^{13}+\cdots\)
768.2.c.a	$768$	$2$	768.c	12.b	$2$	$2$	$2$	$6.133$	\(\Q(\sqrt{-2}) \)	None			384.2.f.b	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta )q^{3}+2\beta q^{5}-2\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
768.2.d.a	$768$	$2$	768.d	8.b	$2$	$2$	$2$	$6.133$	\(\Q(\sqrt{-1}) \)	None			96.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{5}-4q^{7}-q^{9}-4iq^{11}+\cdots\)
784.2.f.a	$784$	$2$	784.f	28.d	$2$	$2$	$2$	$6.260$	\(\Q(\sqrt{-3}) \)	None			112.2.p.a	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\zeta_{6}q^{5}-2q^{9}-\zeta_{6}q^{11}-\zeta_{6}q^{15}+\cdots\)
800.2.d.a	$800$	$2$	800.d	8.b	$2$	$2$	$2$	$6.388$	\(\Q(\sqrt{-7}) \)	None			200.2.d.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}-4q^{7}-4q^{9}+\beta q^{11}-3q^{17}+\cdots\)
801.2.d.b	$801$	$2$	801.d	89.b	$2$	$6$	$6$	$6.396$	6.0.96878912.1	None		✓	801.2.d.b	$2$	$1$	\(-4\)	\(0\)	\(-10\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{4})q^{2}+(2-\beta _{2}+\beta _{4})q^{4}+\cdots\)
810.2.c.b	$810$	$2$	810.c	5.b	$2$	$2$	$2$	$6.468$	\(\Q(\sqrt{-1}) \)	None			90.2.i.a	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+(-1+2i)q^{5}+iq^{7}+\cdots\)
840.2.e.a	$840$	$2$	840.e	24.f	$2$	$4$	$4$	$6.707$	\(\Q(\zeta_{8})\)	None		✓	840.2.e.a	$2$	$1$	\(-4\)	\(-4\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\zeta_{8})q^{2}+(-1+\zeta_{8}^{2})q^{3}-2\zeta_{8}q^{4}+\cdots\)
840.2.j.a	$840$	$2$	840.j	40.f	$2$	$2$	$2$	$6.707$	\(\Q(\sqrt{-1}) \)	None		✓	840.2.j.a	$2$	$1$	\(-2\)	\(-2\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-i)q^{2}-q^{3}+2iq^{4}+(-2+\cdots)q^{5}+\cdots\)
840.2.j.b	$840$	$2$	840.j	40.f	$2$	$2$	$2$	$6.707$	\(\Q(\sqrt{-1}) \)	None		✓	840.2.j.b	$2$	$1$	\(-2\)	\(2\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+i)q^{2}+q^{3}-2iq^{4}+(-2+\cdots)q^{5}+\cdots\)