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Results (1-50 of 41828 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
47.1.b.a	$47$	$1$	47.b	47.b	$2$	$2$	$2$	$0.023$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-47}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots\)
52.1.j.a	$52$	$1$	52.j	52.j	$6$	$2$	$1$	$0.026$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)
57.1.h.a	$57$	$1$	57.h	57.h	$6$	$2$	$1$	$0.028$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)	$1$		\(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{7}-\zeta_{6}q^{9}+q^{12}+\cdots\)
68.1.f.a	$68$	$1$	68.f	68.f	$4$	$2$	$1$	$0.034$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots\)
72.1.p.a	$72$	$1$	72.p	72.p	$6$	$2$	$1$	$0.036$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(-1\)	\(-1\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots\)
79.1.b.a	$79$	$1$	79.b	79.b	$2$	$2$	$2$	$0.039$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-79}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{5}-q^{8}+\cdots\)
84.1.p.a	$84$	$1$	84.p	21.h	$6$	$2$	$1$	$0.042$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots\)
95.1.d.b	$95$	$1$	95.d	95.d	$2$	$2$	$2$	$0.047$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-95}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-\beta q^{2}+\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\cdots\)
99.1.h.a	$99$	$1$	99.h	99.h	$6$	$2$	$1$	$0.049$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\cdots\)
103.1.b.a	$103$	$1$	103.b	103.b	$2$	$2$	$2$	$0.051$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-103}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{7}-q^{8}+\cdots\)
111.1.d.b	$111$	$1$	111.d	111.d	$2$	$2$	$2$	$0.055$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-111}) \)	None	✓	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}-q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{9}+\cdots\)
111.1.h.a	$111$	$1$	111.h	111.h	$6$	$2$	$1$	$0.055$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q-\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
111.1.i.a	$111$	$1$	111.i	111.i	$6$	$2$	$1$	$0.055$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)	$1$		\(q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
112.1.l.a	$112$	$1$	112.l	112.l	$4$	$2$	$1$	$0.056$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-iq^{9}+\cdots\)
117.1.j.a	$117$	$1$	117.j	13.d	$4$	$2$	$1$	$0.058$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+iq^{4}+(-1-i)q^{7}-iq^{13}-q^{16}+\cdots\)
119.1.d.a	$119$	$1$	119.d	119.d	$2$	$2$	$2$	$0.059$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-119}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(-1\)	\(2\)	$1$		\(q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots\)
119.1.d.b	$119$	$1$	119.d	119.d	$2$	$2$	$2$	$0.059$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-119}) \)	None	✓	$2$	$0$	\(-1\)	\(1\)	\(1\)	\(-2\)	$1$		\(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-\beta )q^{4}+\cdots\)
120.1.i.a	$120$	$1$	120.i	120.i	$2$	$2$	$2$	$0.060$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{10}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{2}-iq^{3}-q^{4}+iq^{5}-q^{6}+iq^{8}+\cdots\)
127.1.b.a	$127$	$1$	127.b	127.b	$2$	$2$	$2$	$0.063$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-127}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-1+\beta )q^{2}+(1-\beta )q^{4}-q^{8}+q^{9}+\cdots\)
131.1.b.a	$131$	$1$	131.b	131.b	$2$	$2$	$2$	$0.065$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-131}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)	$1$		\(q+(-1+\beta )q^{3}+q^{4}-\beta q^{5}-\beta q^{7}+\cdots\)
133.1.r.a	$133$	$1$	133.r	133.r	$6$	$2$	$1$	$0.066$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-19}) \)	None		$4$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)	$1$		\(q-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
136.1.j.a	$136$	$1$	136.j	136.j	$4$	$2$	$1$	$0.068$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-iq^{2}+(-1-i)q^{3}-q^{4}+(-1+i+\cdots)q^{6}+\cdots\)
140.1.p.a	$140$	$1$	140.p	140.p	$6$	$2$	$1$	$0.070$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-5}) \)	None		$4$	$0$	\(-1\)	\(1\)	\(-1\)	\(-1\)	$1$		\(q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots\)
140.1.p.b	$140$	$1$	140.p	140.p	$6$	$2$	$1$	$0.070$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-5}) \)	None		$4$	$0$	\(1\)	\(-1\)	\(-1\)	\(1\)	$1$		\(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots\)
143.1.d.a	$143$	$1$	143.d	143.d	$2$	$2$	$2$	$0.071$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-143}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots\)
143.1.d.b	$143$	$1$	143.d	143.d	$2$	$2$	$2$	$0.071$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-143}) \)	None	✓	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(1\)	$1$		\(q+(1-\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots\)
145.1.f.a	$145$	$1$	145.f	145.f	$4$	$2$	$1$	$0.072$	\(\Q(\sqrt{-1}) \)	$D_{4}$	None	\(\Q(\sqrt{5}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+iq^{4}-iq^{5}+iq^{9}+(-1-i)q^{11}+\cdots\)
145.1.h.a	$145$	$1$	145.h	145.h	$4$	$2$	$1$	$0.072$	\(\Q(\sqrt{-1}) \)	$D_{4}$	None	\(\Q(\sqrt{29}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-iq^{4}-iq^{5}+(-1+i)q^{7}+iq^{9}+\cdots\)
148.1.f.a	$148$	$1$	148.f	37.d	$4$	$2$	$1$	$0.074$	\(\Q(\sqrt{-1}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+iq^{3}-q^{7}-iq^{11}+(-1-i)q^{17}+\cdots\)
148.1.i.a	$148$	$1$	148.i	148.i	$6$	$2$	$1$	$0.074$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)
152.1.k.a	$152$	$1$	152.k	152.k	$6$	$2$	$1$	$0.076$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
155.1.c.b	$155$	$1$	155.c	155.c	$2$	$2$	$2$	$0.077$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-31}) \)	None		$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots\)
156.1.o.a	$156$	$1$	156.o	39.i	$6$	$2$	$1$	$0.078$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)	$1$		\(q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{13}+\cdots\)
156.1.s.a	$156$	$1$	156.s	39.h	$6$	$2$	$1$	$0.078$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(1\)	\(0\)	\(-3\)	$1$		\(q+\zeta_{6}q^{3}+(-1-\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
159.1.d.a	$159$	$1$	159.d	159.d	$2$	$2$	$2$	$0.079$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-159}) \)	None	✓	$2$	$0$	\(-1\)	\(2\)	\(-1\)	\(-1\)	$1$		\(q+(-1+\beta )q^{2}+q^{3}+(1-\beta )q^{4}-\beta q^{5}+\cdots\)
159.1.d.b	$159$	$1$	159.d	159.d	$2$	$2$	$2$	$0.079$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-159}) \)	None	✓	$2$	$0$	\(1\)	\(-2\)	\(1\)	\(-1\)	$1$		\(q+(1-\beta )q^{2}-q^{3}+(1-\beta )q^{4}+\beta q^{5}+\cdots\)
160.1.p.a	$160$	$1$	160.p	5.c	$4$	$2$	$1$	$0.080$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{5}+iq^{9}+(-1+i)q^{13}+(-1+\cdots)q^{17}+\cdots\)
164.1.d.b	$164$	$1$	164.d	164.d	$2$	$2$	$2$	$0.082$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-41}) \)	None	✓	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+\beta q^{7}-q^{8}+\cdots\)
165.1.l.a	$165$	$1$	165.l	165.l	$4$	$2$	$1$	$0.082$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-q^{3}+iq^{4}+iq^{5}+q^{9}-iq^{11}+\cdots\)
165.1.l.b	$165$	$1$	165.l	165.l	$4$	$2$	$1$	$0.082$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{3}+iq^{4}-iq^{5}-q^{9}+iq^{11}+\cdots\)
168.1.s.a	$168$	$1$	168.s	168.s	$6$	$2$	$1$	$0.084$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-6}) \)	None		$4$	$0$	\(-1\)	\(-1\)	\(1\)	\(-1\)	$1$		\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots\)
168.1.s.b	$168$	$1$	168.s	168.s	$6$	$2$	$1$	$0.084$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-6}) \)	None		$4$	$0$	\(1\)	\(1\)	\(-1\)	\(-1\)	$1$		\(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\cdots\)
171.1.p.a	$171$	$1$	171.p	19.d	$6$	$2$	$1$	$0.085$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q-\zeta_{6}q^{4}+q^{7}+(-1+\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{16}+\cdots\)
175.1.c.a	$175$	$1$	175.c	35.c	$2$	$2$	$2$	$0.087$	\(\Q(\sqrt{-1}) \)	$D_{3}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{2}+iq^{7}-iq^{8}-q^{9}-q^{11}+\cdots\)
179.1.b.a	$179$	$1$	179.b	179.b	$2$	$2$	$2$	$0.089$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-179}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)	$1$		\(q+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+(1-\beta )q^{9}+\cdots\)
180.1.f.a	$180$	$1$	180.f	20.d	$2$	$2$	$2$	$0.090$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \)	\(\Q(\sqrt{15}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{2}-q^{4}-iq^{5}+iq^{8}-q^{10}+\cdots\)
180.1.p.a	$180$	$1$	180.p	180.p	$6$	$2$	$1$	$0.090$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-5}) \)	None		$4$	$0$	\(-1\)	\(-1\)	\(-1\)	\(1\)	$1$		\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
180.1.p.b	$180$	$1$	180.p	180.p	$6$	$2$	$1$	$0.090$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-5}) \)	None		$4$	$0$	\(1\)	\(1\)	\(-1\)	\(-1\)	$1$		\(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
183.1.d.b	$183$	$1$	183.d	183.d	$2$	$2$	$2$	$0.091$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-183}) \)	None	✓	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}-q^{3}+q^{4}+\beta q^{6}+q^{9}+\beta q^{11}+\cdots\)
184.1.e.b	$184$	$1$	184.e	184.e	$2$	$2$	$2$	$0.092$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-23}) \)	None		$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{2}+(\zeta_{6}+\zeta_{6}^{2})q^{3}-\zeta_{6}q^{4}+\cdots\)