Newform search results

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

Results (1-50 of 87073 matches)

 

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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
37.2.a.a	$37$	$2$	37.a	1.a	$1$	$1$	$1$	$0.295$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(-3\)	\(-2\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-3q^{3}+2q^{4}-2q^{5}+6q^{6}+\cdots\)
43.2.a.a	$43$	$2$	43.a	1.a	$1$	$1$	$1$	$0.343$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(-2\)	\(-4\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-2q^{3}+2q^{4}-4q^{5}+4q^{6}+\cdots\)
53.2.a.a	$53$	$2$	53.a	1.a	$1$	$1$	$1$	$0.423$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-3\)	\(0\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-3q^{3}-q^{4}+3q^{6}-4q^{7}+3q^{8}+\cdots\)
57.2.a.a	$57$	$2$	57.a	1.a	$1$	$1$	$1$	$0.455$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(-1\)	\(-3\)	\(-5\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots\)
58.2.a.a	$58$	$2$	58.a	1.a	$1$	$1$	$1$	$0.463$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-3\)	\(-3\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-3q^{3}+q^{4}-3q^{5}+3q^{6}-2q^{7}+\cdots\)
61.2.a.a	$61$	$2$	61.a	1.a	$1$	$1$	$1$	$0.487$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-2\)	\(-3\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}-q^{4}-3q^{5}+2q^{6}+q^{7}+\cdots\)
61.2.f.a	$61$	$2$	61.f	61.f	$6$	$2$	$1$	$0.487$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-3\)	\(-4\)	\(-3\)	\(-6\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}-2q^{3}+\zeta_{6}q^{4}+(-3+\cdots)q^{5}+\cdots\)
63.2.s.a	$63$	$2$	63.s	63.s	$6$	$2$	$1$	$0.503$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-3\)	\(-3\)	\(-6\)	\(-5\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
65.2.a.a	$65$	$2$	65.a	1.a	$1$	$1$	$1$	$0.519$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-2\)	\(-1\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}-q^{4}-q^{5}+2q^{6}-4q^{7}+\cdots\)
67.2.a.b	$67$	$2$	67.a	1.a	$1$	$2$	$2$	$0.535$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-3\)	\(-3\)	\(-6\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+(-2+\beta )q^{3}+3\beta q^{4}+\cdots\)
73.2.a.b	$73$	$2$	73.a	1.a	$1$	$2$	$2$	$0.583$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-3\)	\(-3\)	\(-3\)	\(-6\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+(-2+\beta )q^{3}+3\beta q^{4}+\cdots\)
77.2.a.a	$77$	$2$	77.a	1.a	$1$	$1$	$1$	$0.615$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-2q^{4}-q^{5}-q^{7}+6q^{9}-q^{11}+\cdots\)
79.2.a.a	$79$	$2$	79.a	1.a	$1$	$1$	$1$	$0.631$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-3\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
80.2.s.a	$80$	$2$	80.s	80.s	$4$	$2$	$1$	$0.639$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(-2\)	\(-4\)	\(-4\)	\(-6\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+i)q^{2}-2q^{3}-2iq^{4}+(-2+\cdots)q^{5}+\cdots\)
82.2.a.a	$82$	$2$	82.a	1.a	$1$	$1$	$1$	$0.655$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-2\)	\(-2\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}-4q^{7}+\cdots\)
83.2.a.a	$83$	$2$	83.a	1.a	$1$	$1$	$1$	$0.663$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-2\)	\(-3\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}-3q^{7}+\cdots\)
85.2.a.b	$85$	$2$	85.a	1.a	$1$	$2$	$2$	$0.679$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(-4\)	\(-2\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(-2-\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
85.2.j.a	$85$	$2$	85.j	85.j	$4$	$2$	$1$	$0.679$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(-2\)	\(-2\)	\(-4\)	\(-6\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-q^{2}+(-1+i)q^{3}-q^{4}+(-2-i)q^{5}+\cdots\)
88.2.a.a	$88$	$2$	88.a	1.a	$1$	$1$	$1$	$0.703$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-3\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-3q^{5}-2q^{7}+6q^{9}-q^{11}+\cdots\)
89.2.a.a	$89$	$2$	89.a	1.a	$1$	$1$	$1$	$0.711$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-1\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}-4q^{7}+\cdots\)
91.2.a.a	$91$	$2$	91.a	1.a	$1$	$1$	$1$	$0.727$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-3\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-3q^{5}-q^{7}-3q^{9}+\cdots\)
91.2.a.b	$91$	$2$	91.a	1.a	$1$	$1$	$1$	$0.727$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{4}-3q^{5}+q^{7}+q^{9}+4q^{12}+\cdots\)
91.2.g.a	$91$	$2$	91.g	91.g	$3$	$2$	$1$	$0.727$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-1\)	\(-6\)	\(-3\)	\(-5\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}-3q^{3}+(1-\zeta_{6})q^{4}+(-3+\cdots)q^{5}+\cdots\)
91.2.u.a	$91$	$2$	91.u	91.u	$6$	$2$	$1$	$0.727$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-3\)	\(-2\)	\(-3\)	\(-5\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\zeta_{6})q^{2}-q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
92.2.a.a	$92$	$2$	92.a	1.a	$1$	$1$	$1$	$0.735$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-2\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-2q^{5}-4q^{7}+6q^{9}+2q^{11}+\cdots\)
93.2.a.a	$93$	$2$	93.a	1.a	$1$	$2$	$2$	$0.743$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-3\)	\(-2\)	\(-4\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(-3+\cdots)q^{5}+\cdots\)
95.2.l.a	$95$	$2$	95.l	95.l	$12$	$4$	$1$	$0.759$	\(\Q(\zeta_{12})\)	None		$4$	$1$	\(-6\)	\(-6\)	\(-4\)	\(-8\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1+\zeta_{12}-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{2}+\cdots\)
13.4.a.a	$13$	$4$	13.a	1.a	$1$	$1$	$1$	$0.767$	\(\Q\)	None	✓	$1$	$1$	\(-5\)	\(-7\)	\(-7\)	\(-13\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{2}-7q^{3}+17q^{4}-7q^{5}+35q^{6}+\cdots\)
97.2.a.a	$97$	$2$	97.a	1.a	$1$	$3$	$3$	$0.775$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(-4\)	\(-4\)	\(-3\)	\(-7\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+(-2+\beta _{1}-\beta _{2})q^{3}+\cdots\)
97.2.g.a	$97$	$2$	97.g	97.g	$12$	$4$	$1$	$0.775$	\(\Q(\zeta_{12})\)	None		$2$	$1$	\(-6\)	\(-6\)	\(-6\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-2+\zeta_{12}^{2})q^{2}+(-2+\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
99.2.a.a	$99$	$2$	99.a	1.a	$1$	$1$	$1$	$0.791$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-4\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-4q^{5}-2q^{7}+3q^{8}+4q^{10}+\cdots\)
101.2.a.a	$101$	$2$	101.a	1.a	$1$	$1$	$1$	$0.806$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{4}-q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots\)
101.2.e.a	$101$	$2$	101.e	101.e	$10$	$4$	$1$	$0.806$	\(\Q(\zeta_{10})\)	None		$2$	$1$	\(-5\)	\(-5\)	\(-6\)	\(-10\)		$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-1-\zeta_{10})q^{2}+(-2+2\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
102.2.a.a	$102$	$2$	102.a	1.a	$1$	$1$	$1$	$0.814$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-4\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-2q^{7}+\cdots\)
103.2.a.a	$103$	$2$	103.a	1.a	$1$	$2$	$2$	$0.822$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-3\)	\(-2\)	\(-3\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(-2+\cdots)q^{5}+\cdots\)
104.2.s.a	$104$	$2$	104.s	104.s	$6$	$4$	$2$	$0.830$	\(\Q(\zeta_{12})\)	None		$2$	$1$	\(-4\)	\(-6\)	\(-8\)	\(-12\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
105.2.s.a	$105$	$2$	105.s	21.g	$6$	$2$	$1$	$0.838$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-3\)	\(-3\)	\(-1\)	\(-5\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+(1+\cdots)q^{4}+\cdots\)
106.2.a.a	$106$	$2$	106.a	1.a	$1$	$1$	$1$	$0.846$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-4\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{8}+\cdots\)
107.2.a.a	$107$	$2$	107.a	1.a	$1$	$2$	$2$	$0.854$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-1\)	\(-3\)	\(-3\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
109.2.a.b	$109$	$2$	109.a	1.a	$1$	$3$	$3$	$0.870$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(-2\)	\(-4\)	\(-6\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(-1+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
111.2.j.a	$111$	$2$	111.j	37.e	$6$	$2$	$1$	$0.886$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-3\)	\(-1\)	\(-6\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}-\zeta_{6}q^{3}+\zeta_{6}q^{4}+(-4+\cdots)q^{5}+\cdots\)
112.2.a.a	$112$	$2$	112.a	1.a	$1$	$1$	$1$	$0.894$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-4q^{5}-q^{7}+q^{9}+8q^{15}+\cdots\)
112.2.m.a	$112$	$2$	112.m	16.e	$4$	$2$	$1$	$0.894$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(-2\)	\(-4\)	\(-4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+i)q^{2}+(-2+2i)q^{3}-2iq^{4}+\cdots\)
113.2.a.c	$113$	$2$	113.a	1.a	$1$	$3$	$3$	$0.902$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(-2\)	\(-5\)	\(-1\)	\(-10\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+\cdots\)
114.2.h.a	$114$	$2$	114.h	57.f	$6$	$2$	$1$	$0.910$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-1\)	\(-3\)	\(-6\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
115.2.a.b	$115$	$2$	115.a	1.a	$1$	$2$	$2$	$0.918$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-3\)	\(-2\)	\(-2\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}-q^{5}+\cdots\)
117.2.a.a	$117$	$2$	117.a	1.a	$1$	$1$	$1$	$0.934$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{5}-4q^{7}+3q^{8}+2q^{10}+\cdots\)
117.2.e.a	$117$	$2$	117.e	9.c	$3$	$2$	$1$	$0.934$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-2\)	\(-3\)	\(-4\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
117.2.r.a	$117$	$2$	117.r	117.r	$6$	$2$	$1$	$0.934$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-3\)	\(-3\)	\(-3\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+(1+\cdots)q^{4}+\cdots\)
117.2.t.a	$117$	$2$	117.t	117.t	$6$	$2$	$1$	$0.934$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(-3\)	\(-6\)	\(-6\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(-2+\cdots)q^{5}+\cdots\)