Newform search results

Results (1-50 of 165035 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
11.2.a.a	$11$	$2$	11.a	1.a	$1$	$1$	$1$	$0.088$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(-1\)	\(1\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots\)
14.2.a.a	$14$	$2$	14.a	1.a	$1$	$1$	$1$	$0.112$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(-2\)	\(0\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}+2q^{6}+q^{7}-q^{8}+\cdots\)
15.2.a.a	$15$	$2$	15.a	1.a	$1$	$1$	$1$	$0.120$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(-1\)	\(1\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots\)
17.2.a.a	$17$	$2$	17.a	1.a	$1$	$1$	$1$	$0.136$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots\)
19.2.a.a	$19$	$2$	19.a	1.a	$1$	$1$	$1$	$0.152$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(3\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+3q^{11}+\cdots\)
20.2.a.a	$20$	$2$	20.a	1.a	$1$	$1$	$1$	$0.160$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\)
21.2.a.a	$21$	$2$	21.a	1.a	$1$	$1$	$1$	$0.168$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(-2\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
23.2.a.a	$23$	$2$	23.a	1.a	$1$	$2$	$2$	$0.184$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
24.2.a.a	$24$	$2$	24.a	1.a	$1$	$1$	$1$	$0.192$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
26.2.a.a	$26$	$2$	26.a	1.a	$1$	$1$	$1$	$0.208$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(-3\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
26.2.a.b	$26$	$2$	26.a	1.a	$1$	$1$	$1$	$0.208$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-3\)	\(-1\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)
29.2.a.a	$29$	$2$	29.a	1.a	$1$	$2$	$2$	$0.232$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(-2\)	\(2\)	\(-2\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
30.2.a.a	$30$	$2$	30.a	1.a	$1$	$1$	$1$	$0.240$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(-1\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots\)
31.2.a.a	$31$	$2$	31.a	1.a	$1$	$2$	$2$	$0.248$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(1\)	\(-2\)	\(2\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-2\beta q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots\)
33.2.a.a	$33$	$2$	33.a	1.a	$1$	$1$	$1$	$0.264$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(-2\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}+4q^{7}+\cdots\)
34.2.a.a	$34$	$2$	34.a	1.a	$1$	$1$	$1$	$0.271$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-2\)	\(0\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}-2q^{6}-4q^{7}+q^{8}+\cdots\)
35.2.a.a	$35$	$2$	35.a	1.a	$1$	$1$	$1$	$0.279$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-q^{5}+q^{7}-2q^{9}-3q^{11}+\cdots\)
35.2.a.b	$35$	$2$	35.a	1.a	$1$	$2$	$2$	$0.279$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(-1\)	\(-1\)	\(2\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{3}+(2+\beta )q^{4}+q^{5}+\cdots\)
5.4.a.a	$5$	$4$	5.a	1.a	$1$	$1$	$1$	$0.295$	\(\Q\)	None	✓	$1$	$0$	\(-4\)	\(2\)	\(-5\)	\(6\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2q^{3}+8q^{4}-5q^{5}-8q^{6}+\cdots\)
37.2.a.a	$37$	$2$	37.a	1.a	$1$	$1$	$1$	$0.295$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(-3\)	\(-2\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-3q^{3}+2q^{4}-2q^{5}+6q^{6}+\cdots\)
37.2.a.b	$37$	$2$	37.a	1.a	$1$	$1$	$1$	$0.295$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-q^{7}-2q^{9}+3q^{11}+\cdots\)
38.2.a.a	$38$	$2$	38.a	1.a	$1$	$1$	$1$	$0.303$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
38.2.a.b	$38$	$2$	38.a	1.a	$1$	$1$	$1$	$0.303$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(-4\)	\(3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+3q^{7}+\cdots\)
39.2.a.a	$39$	$2$	39.a	1.a	$1$	$1$	$1$	$0.311$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(2\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}+2q^{5}-q^{6}-4q^{7}+\cdots\)
39.2.a.b	$39$	$2$	39.a	1.a	$1$	$2$	$2$	$0.311$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(-2\)	\(2\)	\(0\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}-2\beta q^{5}+\cdots\)
40.2.a.a	$40$	$2$	40.a	1.a	$1$	$1$	$1$	$0.319$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}-3q^{9}+4q^{11}-2q^{13}+\cdots\)
41.2.a.a	$41$	$2$	41.a	1.a	$1$	$3$	$3$	$0.327$	3.3.148.1	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(6\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
42.2.a.a	$42$	$2$	42.a	1.a	$1$	$1$	$1$	$0.335$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(-2\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
43.2.a.a	$43$	$2$	43.a	1.a	$1$	$1$	$1$	$0.343$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(-2\)	\(-4\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-2q^{3}+2q^{4}-4q^{5}+4q^{6}+\cdots\)
43.2.a.b	$43$	$2$	43.a	1.a	$1$	$2$	$2$	$0.343$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-\beta q^{3}+(2-\beta )q^{5}-2q^{6}+(-2+\cdots)q^{7}+\cdots\)
44.2.a.a	$44$	$2$	44.a	1.a	$1$	$1$	$1$	$0.351$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+2q^{7}-2q^{9}-q^{11}+\cdots\)
6.4.a.a	$6$	$4$	6.a	1.a	$1$	$1$	$1$	$0.354$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(-3\)	\(6\)	\(-16\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-3q^{3}+4q^{4}+6q^{5}+6q^{6}+\cdots\)
45.2.a.a	$45$	$2$	45.a	1.a	$1$	$1$	$1$	$0.359$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}+4q^{11}+\cdots\)
46.2.a.a	$46$	$2$	46.a	1.a	$1$	$1$	$1$	$0.367$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(4\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+4q^{5}-4q^{7}-q^{8}-3q^{9}+\cdots\)
47.2.a.a	$47$	$2$	47.a	1.a	$1$	$4$	$4$	$0.375$	4.4.1957.1	None	✓	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
48.2.a.a	$48$	$2$	48.a	1.a	$1$	$1$	$1$	$0.383$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
50.2.a.a	$50$	$2$	50.a	1.a	$1$	$1$	$1$	$0.399$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
50.2.a.b	$50$	$2$	50.a	1.a	$1$	$1$	$1$	$0.399$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
51.2.a.a	$51$	$2$	51.a	1.a	$1$	$1$	$1$	$0.407$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+3q^{5}-4q^{7}+q^{9}-3q^{11}+\cdots\)
51.2.a.b	$51$	$2$	51.a	1.a	$1$	$2$	$2$	$0.407$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(-1\)	\(-2\)	\(3\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+(1+\beta )q^{5}+\cdots\)
7.4.a.a	$7$	$4$	7.a	1.a	$1$	$1$	$1$	$0.413$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(-2\)	\(16\)	\(-7\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}-7q^{4}+2^{4}q^{5}+2q^{6}+\cdots\)
52.2.a.a	$52$	$2$	52.a	1.a	$1$	$1$	$1$	$0.415$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{7}-3q^{9}-2q^{11}-q^{13}+\cdots\)
53.2.a.a	$53$	$2$	53.a	1.a	$1$	$1$	$1$	$0.423$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-3\)	\(0\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-3q^{3}-q^{4}+3q^{6}-4q^{7}+3q^{8}+\cdots\)
53.2.a.b	$53$	$2$	53.a	1.a	$1$	$3$	$3$	$0.423$	3.3.148.1	None	✓	$1$	$0$	\(-1\)	\(3\)	\(-2\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
54.2.a.a	$54$	$2$	54.a	1.a	$1$	$1$	$1$	$0.431$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}-q^{7}-q^{8}-3q^{10}+\cdots\)
54.2.a.b	$54$	$2$	54.a	1.a	$1$	$1$	$1$	$0.431$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-3\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}-q^{7}+q^{8}-3q^{10}+\cdots\)
55.2.a.a	$55$	$2$	55.a	1.a	$1$	$1$	$1$	$0.439$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(0\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-3q^{8}-3q^{9}+q^{10}+\cdots\)
55.2.a.b	$55$	$2$	55.a	1.a	$1$	$2$	$2$	$0.439$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}-2\beta q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots\)
56.2.a.a	$56$	$2$	56.a	1.a	$1$	$1$	$1$	$0.447$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}-3q^{9}-4q^{11}+2q^{13}+\cdots\)
56.2.a.b	$56$	$2$	56.a	1.a	$1$	$1$	$1$	$0.447$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-4q^{5}+q^{7}+q^{9}-8q^{15}+\cdots\)