Learn more

Refine search


Results (1-50 of 28466 matches)

Next   displayed columns for results
Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5.4.a.a 5.a 1.a $1$ $0.295$ \(\Q\) None \(-4\) \(2\) \(-5\) \(6\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+2q^{3}+8q^{4}-5q^{5}-8q^{6}+\cdots\)
6.4.a.a 6.a 1.a $1$ $0.354$ \(\Q\) None \(-2\) \(-3\) \(6\) \(-16\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+6q^{5}+6q^{6}+\cdots\)
7.4.a.a 7.a 1.a $1$ $0.413$ \(\Q\) None \(-1\) \(-2\) \(16\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}-7q^{4}+2^{4}q^{5}+2q^{6}+\cdots\)
7.4.c.a 7.c 7.c $2$ $0.413$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-7\) \(-7\) \(28\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-7\zeta_{6}q^{3}+4\zeta_{6}q^{4}+\cdots\)
8.4.a.a 8.a 1.a $1$ $0.472$ \(\Q\) None \(0\) \(-4\) \(-2\) \(24\) $+$ $\mathrm{SU}(2)$ \(q-4q^{3}-2q^{5}+24q^{7}-11q^{9}-44q^{11}+\cdots\)
8.4.b.a 8.b 8.b $2$ $0.472$ \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta )q^{2}+2\beta q^{3}+(-6+2\beta )q^{4}+\cdots\)
9.4.a.a 9.a 1.a $1$ $0.531$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(20\) $+$ $N(\mathrm{U}(1))$ \(q-8q^{4}+20q^{7}-70q^{13}+2^{6}q^{16}+\cdots\)
9.4.c.a 9.c 9.c $4$ $0.531$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-3\) \(-3\) \(-15\) \(-7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
10.4.a.a 10.a 1.a $1$ $0.590$ \(\Q\) None \(2\) \(-8\) \(5\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-8q^{3}+4q^{4}+5q^{5}-2^{4}q^{6}+\cdots\)
10.4.b.a 10.b 5.b $2$ $0.590$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}-4q^{4}+(-5-5i)q^{5}+\cdots\)
11.4.a.a 11.a 1.a $2$ $0.649$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(2\) \(20\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(-1-4\beta )q^{3}+(-4+2\beta )q^{4}+\cdots\)
11.4.c.a 11.c 11.c $8$ $0.649$ 8.0.\(\cdots\).1 None \(-7\) \(-3\) \(-7\) \(-35\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\beta _{1}+\beta _{2}-\beta _{4})q^{2}+(-2-2\beta _{2}+\cdots)q^{3}+\cdots\)
12.4.a.a 12.a 1.a $1$ $0.708$ \(\Q\) None \(0\) \(3\) \(-18\) \(8\) $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-18q^{5}+8q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
12.4.b.a 12.b 12.b $4$ $0.708$ \(\Q(\sqrt{3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
13.4.a.a 13.a 1.a $1$ $0.767$ \(\Q\) None \(-5\) \(-7\) \(-7\) \(-13\) $-$ $\mathrm{SU}(2)$ \(q-5q^{2}-7q^{3}+17q^{4}-7q^{5}+35q^{6}+\cdots\)
13.4.a.b 13.a 1.a $2$ $0.767$ \(\Q(\sqrt{17}) \) None \(1\) \(5\) \(-3\) \(-9\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(4-3\beta )q^{3}+(-4+\beta )q^{4}+\cdots\)
13.4.b.a 13.b 13.b $2$ $0.767$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{3}-q^{4}-3iq^{5}-iq^{6}+\cdots\)
13.4.c.a 13.c 13.c $2$ $0.767$ \(\Q(\sqrt{-3}) \) None \(-4\) \(-2\) \(34\) \(-20\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4+4\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\cdots\)
13.4.c.b 13.c 13.c $4$ $0.767$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(5\) \(-5\) \(-30\) \(-15\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-\beta _{1}-2\beta _{2}-\beta _{3})q^{2}+(-1+3\beta _{1}+\cdots)q^{3}+\cdots\)
13.4.e.a 13.e 13.e $2$ $0.767$ \(\Q(\sqrt{-3}) \) None \(-6\) \(7\) \(0\) \(39\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2-2\zeta_{6})q^{2}+(7-7\zeta_{6})q^{3}+4\zeta_{6}q^{4}+\cdots\)
13.4.e.b 13.e 13.e $2$ $0.767$ \(\Q(\sqrt{-3}) \) None \(3\) \(-2\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-5\zeta_{6}q^{4}+\cdots\)
14.4.a.a 14.a 1.a $1$ $0.826$ \(\Q\) None \(-2\) \(8\) \(-14\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+8q^{3}+4q^{4}-14q^{5}-2^{4}q^{6}+\cdots\)
14.4.a.b 14.a 1.a $1$ $0.826$ \(\Q\) None \(2\) \(-2\) \(-12\) \(7\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-2q^{3}+4q^{4}-12q^{5}-4q^{6}+\cdots\)
14.4.c.a 14.c 7.c $2$ $0.826$ \(\Q(\sqrt{-3}) \) None \(-2\) \(5\) \(9\) \(-28\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}+5\zeta_{6}q^{3}-4\zeta_{6}q^{4}+\cdots\)
14.4.c.b 14.c 7.c $2$ $0.826$ \(\Q(\sqrt{-3}) \) None \(2\) \(1\) \(-7\) \(-20\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-7+\cdots)q^{5}+\cdots\)
15.4.a.a 15.a 1.a $1$ $0.885$ \(\Q\) None \(1\) \(3\) \(5\) \(-24\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}-7q^{4}+5q^{5}+3q^{6}+\cdots\)
15.4.a.b 15.a 1.a $1$ $0.885$ \(\Q\) None \(3\) \(-3\) \(-5\) \(20\) $+$ $\mathrm{SU}(2)$ \(q+3q^{2}-3q^{3}+q^{4}-5q^{5}-9q^{6}+\cdots\)
15.4.b.a 15.b 5.b $4$ $0.885$ \(\Q(i, \sqrt{41})\) None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(-5+\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots\)
15.4.e.a 15.e 15.e $8$ $0.885$ 8.0.\(\cdots\).8 None \(0\) \(-6\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots\)
16.4.a.a 16.a 1.a $1$ $0.944$ \(\Q\) None \(0\) \(4\) \(-2\) \(-24\) $+$ $\mathrm{SU}(2)$ \(q+4q^{3}-2q^{5}-24q^{7}-11q^{9}+44q^{11}+\cdots\)
16.4.e.a 16.e 16.e $10$ $0.944$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{4}q^{2}-\beta _{5}q^{3}+(1-\beta _{2}+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
17.4.a.a 17.a 1.a $1$ $1.003$ \(\Q\) None \(-3\) \(-8\) \(6\) \(-28\) $-$ $\mathrm{SU}(2)$ \(q-3q^{2}-8q^{3}+q^{4}+6q^{5}+24q^{6}+\cdots\)
17.4.a.b 17.a 1.a $3$ $1.003$ 3.3.2636.1 None \(1\) \(4\) \(-8\) \(22\) $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{2})q^{2}+(2-\beta _{1}+2\beta _{2})q^{3}+\cdots\)
17.4.b.a 17.b 17.b $4$ $1.003$ 4.0.4669632.2 None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}+\cdots\)
17.4.c.a 17.c 17.c $8$ $1.003$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(14\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{1}-\beta _{3})q^{2}+\beta _{4}q^{3}+(-5-\beta _{2}+\cdots)q^{4}+\cdots\)
17.4.d.a 17.d 17.d $12$ $1.003$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-4\) \(-4\) \(-20\) \(-4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-\beta _{3}-\beta _{10})q^{2}+\beta _{8}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
18.4.a.a 18.a 1.a $1$ $1.062$ \(\Q\) None \(2\) \(0\) \(-6\) \(-16\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}-6q^{5}-2^{4}q^{7}+8q^{8}+\cdots\)
18.4.c.a 18.c 9.c $2$ $1.062$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(9\) \(31\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(3-6\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
18.4.c.b 18.c 9.c $4$ $1.062$ \(\Q(\sqrt{-3}, \sqrt{-35})\) None \(4\) \(3\) \(9\) \(-19\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-4-4\beta _{1}+\cdots)q^{4}+\cdots\)
19.4.a.a 19.a 1.a $1$ $1.121$ \(\Q\) None \(-3\) \(-5\) \(-12\) \(11\) $-$ $\mathrm{SU}(2)$ \(q-3q^{2}-5q^{3}+q^{4}-12q^{5}+15q^{6}+\cdots\)
19.4.a.b 19.a 1.a $3$ $1.121$ 3.3.3144.1 None \(3\) \(1\) \(14\) \(-35\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1}-\beta _{2})q^{2}+(-\beta _{1}+2\beta _{2})q^{3}+\cdots\)
19.4.c.a 19.c 19.c $4$ $1.121$ \(\Q(\sqrt{-3}, \sqrt{55})\) None \(-2\) \(0\) \(14\) \(-28\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(7+7\beta _{2})q^{4}+\cdots\)
19.4.c.b 19.c 19.c $4$ $1.121$ \(\Q(\sqrt{-3}, \sqrt{73})\) None \(-1\) \(-2\) \(-19\) \(40\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(-11+\beta _{1}+10\beta _{2}+\cdots)q^{4}+\cdots\)
19.4.e.a 19.e 19.e $24$ $1.121$ None \(-6\) \(-3\) \(-6\) \(3\) $\mathrm{SU}(2)[C_{9}]$
20.4.a.a 20.a 1.a $1$ $1.180$ \(\Q\) None \(0\) \(4\) \(5\) \(-16\) $+$ $\mathrm{SU}(2)$ \(q+4q^{3}+5q^{5}-2^{4}q^{7}-11q^{9}-60q^{11}+\cdots\)
20.4.c.a 20.c 5.b $2$ $1.180$ \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(14\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{3}+(7+\beta )q^{5}+\beta q^{7}-7^{2}q^{9}+\cdots\)
20.4.e.a 20.e 20.e $2$ $1.180$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(4\) \(0\) \(-4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(2+2i)q^{2}+8iq^{4}+(-2-11i)q^{5}+\cdots\)
20.4.e.b 20.e 20.e $12$ $1.180$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{1}-\beta _{5})q^{2}-\beta _{9}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
21.4.a.a 21.a 1.a $1$ $1.239$ \(\Q\) None \(-3\) \(-3\) \(-18\) \(7\) $-$ $\mathrm{SU}(2)$ \(q-3q^{2}-3q^{3}+q^{4}-18q^{5}+9q^{6}+\cdots\)
21.4.a.b 21.a 1.a $1$ $1.239$ \(\Q\) None \(4\) \(-3\) \(-4\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q+4q^{2}-3q^{3}+8q^{4}-4q^{5}-12q^{6}+\cdots\)
Next   displayed columns for results