Learn more

Refine search


Results (1-50 of 12713 matches)

Next   Download to        
Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
7.3.b.a 7.b 7.b $1$ $0.191$ \(\Q\) \(\Q(\sqrt{-7}) \) \(-3\) \(0\) \(0\) \(-7\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{2}+5q^{4}-7q^{7}-3q^{8}+9q^{9}+\cdots\)
8.3.d.a 8.d 8.d $1$ $0.218$ \(\Q\) \(\Q(\sqrt{-2}) \) \(-2\) \(-2\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-8q^{8}+\cdots\)
9.3.d.a 9.d 9.d $2$ $0.245$ \(\Q(\sqrt{-3}) \) None \(-3\) \(-3\) \(6\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
10.3.c.a 10.c 5.c $2$ $0.272$ \(\Q(\sqrt{-1}) \) None \(-2\) \(-4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{2}+(-2+2i)q^{3}+2iq^{4}+\cdots\)
11.3.b.a 11.b 11.b $1$ $0.300$ \(\Q\) \(\Q(\sqrt{-11}) \) \(0\) \(-5\) \(-1\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-5q^{3}+4q^{4}-q^{5}+2^{4}q^{9}-11q^{11}+\cdots\)
11.3.d.a 11.d 11.d $4$ $0.300$ \(\Q(\zeta_{10})\) None \(-5\) \(0\) \(-4\) \(10\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-2\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-2+\cdots)q^{3}+\cdots\)
12.3.c.a 12.c 3.b $1$ $0.327$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(2\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{3}+2q^{7}+9q^{9}-22q^{13}+26q^{19}+\cdots\)
12.3.d.a 12.d 4.b $2$ $0.327$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
13.3.d.a 13.d 13.d $4$ $0.354$ \(\Q(i, \sqrt{10})\) None \(-4\) \(-4\) \(8\) \(-12\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+\cdots\)
13.3.f.a 13.f 13.f $4$ $0.354$ \(\Q(\zeta_{12})\) None \(-2\) \(-2\) \(-14\) \(16\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
14.3.d.a 14.d 7.d $4$ $0.381$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-6\) \(-6\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-2-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots\)
15.3.c.a 15.c 3.b $2$ $0.409$ \(\Q(\sqrt{-5}) \) None \(0\) \(-4\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(-2-\beta )q^{3}-q^{4}-\beta q^{5}+\cdots\)
15.3.d.a 15.d 15.d $1$ $0.409$ \(\Q\) \(\Q(\sqrt{-15}) \) \(-1\) \(3\) \(-5\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-q^{2}+3q^{3}-3q^{4}-5q^{5}-3q^{6}+\cdots\)
15.3.d.b 15.d 15.d $1$ $0.409$ \(\Q\) \(\Q(\sqrt{-15}) \) \(1\) \(-3\) \(5\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+q^{2}-3q^{3}-3q^{4}+5q^{5}-3q^{6}+\cdots\)
15.3.f.a 15.f 5.c $4$ $0.409$ \(\Q(i, \sqrt{6})\) None \(-4\) \(0\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
16.3.c.a 16.c 4.b $1$ $0.436$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-6\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-6q^{5}+9q^{9}+10q^{13}-30q^{17}+\cdots\)
16.3.f.a 16.f 16.f $6$ $0.436$ 6.0.399424.1 None \(-2\) \(-2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)
17.3.e.a 17.e 17.e $8$ $0.463$ \(\Q(\zeta_{16})\) None \(-8\) \(-8\) \(16\) \(8\) $\mathrm{SU}(2)[C_{16}]$ \(q+(-1+\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
17.3.e.b 17.e 17.e $8$ $0.463$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(-24\) \(-16\) $\mathrm{SU}(2)[C_{16}]$ \(q+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(2\zeta_{16}^{2}+\cdots)q^{3}+\cdots\)
18.3.b.a 18.b 3.b $2$ $0.490$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-2q^{4}-3\beta q^{5}-4q^{7}-2\beta q^{8}+\cdots\)
18.3.d.a 18.d 9.d $4$ $0.490$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(-18\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots\)
19.3.b.a 19.b 19.b $1$ $0.518$ \(\Q\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-9\) \(-5\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{4}-9q^{5}-5q^{7}+9q^{9}+3q^{11}+\cdots\)
19.3.b.b 19.b 19.b $2$ $0.518$ \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(8\) \(-10\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-\beta q^{3}-9q^{4}+4q^{5}+13q^{6}+\cdots\)
19.3.d.a 19.d 19.d $6$ $0.518$ 6.0.6967728.1 None \(-3\) \(-9\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{5})q^{2}+(\beta _{1}+2\beta _{2}+\beta _{3}+\beta _{5})q^{3}+\cdots\)
19.3.f.a 19.f 19.f $12$ $0.518$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-6\) \(0\) \(-6\) \(6\) $\mathrm{SU}(2)[C_{18}]$ \(q+\beta _{10}q^{2}+(\beta _{1}-\beta _{4}-\beta _{5}+\beta _{6}-\beta _{7}+\cdots)q^{3}+\cdots\)
20.3.b.a 20.b 4.b $4$ $0.545$ \(\Q(\zeta_{10})\) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{10}^{2}q^{2}+\zeta_{10}^{3}q^{3}+(-2-\zeta_{10}+\cdots)q^{4}+\cdots\)
20.3.d.a 20.d 20.d $1$ $0.545$ \(\Q\) \(\Q(\sqrt{-5}) \) \(-2\) \(4\) \(-5\) \(-4\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
20.3.d.b 20.d 20.d $1$ $0.545$ \(\Q\) \(\Q(\sqrt{-5}) \) \(2\) \(-4\) \(-5\) \(4\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}-4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
20.3.d.c 20.d 20.d $2$ $0.545$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(6\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{2}-4q^{4}+(3-2i)q^{5}-4iq^{8}+\cdots\)
20.3.f.a 20.f 5.c $2$ $0.545$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-6\) \(-14\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(-3+4i)q^{5}+(-7-7i)q^{7}+\cdots\)
21.3.b.a 21.b 3.b $4$ $0.572$ 4.0.65856.1 None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-3+\cdots)q^{4}+\cdots\)
21.3.d.a 21.d 7.b $2$ $0.572$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\zeta_{6}q^{3}-3q^{4}-4\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots\)
21.3.f.a 21.f 7.d $2$ $0.572$ \(\Q(\sqrt{-3}) \) None \(-3\) \(-3\) \(9\) \(13\) $\mathrm{SU}(2)[C_{6}]$ \(q-3\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-5+5\zeta_{6})q^{4}+\cdots\)
21.3.f.b 21.f 7.d $2$ $0.572$ \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(-9\) \(-7\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots\)
21.3.f.c 21.f 7.d $2$ $0.572$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(-6\) \(-7\) $\mathrm{SU}(2)[C_{6}]$ \(q+2\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+\cdots\)
21.3.h.a 21.h 21.h $2$ $0.572$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(-13\) $\mathrm{U}(1)[D_{6}]$ \(q+3\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-5-3\zeta_{6})q^{7}+\cdots\)
21.3.h.b 21.h 21.h $4$ $0.572$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(0\) \(-4\) \(0\) \(14\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
22.3.b.a 22.b 11.b $2$ $0.599$ \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+q^{3}-2q^{4}-q^{5}+\beta q^{6}-6\beta q^{7}+\cdots\)
22.3.d.a 22.d 11.d $8$ $0.599$ 8.0.64000000.1 None \(0\) \(-2\) \(2\) \(-30\) $\mathrm{SU}(2)[C_{10}]$ \(q+\beta _{1}q^{2}+(1-\beta _{1}-2\beta _{2}+\beta _{3}+2\beta _{4}+\cdots)q^{3}+\cdots\)
23.3.b.a 23.b 23.b $3$ $0.627$ 3.3.621.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+(4+\cdots)q^{4}+\cdots\)
23.3.d.a 23.d 23.d $30$ $0.627$ None \(-11\) \(-11\) \(-11\) \(-11\) $\mathrm{SU}(2)[C_{22}]$
24.3.b.a 24.b 8.d $4$ $0.654$ 4.0.4752.1 None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots\)
24.3.e.a 24.e 3.b $2$ $0.654$ \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta )q^{3}-2\beta q^{5}-6q^{7}+(-7+2\beta )q^{9}+\cdots\)
24.3.h.a 24.h 24.h $1$ $0.654$ \(\Q\) \(\Q(\sqrt{-6}) \) \(-2\) \(3\) \(2\) \(-10\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots\)
24.3.h.b 24.h 24.h $1$ $0.654$ \(\Q\) \(\Q(\sqrt{-6}) \) \(2\) \(-3\) \(-2\) \(-10\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}-3q^{3}+4q^{4}-2q^{5}-6q^{6}+\cdots\)
24.3.h.c 24.h 24.h $4$ $0.654$ \(\Q(\sqrt{2}, \sqrt{-7})\) None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(-3+\beta _{3})q^{4}+\cdots\)
25.3.c.a 25.c 5.c $4$ $0.681$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}-3q^{6}-4\beta _{1}q^{7}+\cdots\)
25.3.f.a 25.f 25.f $32$ $0.681$ None \(-10\) \(-10\) \(-10\) \(-10\) $\mathrm{SU}(2)[C_{20}]$
26.3.d.a 26.d 13.d $2$ $0.708$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-6\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{2}+2iq^{4}+(-3-3i)q^{5}+\cdots\)
26.3.f.a 26.f 13.f $4$ $0.708$ \(\Q(\zeta_{12})\) None \(2\) \(0\) \(0\) \(-22\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
Next   Download to