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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
11.2.a.a 11.a 1.a $1$ $0.088$ \(\Q\) None \(-2\) \(-1\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots\)
13.2.e.a 13.e 13.e $2$ $0.104$ \(\Q(\sqrt{-3}) \) None \(-3\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
14.2.a.a 14.a 1.a $1$ $0.112$ \(\Q\) None \(-1\) \(-2\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{6}+q^{7}-q^{8}+\cdots\)
15.2.a.a 15.a 1.a $1$ $0.120$ \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots\)
16.2.e.a 16.e 16.e $2$ $0.128$ \(\Q(\sqrt{-1}) \) None \(-2\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{2}+(-1+i)q^{3}+2iq^{4}+\cdots\)
17.2.a.a 17.a 1.a $1$ $0.136$ \(\Q\) None \(-1\) \(0\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots\)
17.2.d.a 17.d 17.d $4$ $0.136$ \(\Q(\zeta_{8})\) None \(-4\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)
18.2.c.a 18.c 9.c $2$ $0.144$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
19.2.a.a 19.a 1.a $1$ $0.152$ \(\Q\) None \(0\) \(-2\) \(3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+3q^{11}+\cdots\)
19.2.e.a 19.e 19.e $6$ $0.152$ \(\Q(\zeta_{18})\) None \(-6\) \(-3\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-1+\zeta_{18}-\zeta_{18}^{2})q^{2}+(-1+\zeta_{18}^{2}+\cdots)q^{3}+\cdots\)
20.2.a.a 20.a 1.a $1$ $0.160$ \(\Q\) None \(0\) \(-2\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\)
20.2.e.a 20.e 20.e $2$ $0.160$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(-2\) \(0\) \(-4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1-i)q^{2}+2iq^{4}+(-2+i)q^{5}+\cdots\)
21.2.a.a 21.a 1.a $1$ $0.168$ \(\Q\) None \(-1\) \(1\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
21.2.e.a 21.e 7.c $2$ $0.168$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-1\) \(2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-\zeta_{6}q^{3}-2\zeta_{6}q^{4}+\cdots\)
21.2.g.a 21.g 21.g $2$ $0.168$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(1\) $\mathrm{U}(1)[D_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(2+\cdots)q^{7}+\cdots\)
22.2.c.a 22.c 11.c $4$ $0.176$ \(\Q(\zeta_{10})\) None \(-1\) \(-4\) \(-6\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots\)
23.2.a.a 23.a 1.a $2$ $0.184$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
23.2.c.a 23.c 23.c $10$ $0.184$ \(\Q(\zeta_{22})\) None \(-7\) \(-7\) \(-3\) \(-5\) $\mathrm{SU}(2)[C_{11}]$ \(q+(-\zeta_{22}+\zeta_{22}^{4}-\zeta_{22}^{5}+\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
24.2.a.a 24.a 1.a $1$ $0.192$ \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
24.2.d.a 24.d 8.b $2$ $0.192$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{2}+iq^{3}-2iq^{4}-2iq^{5}+\cdots\)
24.2.f.a 24.f 24.f $2$ $0.192$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(-2\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}+(-1-\beta )q^{3}-2q^{4}+(2-\beta )q^{6}+\cdots\)
25.2.d.a 25.d 25.d $4$ $0.200$ \(\Q(\zeta_{10})\) None \(-2\) \(-1\) \(-5\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)
25.2.e.a 25.e 25.e $8$ $0.200$ 8.0.58140625.2 None \(-5\) \(-5\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{2}-\beta _{3}+\beta _{7})q^{3}+\cdots\)
26.2.a.a 26.a 1.a $1$ $0.208$ \(\Q\) None \(-1\) \(1\) \(-3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
26.2.a.b 26.a 1.a $1$ $0.208$ \(\Q\) None \(1\) \(-3\) \(-1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)
26.2.b.a 26.b 13.b $2$ $0.208$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{3}-q^{4}-3iq^{5}-iq^{6}+\cdots\)
26.2.c.a 26.c 13.c $2$ $0.208$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}-4\zeta_{6}q^{7}+\cdots\)
27.2.a.a 27.a 1.a $1$ $0.216$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-1\) $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}-q^{7}+5q^{13}+4q^{16}-7q^{19}+\cdots\)
27.2.e.a 27.e 27.e $12$ $0.216$ 12.0.\(\cdots\).1 None \(-6\) \(-6\) \(-3\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-1-\beta _{3}+\beta _{8})q^{2}+(-1-\beta _{2}+\beta _{6}+\cdots)q^{3}+\cdots\)
28.2.d.a 28.d 28.d $2$ $0.224$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) \(-1\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{2}+(-2+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots\)
28.2.e.a 28.e 7.c $2$ $0.224$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{3}+(-3+3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
28.2.f.a 28.f 28.f $4$ $0.224$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\cdots)q^{3}+\cdots\)
29.2.a.a 29.a 1.a $2$ $0.232$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
29.2.b.a 29.b 29.b $2$ $0.232$ \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(-6\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-\beta q^{3}-3q^{4}-3q^{5}+5q^{6}+\cdots\)
29.2.d.a 29.d 29.d $6$ $0.232$ \(\Q(\zeta_{14})\) None \(-2\) \(-5\) \(1\) \(1\) $\mathrm{SU}(2)[C_{7}]$ \(q+(-1+\zeta_{14}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)
29.2.e.a 29.e 29.e $12$ $0.232$ 12.0.\(\cdots\).1 None \(-7\) \(-7\) \(-1\) \(-11\) $\mathrm{SU}(2)[C_{14}]$ \(q+(-1+\beta _{3}+\beta _{7}+\beta _{9}+\beta _{10})q^{2}+\cdots\)
30.2.a.a 30.a 1.a $1$ $0.240$ \(\Q\) None \(-1\) \(1\) \(-1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots\)
30.2.c.a 30.c 5.b $2$ $0.240$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}-q^{4}+(-2+i)q^{5}+\cdots\)
30.2.e.a 30.e 15.e $4$ $0.240$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
31.2.a.a 31.a 1.a $2$ $0.248$ \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-2\beta q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots\)
31.2.c.a 31.c 31.c $4$ $0.248$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-4\) \(2\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots\)
31.2.d.a 31.d 31.d $4$ $0.248$ \(\Q(\zeta_{10})\) None \(-3\) \(1\) \(-6\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
31.2.g.a 31.g 31.g $16$ $0.248$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-6\) \(-12\) \(-3\) \(2\) $\mathrm{SU}(2)[C_{15}]$ \(q+(-1-\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots\)
32.2.a.a 32.a 1.a $1$ $0.256$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q-2q^{5}-3q^{9}+6q^{13}+2q^{17}-q^{25}+\cdots\)
32.2.g.a 32.g 32.g $4$ $0.256$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+(\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots\)
32.2.g.b 32.g 32.g $8$ $0.256$ 8.0.18939904.2 None \(-4\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{8}]$ \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{3}+\beta _{5}+\beta _{7})q^{3}+\cdots\)
33.2.a.a 33.a 1.a $1$ $0.264$ \(\Q\) None \(1\) \(-1\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}+4q^{7}+\cdots\)
33.2.d.a 33.d 33.d $2$ $0.264$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) \(0\) \(1\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{3}-2q^{4}+(1-2\beta )q^{5}+(-3+\beta )q^{9}+\cdots\)
33.2.e.a 33.e 11.c $4$ $0.264$ \(\Q(\zeta_{10})\) None \(-3\) \(-1\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1-\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(\zeta_{10}+\cdots)q^{4}+\cdots\)
33.2.e.b 33.e 11.c $4$ $0.264$ \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(-3\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+2\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{3}q^{3}+\cdots\)
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