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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1100.1.e.a 1100.e 55.d $2$ $0.549$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+q^{11}-iq^{23}-iq^{27}-q^{31}+\cdots\)
1100.1.f.a 1100.f 11.b $1$ $0.549$ \(\Q\) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{11}+q^{23}-q^{27}-q^{31}+\cdots\)
1100.1.f.b 1100.f 11.b $2$ $0.549$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{3}+2q^{9}-q^{11}+\beta q^{23}-\beta q^{27}+\cdots\)
1100.1.i.a 1100.i 220.i $2$ $0.549$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-55}) \) None \(-2\) \(0\) \(0\) \(2\) \(q-q^{2}+q^{4}+(1-i)q^{7}-q^{8}+iq^{9}+\cdots\)
1100.1.i.b 1100.i 220.i $2$ $0.549$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-iq^{2}-q^{4}+(-1+i)q^{7}+iq^{8}+\cdots\)
1100.1.i.c 1100.i 220.i $2$ $0.549$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{2}-q^{4}+(1-i)q^{7}-iq^{8}+iq^{9}+\cdots\)
1100.1.i.d 1100.i 220.i $2$ $0.549$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-55}) \) None \(2\) \(0\) \(0\) \(-2\) \(q+q^{2}+q^{4}+(-1+i)q^{7}+q^{8}+iq^{9}+\cdots\)
1100.1.x.a 1100.x 275.v $8$ $0.549$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-11}) \) None \(0\) \(2\) \(-4\) \(0\) \(q+(\zeta_{30}^{2}+\zeta_{30}^{4})q^{3}-\zeta_{30}^{5}q^{5}+(\zeta_{30}^{4}+\cdots)q^{9}+\cdots\)
1100.1.cd.a 1100.cd 275.s $8$ $0.549$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(-\zeta_{30}-\zeta_{30}^{2})q^{3}-\zeta_{30}^{10}q^{5}+\cdots\)
1100.2.a.a 1100.a 1.a $1$ $8.784$ \(\Q\) None None \(0\) \(-2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{9}+q^{11}+4q^{17}-4q^{19}+\cdots\)
1100.2.a.b 1100.a 1.a $1$ $8.784$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}-2q^{9}-q^{11}+4q^{13}+\cdots\)
1100.2.a.c 1100.a 1.a $1$ $8.784$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{9}-q^{11}+6q^{13}+2q^{17}+\cdots\)
1100.2.a.d 1100.a 1.a $1$ $8.784$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{9}-q^{11}-6q^{13}-2q^{17}+\cdots\)
1100.2.a.e 1100.a 1.a $1$ $8.784$ \(\Q\) None None \(0\) \(2\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+4q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
1100.2.a.f 1100.a 1.a $2$ $8.784$ \(\Q(\sqrt{13}) \) None None \(0\) \(-3\) \(0\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-2-\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
1100.2.a.g 1100.a 1.a $2$ $8.784$ \(\Q(\sqrt{21}) \) None None \(0\) \(-1\) \(0\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-3+\beta )q^{7}+(2+\beta )q^{9}-q^{11}+\cdots\)
1100.2.a.h 1100.a 1.a $2$ $8.784$ \(\Q(\sqrt{21}) \) None None \(0\) \(1\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(3-\beta )q^{7}+(2+\beta )q^{9}-q^{11}+\cdots\)
1100.2.a.i 1100.a 1.a $2$ $8.784$ \(\Q(\sqrt{13}) \) None None \(0\) \(3\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(2+\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
1100.2.a.j 1100.a 1.a $4$ $8.784$ \(\Q(\sqrt{3}, \sqrt{19})\) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{7}+(3+\beta _{3})q^{9}+\cdots\)
1100.2.b.a 1100.b 5.b $2$ $8.784$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-2iq^{7}-q^{9}-q^{11}+2iq^{13}+\cdots\)
1100.2.b.b 1100.b 5.b $2$ $8.784$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-q^{9}+q^{11}+2iq^{17}+4q^{19}+\cdots\)
1100.2.b.c 1100.b 5.b $2$ $8.784$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-2iq^{7}+2q^{9}-q^{11}-4iq^{13}+\cdots\)
1100.2.b.d 1100.b 5.b $4$ $8.784$ \(\Q(i, \sqrt{21})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(\beta _{1}+3\beta _{2})q^{7}+(-3+\beta _{3})q^{9}+\cdots\)
1100.2.b.e 1100.b 5.b $4$ $8.784$ \(\Q(i, \sqrt{13})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2})q^{7}+(-4+\cdots)q^{9}+\cdots\)
1100.2.k.a 1100.k 55.e $4$ $8.784$ \(\Q(i, \sqrt{11})\) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{1})q^{3}+(\beta _{2}+\beta _{3})q^{7}-\beta _{1}q^{9}+\cdots\)
1100.2.k.b 1100.k 55.e $8$ $8.784$ 8.0.303595776.1 \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q-\beta _{1}q^{3}+(-\beta _{1}-4\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{9}+\cdots\)
1100.2.k.c 1100.k 55.e $8$ $8.784$ 8.0.40960000.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{3}-\beta _{7}q^{7}+\beta _{1}q^{9}+(-1-\beta _{5}+\cdots)q^{11}+\cdots\)
1100.2.k.d 1100.k 55.e $8$ $8.784$ 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(-2\beta _{1}+\beta _{3})q^{7}+\beta _{6}q^{9}+\cdots\)
1100.2.k.e 1100.k 55.e $8$ $8.784$ 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(2\beta _{1}-\beta _{3})q^{7}+\beta _{6}q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
1100.2.n.a 1100.n 11.c $4$ $8.784$ \(\Q(\zeta_{10})\) None None \(0\) \(1\) \(0\) \(7\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(3-3\zeta_{10}+\cdots)q^{7}+\cdots\)
1100.2.n.b 1100.n 11.c $8$ $8.784$ 8.0.159390625.1 None None \(0\) \(-5\) \(0\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5}-\beta _{6}+\beta _{7})q^{3}+\cdots\)
1100.2.n.c 1100.n 11.c $8$ $8.784$ 8.0.26265625.1 None None \(0\) \(1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{1}+\beta _{7})q^{3}+(1-\beta _{1}-2\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots\)
1100.2.n.d 1100.n 11.c $16$ $8.784$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}+\beta _{4}-\beta _{7}-\beta _{12})q^{3}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1100.2.n.e 1100.n 11.c $16$ $8.784$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{1}-\beta _{4}+\beta _{7}+\beta _{12})q^{3}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1100.2.n.f 1100.n 11.c $24$ $8.784$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{5}]$
1100.2.q.a 1100.q 25.d $44$ $8.784$ None None \(0\) \(-2\) \(9\) \(0\) $\mathrm{SU}(2)[C_{5}]$
1100.2.q.b 1100.q 25.d $52$ $8.784$ None None \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{5}]$
1100.2.cb.a 1100.cb 55.j $8$ $8.784$ \(\Q(\zeta_{20})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(2\zeta_{20}+\zeta_{20}^{5}-\zeta_{20}^{7})q^{3}+(2\zeta_{20}+\cdots)q^{7}+\cdots\)
1100.2.cb.b 1100.cb 55.j $16$ $8.784$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\beta _{2}-\beta _{6}-\beta _{10}-\beta _{12}-\beta _{13}+\beta _{14}+\cdots)q^{3}+\cdots\)
1100.2.cb.c 1100.cb 55.j $16$ $8.784$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(2\beta _{1}-\beta _{2}+\beta _{7}-\beta _{9}-\beta _{11}+\beta _{13}+\cdots)q^{3}+\cdots\)
1100.2.cb.d 1100.cb 55.j $32$ $8.784$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
1100.3.e.a 1100.e 55.d $4$ $29.973$ \(\Q(i, \sqrt{33})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{3}+(-6+\beta _{3})q^{9}-11q^{11}+\cdots\)
1100.3.e.b 1100.e 55.d $16$ $29.973$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{9}+\beta _{10})q^{3}-\beta _{4}q^{7}+(-3+\beta _{1}+\cdots)q^{9}+\cdots\)
1100.3.e.c 1100.e 55.d $16$ $29.973$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{8}q^{3}+\beta _{3}q^{7}+(-2+\beta _{5})q^{9}-\beta _{14}q^{11}+\cdots\)
1100.3.f.a 1100.f 11.b $2$ $29.973$ \(\Q(\sqrt{33}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(-5\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-2-\beta )q^{3}+(3+5\beta )q^{9}-11q^{11}+\cdots\)
1100.3.f.b 1100.f 11.b $4$ $29.973$ \(\Q(\sqrt{3}, \sqrt{11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{3}+(13+\beta _{3})q^{9}+11q^{11}+(5\beta _{1}+\cdots)q^{23}+\cdots\)
1100.3.f.c 1100.f 11.b $8$ $29.973$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{2})q^{3}-\beta _{1}q^{7}+(2+\beta _{3})q^{9}+\cdots\)
1100.3.f.d 1100.f 11.b $8$ $29.973$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{3}+\beta _{4}q^{7}+(-3-\beta _{1})q^{9}+(-5+\cdots)q^{11}+\cdots\)
1100.3.f.e 1100.f 11.b $8$ $29.973$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{2})q^{3}+\beta _{1}q^{7}+(2+\beta _{3})q^{9}+\cdots\)
1100.3.f.f 1100.f 11.b $8$ $29.973$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{1})q^{3}-\beta _{4}q^{7}+(4+\beta _{1}-\beta _{7})q^{9}+\cdots\)
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