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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3072.1.e.a 3072.e 3.b $2$ $1.533$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}-\beta q^{7}+q^{9}-\beta q^{13}+\beta q^{21}+\cdots\)
3072.1.e.b 3072.e 3.b $2$ $1.533$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}-\beta q^{7}+q^{9}+\beta q^{13}-\beta q^{21}+\cdots\)
3072.1.h.a 3072.h 24.h $4$ $1.533$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{3}+(\zeta_{8}-\zeta_{8}^{3})q^{7}-q^{9}+(\zeta_{8}+\cdots)q^{13}+\cdots\)
3072.1.i.a 3072.i 48.i $2$ $1.533$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}+q^{9}+(-1+i)q^{11}-iq^{17}+\cdots\)
3072.1.i.b 3072.i 48.i $2$ $1.533$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-q^{9}+(-1+i)q^{11}+iq^{17}+\cdots\)
3072.1.i.c 3072.i 48.i $2$ $1.533$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-q^{9}+(1-i)q^{11}+iq^{17}+\cdots\)
3072.1.i.d 3072.i 48.i $2$ $1.533$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}+q^{9}+(1-i)q^{11}-iq^{17}+(-1+\cdots)q^{19}+\cdots\)
3072.1.i.e 3072.i 48.i $4$ $1.533$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{8}^{3}q^{3}+(-1-\zeta_{8}^{2})q^{5}+(\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{7}+\cdots\)
3072.1.i.f 3072.i 48.i $4$ $1.533$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{9}-\zeta_{8}q^{11}-\zeta_{8}^{2}q^{25}+\cdots\)
3072.1.i.g 3072.i 48.i $4$ $1.533$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{6}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}-\zeta_{8}q^{19}-\zeta_{8}^{2}q^{25}+\cdots\)
3072.1.i.h 3072.i 48.i $4$ $1.533$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{8}^{3}q^{3}+(1+\zeta_{8}^{2})q^{5}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots\)
3072.1.p.a 3072.p 96.p $8$ $1.533$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}q^{3}+(\zeta_{16}^{5}+\zeta_{16}^{7})q^{7}+\zeta_{16}^{2}q^{9}+\cdots\)
3072.1.p.b 3072.p 96.p $8$ $1.533$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}q^{3}+(\zeta_{16}-\zeta_{16}^{3})q^{7}+\zeta_{16}^{2}q^{9}+\cdots\)
3072.1.p.c 3072.p 96.p $8$ $1.533$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}q^{3}+(-\zeta_{16}+\zeta_{16}^{3})q^{7}+\zeta_{16}^{2}q^{9}+\cdots\)
3072.1.p.d 3072.p 96.p $8$ $1.533$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}q^{3}+(-\zeta_{16}^{5}-\zeta_{16}^{7})q^{7}+\zeta_{16}^{2}q^{9}+\cdots\)
3072.2.a.a 3072.a 1.a $2$ $24.530$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{7}+q^{9}+\beta q^{13}-6q^{17}+\cdots\)
3072.2.a.b 3072.a 1.a $2$ $24.530$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+2\beta q^{7}+q^{9}-3\beta q^{13}+\cdots\)
3072.2.a.c 3072.a 1.a $2$ $24.530$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+q^{9}+4q^{11}-\beta q^{13}+\cdots\)
3072.2.a.d 3072.a 1.a $2$ $24.530$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2\beta q^{5}-3\beta q^{7}+q^{9}+4q^{11}+\cdots\)
3072.2.a.e 3072.a 1.a $2$ $24.530$ \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}+q^{9}-4q^{11}-\beta q^{13}+\cdots\)
3072.2.a.f 3072.a 1.a $2$ $24.530$ \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2\beta q^{5}+3\beta q^{7}+q^{9}-4q^{11}+\cdots\)
3072.2.a.g 3072.a 1.a $2$ $24.530$ \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{7}+q^{9}+\beta q^{13}-6q^{17}+\cdots\)
3072.2.a.h 3072.a 1.a $2$ $24.530$ \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}-2\beta q^{7}+q^{9}-3\beta q^{13}+\cdots\)
3072.2.a.i 3072.a 1.a $4$ $24.530$ 4.4.4352.1 None None \(0\) \(-4\) \(-4\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta _{3})q^{5}+(1+\beta _{2})q^{7}+\cdots\)
3072.2.a.j 3072.a 1.a $4$ $24.530$ \(\Q(\zeta_{16})^+\) None None \(0\) \(-4\) \(0\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(\beta _{2}-\beta _{3})q^{5}+(-2-\beta _{3})q^{7}+\cdots\)
3072.2.a.k 3072.a 1.a $4$ $24.530$ \(\Q(\sqrt{2}, \sqrt{5})\) None None \(0\) \(-4\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{2}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
3072.2.a.l 3072.a 1.a $4$ $24.530$ \(\Q(\zeta_{24})^+\) None None \(0\) \(-4\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+q^{9}+\cdots\)
3072.2.a.m 3072.a 1.a $4$ $24.530$ \(\Q(\zeta_{16})^+\) None None \(0\) \(-4\) \(0\) \(8\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-\beta _{2}-\beta _{3})q^{5}+(2-\beta _{3})q^{7}+\cdots\)
3072.2.a.n 3072.a 1.a $4$ $24.530$ 4.4.4352.1 None None \(0\) \(-4\) \(4\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta _{3})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
3072.2.a.o 3072.a 1.a $4$ $24.530$ 4.4.4352.1 None None \(0\) \(4\) \(-4\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta _{3})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
3072.2.a.p 3072.a 1.a $4$ $24.530$ \(\Q(\zeta_{16})^+\) None None \(0\) \(4\) \(0\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-\beta _{2}-\beta _{3})q^{5}+(-2+\beta _{3})q^{7}+\cdots\)
3072.2.a.q 3072.a 1.a $4$ $24.530$ \(\Q(\sqrt{2}, \sqrt{5})\) None None \(0\) \(4\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{2}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots\)
3072.2.a.r 3072.a 1.a $4$ $24.530$ \(\Q(\zeta_{24})^+\) None None \(0\) \(4\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots\)
3072.2.a.s 3072.a 1.a $4$ $24.530$ \(\Q(\zeta_{16})^+\) None None \(0\) \(4\) \(0\) \(8\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(\beta _{2}-\beta _{3})q^{5}+(2+\beta _{3})q^{7}+q^{9}+\cdots\)
3072.2.a.t 3072.a 1.a $4$ $24.530$ 4.4.4352.1 None None \(0\) \(4\) \(4\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta _{3})q^{5}+(1+\beta _{2})q^{7}+q^{9}+\cdots\)
3072.2.d.a 3072.d 8.b $4$ $24.530$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{3}-\zeta_{8}^{3}q^{7}-q^{9}-\zeta_{8}^{2}q^{13}+\cdots\)
3072.2.d.b 3072.d 8.b $4$ $24.530$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{3}-\zeta_{8}^{2}q^{5}-q^{9}+4\zeta_{8}q^{11}+\cdots\)
3072.2.d.c 3072.d 8.b $4$ $24.530$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+2\zeta_{8}^{3}q^{7}-q^{9}+\cdots\)
3072.2.d.d 3072.d 8.b $4$ $24.530$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{3}+2\zeta_{8}^{2}q^{5}+3\zeta_{8}^{3}q^{7}-q^{9}+\cdots\)
3072.2.d.e 3072.d 8.b $8$ $24.530$ \(\Q(\zeta_{16})\) None None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{16}q^{3}+(\zeta_{16}^{2}-\zeta_{16}^{3})q^{5}+(-2+\cdots)q^{7}+\cdots\)
3072.2.d.f 3072.d 8.b $8$ $24.530$ 8.0.18939904.2 None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{3}+(\beta _{4}+\beta _{6})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
3072.2.d.g 3072.d 8.b $8$ $24.530$ 8.0.40960000.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{6}q^{5}+(\beta _{2}-\beta _{7})q^{7}-q^{9}+\cdots\)
3072.2.d.h 3072.d 8.b $8$ $24.530$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{24}q^{3}+(-\zeta_{24}^{2}-\zeta_{24}^{7})q^{5}+\zeta_{24}^{3}q^{7}+\cdots\)
3072.2.d.i 3072.d 8.b $8$ $24.530$ 8.0.18939904.2 None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{3}+(\beta _{4}+\beta _{6})q^{5}+(1-\beta _{1})q^{7}+\cdots\)
3072.2.d.j 3072.d 8.b $8$ $24.530$ \(\Q(\zeta_{16})\) None None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{16}q^{3}+(\zeta_{16}^{2}-\zeta_{16}^{3})q^{5}+(2-\zeta_{16}^{5}+\cdots)q^{7}+\cdots\)
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