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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1200.1.c.a 1200.c 15.d $2$ $0.599$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{7}-q^{9}-iq^{13}-q^{19}+\cdots\)
1200.1.l.a 1200.l 3.b $1$ $0.599$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(1\) \(q-q^{3}+q^{7}+q^{9}-q^{13}+q^{19}-q^{21}+\cdots\)
1200.1.l.b 1200.l 3.b $1$ $0.599$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-1\) \(q+q^{3}-q^{7}+q^{9}+q^{13}+q^{19}-q^{21}+\cdots\)
1200.1.r.a 1200.r 48.i $4$ $0.599$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{2}q^{6}+\cdots\)
1200.1.z.a 1200.z 240.z $2$ $0.599$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+iq^{3}+q^{4}-iq^{6}-q^{8}-q^{9}+\cdots\)
1200.1.z.b 1200.z 240.z $2$ $0.599$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}-iq^{3}+q^{4}-iq^{6}+q^{8}-q^{9}+\cdots\)
1200.1.bd.a 1200.bd 240.ad $2$ $0.599$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}-q^{3}-q^{4}+iq^{6}+iq^{8}+q^{9}+\cdots\)
1200.1.bd.b 1200.bd 240.ad $2$ $0.599$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \) None \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+q^{3}-q^{4}+iq^{6}-iq^{8}+q^{9}+\cdots\)
1200.1.bj.a 1200.bj 60.l $4$ $0.599$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{15}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}-2q^{21}+\cdots\)
1200.1.bj.b 1200.bj 60.l $8$ $0.599$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{3}q^{3}+\zeta_{24}^{9}q^{7}+\zeta_{24}^{6}q^{9}+\cdots\)
1200.2.a.a 1200.a 1.a $1$ $9.582$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{7}+q^{9}+4q^{11}+4q^{17}+\cdots\)
1200.2.a.b 1200.a 1.a $1$ $9.582$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{7}+q^{9}-2q^{11}-3q^{13}+\cdots\)
1200.2.a.c 1200.a 1.a $1$ $9.582$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{7}+q^{9}-2q^{11}-q^{13}+\cdots\)
1200.2.a.d 1200.a 1.a $1$ $9.582$ \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}-4q^{11}+2q^{13}-2q^{17}+\cdots\)
1200.2.a.e 1200.a 1.a $1$ $9.582$ \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
1200.2.a.f 1200.a 1.a $1$ $9.582$ \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}-6q^{11}+5q^{13}+\cdots\)
1200.2.a.g 1200.a 1.a $1$ $9.582$ \(\Q\) None None \(0\) \(-1\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
1200.2.a.h 1200.a 1.a $1$ $9.582$ \(\Q\) None None \(0\) \(-1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
1200.2.a.i 1200.a 1.a $1$ $9.582$ \(\Q\) None None \(0\) \(-1\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+5q^{7}+q^{9}+6q^{11}-3q^{13}+\cdots\)
1200.2.a.j 1200.a 1.a $1$ $9.582$ \(\Q\) None None \(0\) \(1\) \(0\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-5q^{7}+q^{9}+6q^{11}+3q^{13}+\cdots\)
1200.2.a.k 1200.a 1.a $1$ $9.582$ \(\Q\) None None \(0\) \(1\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{7}+q^{9}-2q^{13}-6q^{17}+\cdots\)
1200.2.a.l 1200.a 1.a $1$ $9.582$ \(\Q\) None None \(0\) \(1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
1200.2.a.m 1200.a 1.a $1$ $9.582$ \(\Q\) None None \(0\) \(1\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
1200.2.a.n 1200.a 1.a $1$ $9.582$ \(\Q\) None None \(0\) \(1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}+q^{9}-6q^{11}-5q^{13}+\cdots\)
1200.2.a.o 1200.a 1.a $1$ $9.582$ \(\Q\) None None \(0\) \(1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}+4q^{11}-6q^{13}+6q^{17}+\cdots\)
1200.2.a.p 1200.a 1.a $1$ $9.582$ \(\Q\) None None \(0\) \(1\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{7}+q^{9}-2q^{11}+q^{13}+\cdots\)
1200.2.a.q 1200.a 1.a $1$ $9.582$ \(\Q\) None None \(0\) \(1\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{7}+q^{9}-2q^{11}+3q^{13}+\cdots\)
1200.2.a.r 1200.a 1.a $1$ $9.582$ \(\Q\) None None \(0\) \(1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{7}+q^{9}+6q^{13}+2q^{17}+\cdots\)
1200.2.a.s 1200.a 1.a $1$ $9.582$ \(\Q\) None None \(0\) \(1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{7}+q^{9}+4q^{11}-4q^{17}+\cdots\)
1200.2.f.a 1200.f 5.b $2$ $9.582$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+iq^{7}-q^{9}-6q^{11}-5iq^{13}+\cdots\)
1200.2.f.b 1200.f 5.b $2$ $9.582$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}-q^{9}-4q^{11}+2iq^{13}+2iq^{17}+\cdots\)
1200.2.f.c 1200.f 5.b $2$ $9.582$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+3iq^{7}-q^{9}-2q^{11}-3iq^{13}+\cdots\)
1200.2.f.d 1200.f 5.b $2$ $9.582$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+3iq^{7}-q^{9}-2q^{11}-iq^{13}+\cdots\)
1200.2.f.e 1200.f 5.b $2$ $9.582$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+4iq^{7}-q^{9}-2iq^{13}+6iq^{17}+\cdots\)
1200.2.f.f 1200.f 5.b $2$ $9.582$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+4iq^{7}-q^{9}-6iq^{13}+2iq^{17}+\cdots\)
1200.2.f.g 1200.f 5.b $2$ $9.582$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-q^{9}+4q^{11}-6iq^{13}-6iq^{17}+\cdots\)
1200.2.f.h 1200.f 5.b $2$ $9.582$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-q^{9}+4q^{11}-2iq^{13}-2iq^{17}+\cdots\)
1200.2.f.i 1200.f 5.b $2$ $9.582$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+5iq^{7}-q^{9}+6q^{11}+3iq^{13}+\cdots\)
1200.2.h.a 1200.h 12.b $2$ $9.582$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\zeta_{6})q^{3}+3\zeta_{6}q^{9}-3q^{11}+\cdots\)
1200.2.h.b 1200.h 12.b $2$ $9.582$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\zeta_{6})q^{3}+3\zeta_{6}q^{9}+3q^{11}+\cdots\)
1200.2.h.c 1200.h 12.b $2$ $9.582$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{3}-3\zeta_{6}q^{7}-3q^{9}-7q^{13}+\cdots\)
1200.2.h.d 1200.h 12.b $2$ $9.582$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\zeta_{6}q^{3}-\zeta_{6}q^{7}-3q^{9}-5q^{13}-5\zeta_{6}q^{19}+\cdots\)
1200.2.h.e 1200.h 12.b $2$ $9.582$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\zeta_{6}q^{3}-2\zeta_{6}q^{7}-3q^{9}+2q^{13}+\cdots\)
1200.2.h.f 1200.h 12.b $2$ $9.582$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\zeta_{6}q^{3}-\zeta_{6}q^{7}-3q^{9}+5q^{13}+5\zeta_{6}q^{19}+\cdots\)
1200.2.h.g 1200.h 12.b $2$ $9.582$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{3}-3\zeta_{6}q^{7}-3q^{9}+7q^{13}+\cdots\)
1200.2.h.h 1200.h 12.b $2$ $9.582$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\zeta_{6})q^{3}+3\zeta_{6}q^{9}-3q^{11}-2q^{13}+\cdots\)
1200.2.h.i 1200.h 12.b $2$ $9.582$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2-\zeta_{6})q^{3}+(3-3\zeta_{6})q^{9}+3q^{11}+\cdots\)
1200.2.h.j 1200.h 12.b $4$ $9.582$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{1})q^{3}+(-1-2\beta _{1})q^{9}+\beta _{3}q^{11}+\cdots\)
1200.2.h.k 1200.h 12.b $4$ $9.582$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{7}+\beta _{2}q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
1200.2.h.l 1200.h 12.b $4$ $9.582$ \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{7}+(2+\beta _{2})q^{9}+\cdots\)
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