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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1728.1.b.a 1728.b 8.d $4$ $0.862$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
1728.1.b.b 1728.b 8.d $4$ $0.862$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{7}+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{13}+\cdots\)
1728.1.e.a 1728.e 3.b $1$ $0.862$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-q^{7}+q^{13}+q^{19}+q^{25}+2q^{31}+\cdots\)
1728.1.e.b 1728.e 3.b $1$ $0.862$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+q^{7}+q^{13}-q^{19}+q^{25}-2q^{31}+\cdots\)
1728.1.g.a 1728.g 4.b $2$ $0.862$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
1728.1.h.a 1728.h 24.h $4$ $0.862$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{5})q^{7}+(-\zeta_{12}^{2}-\zeta_{12}^{4}+\cdots)q^{13}+\cdots\)
1728.1.j.a 1728.j 48.i $4$ $0.862$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{5}+\zeta_{8}^{2}q^{7}-\zeta_{8}q^{11}+(-1+\cdots)q^{13}+\cdots\)
1728.1.n.a 1728.n 72.j $4$ $0.862$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{11}+(\zeta_{12}^{2}+\zeta_{12}^{4}+\cdots)q^{17}+\cdots\)
1728.1.o.a 1728.o 36.f $4$ $0.862$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}^{4}q^{5}+\zeta_{12}^{5}q^{7}-\zeta_{12}^{5}q^{11}+\cdots\)
1728.1.bn.a 1728.bn 216.x $12$ $0.862$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{36}^{11}q^{3}-\zeta_{36}^{4}q^{9}+(-\zeta_{36}-\zeta_{36}^{3}+\cdots)q^{11}+\cdots\)
1728.2.a.a 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(-4\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-4q^{5}-3q^{7}-4q^{11}-q^{13}-4q^{17}+\cdots\)
1728.2.a.b 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(-4\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-4q^{5}+3q^{7}+4q^{11}-q^{13}-4q^{17}+\cdots\)
1728.2.a.c 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(-3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-3q^{5}-q^{7}+3q^{11}+4q^{13}-2q^{19}+\cdots\)
1728.2.a.d 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(-3\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-3q^{5}+q^{7}-3q^{11}+4q^{13}+2q^{19}+\cdots\)
1728.2.a.e 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-3q^{7}+6q^{11}+3q^{13}-2q^{17}+\cdots\)
1728.2.a.f 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+2q^{11}-q^{13}+6q^{17}+\cdots\)
1728.2.a.g 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(-2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-2q^{11}-q^{13}+6q^{17}+\cdots\)
1728.2.a.h 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(-2\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+3q^{7}-6q^{11}+3q^{13}-2q^{17}+\cdots\)
1728.2.a.i 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{7}-5q^{11}-4q^{13}+8q^{17}+\cdots\)
1728.2.a.j 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{7}+3q^{11}-4q^{17}+6q^{19}+\cdots\)
1728.2.a.k 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(-1\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{7}-3q^{11}-4q^{17}-6q^{19}+\cdots\)
1728.2.a.l 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(-1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{7}+5q^{11}-4q^{13}+8q^{17}+\cdots\)
1728.2.a.m 1728.a 1.a $1$ $13.798$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-5\) $-$ $N(\mathrm{U}(1))$ \(q-5q^{7}+7q^{13}-q^{19}-5q^{25}+4q^{31}+\cdots\)
1728.2.a.n 1728.a 1.a $1$ $13.798$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) $+$ $N(\mathrm{U}(1))$ \(q-q^{7}-5q^{13}+7q^{19}-5q^{25}-4q^{31}+\cdots\)
1728.2.a.o 1728.a 1.a $1$ $13.798$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) $+$ $N(\mathrm{U}(1))$ \(q+q^{7}-5q^{13}-7q^{19}-5q^{25}+4q^{31}+\cdots\)
1728.2.a.p 1728.a 1.a $1$ $13.798$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(5\) $-$ $N(\mathrm{U}(1))$ \(q+5q^{7}+7q^{13}+q^{19}-5q^{25}-4q^{31}+\cdots\)
1728.2.a.q 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{7}-3q^{11}+4q^{17}+6q^{19}+\cdots\)
1728.2.a.r 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{7}+5q^{11}-4q^{13}-8q^{17}+\cdots\)
1728.2.a.s 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(1\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}+3q^{7}-5q^{11}-4q^{13}-8q^{17}+\cdots\)
1728.2.a.t 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+3q^{7}+3q^{11}+4q^{17}-6q^{19}+\cdots\)
1728.2.a.u 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(2\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-3q^{7}-6q^{11}+3q^{13}+2q^{17}+\cdots\)
1728.2.a.v 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-2q^{11}-q^{13}-6q^{17}+\cdots\)
1728.2.a.w 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}+2q^{11}-q^{13}-6q^{17}+\cdots\)
1728.2.a.x 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(2\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+3q^{7}+6q^{11}+3q^{13}+2q^{17}+\cdots\)
1728.2.a.y 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{5}-q^{7}-3q^{11}+4q^{13}-2q^{19}+\cdots\)
1728.2.a.z 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{5}+q^{7}+3q^{11}+4q^{13}+2q^{19}+\cdots\)
1728.2.a.ba 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(4\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-3q^{7}+4q^{11}-q^{13}+4q^{17}+\cdots\)
1728.2.a.bb 1728.a 1.a $1$ $13.798$ \(\Q\) None None \(0\) \(0\) \(4\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+3q^{7}-4q^{11}-q^{13}+4q^{17}+\cdots\)
1728.2.a.bc 1728.a 1.a $2$ $13.798$ \(\Q(\sqrt{13}) \) None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{5}+\beta q^{7}-q^{11}-4q^{13}+2\beta q^{19}+\cdots\)
1728.2.a.bd 1728.a 1.a $2$ $13.798$ \(\Q(\sqrt{13}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{5}-\beta q^{7}+q^{11}-4q^{13}-2\beta q^{19}+\cdots\)
1728.2.c.a 1728.c 12.b $2$ $13.798$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{7}-7q^{13}+5\zeta_{6}q^{19}+5q^{25}+\cdots\)
1728.2.c.b 1728.c 12.b $2$ $13.798$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{7}+5q^{13}+\zeta_{6}q^{19}+5q^{25}+\cdots\)
1728.2.c.c 1728.c 12.b $4$ $13.798$ \(\Q(\sqrt{3}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{5}-\beta _{2}q^{7}-\beta _{3}q^{11}-2q^{13}+\cdots\)
1728.2.c.d 1728.c 12.b $4$ $13.798$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{3}q^{11}+q^{13}+\cdots\)
1728.2.c.e 1728.c 12.b $4$ $13.798$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{5}-\zeta_{12}^{2}q^{7}+\zeta_{12}^{3}q^{11}+\cdots\)
1728.2.c.f 1728.c 12.b $8$ $13.798$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{24}^{2}q^{5}+(\zeta_{24}+\zeta_{24}^{3})q^{7}-\zeta_{24}^{6}q^{11}+\cdots\)
1728.2.c.g 1728.c 12.b $8$ $13.798$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}^{3}q^{5}-\zeta_{24}^{7}q^{7}+(\zeta_{24}+\zeta_{24}^{5}+\cdots)q^{11}+\cdots\)
1728.2.d.a 1728.d 8.b $2$ $13.798$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{5}-3q^{7}-3iq^{11}+6iq^{13}+\cdots\)
1728.2.d.b 1728.d 8.b $2$ $13.798$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{5}-3q^{7}-3iq^{11}-6iq^{13}+\cdots\)
1728.2.d.c 1728.d 8.b $2$ $13.798$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{5}+3q^{7}+3iq^{11}+6iq^{13}+\cdots\)
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