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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1296.1.g.a 1296.g 4.b $2$ $0.647$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{5}+q^{13}+\beta q^{17}+2q^{25}+\beta q^{29}+\cdots\)
1296.1.o.a 1296.o 36.f $2$ $0.647$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-3\) \(q+(-1+\zeta_{6}^{2})q^{7}+\zeta_{6}^{2}q^{13}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
1296.1.o.b 1296.o 36.f $2$ $0.647$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{13}+\zeta_{6}q^{25}+q^{37}+\zeta_{6}^{2}q^{49}+\cdots\)
1296.1.o.c 1296.o 36.f $2$ $0.647$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(3\) \(q+(1-\zeta_{6}^{2})q^{7}+\zeta_{6}^{2}q^{13}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
1296.1.o.d 1296.o 36.f $4$ $0.647$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{5}-\zeta_{12}^{2}q^{13}+(\zeta_{12}+\cdots)q^{17}+\cdots\)
1296.1.q.a 1296.q 9.d $2$ $0.647$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-\zeta_{6}q^{7}-\zeta_{6}^{2}q^{13}+q^{19}-\zeta_{6}q^{25}+\cdots\)
1296.1.x.a 1296.x 144.w $8$ $0.647$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+\zeta_{24}^{5}q^{5}-\zeta_{24}^{10}q^{7}+\cdots\)
1296.2.a.a 1296.a 1.a $1$ $10.349$ \(\Q\) None None \(0\) \(0\) \(-3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-3q^{5}-2q^{7}-6q^{11}+5q^{13}+3q^{17}+\cdots\)
1296.2.a.b 1296.a 1.a $1$ $10.349$ \(\Q\) None None \(0\) \(0\) \(-3\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-3q^{5}+q^{7}+3q^{11}-q^{13}-6q^{17}+\cdots\)
1296.2.a.c 1296.a 1.a $1$ $10.349$ \(\Q\) None None \(0\) \(0\) \(-3\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-3q^{5}+4q^{7}-q^{13}-3q^{17}+4q^{19}+\cdots\)
1296.2.a.d 1296.a 1.a $1$ $10.349$ \(\Q\) None None \(0\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{11}-5q^{13}-5q^{17}-8q^{19}+\cdots\)
1296.2.a.e 1296.a 1.a $1$ $10.349$ \(\Q\) None None \(0\) \(0\) \(-1\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{7}-5q^{11}-5q^{13}-2q^{17}+\cdots\)
1296.2.a.f 1296.a 1.a $1$ $10.349$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{11}+2q^{13}+3q^{17}+q^{19}+\cdots\)
1296.2.a.g 1296.a 1.a $1$ $10.349$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{7}+3q^{11}+2q^{13}-3q^{17}+q^{19}+\cdots\)
1296.2.a.h 1296.a 1.a $1$ $10.349$ \(\Q\) None None \(0\) \(0\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{11}-5q^{13}+5q^{17}-8q^{19}+\cdots\)
1296.2.a.i 1296.a 1.a $1$ $10.349$ \(\Q\) None None \(0\) \(0\) \(1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+3q^{7}+5q^{11}-5q^{13}+2q^{17}+\cdots\)
1296.2.a.j 1296.a 1.a $1$ $10.349$ \(\Q\) None None \(0\) \(0\) \(3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+3q^{5}-2q^{7}+6q^{11}+5q^{13}-3q^{17}+\cdots\)
1296.2.a.k 1296.a 1.a $1$ $10.349$ \(\Q\) None None \(0\) \(0\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{5}+q^{7}-3q^{11}-q^{13}+6q^{17}+\cdots\)
1296.2.a.l 1296.a 1.a $1$ $10.349$ \(\Q\) None None \(0\) \(0\) \(3\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+3q^{5}+4q^{7}-q^{13}+3q^{17}+4q^{19}+\cdots\)
1296.2.a.m 1296.a 1.a $2$ $10.349$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(-4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{5}+2\beta q^{7}+2q^{11}+(1+\cdots)q^{13}+\cdots\)
1296.2.a.n 1296.a 1.a $2$ $10.349$ \(\Q(\sqrt{33}) \) None None \(0\) \(0\) \(-1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{5}+(-2+\beta )q^{7}-q^{11}+(2+\beta )q^{13}+\cdots\)
1296.2.a.o 1296.a 1.a $2$ $10.349$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-2q^{7}-2\beta q^{11}-q^{13}-3\beta q^{17}+\cdots\)
1296.2.a.p 1296.a 1.a $2$ $10.349$ \(\Q(\sqrt{33}) \) None None \(0\) \(0\) \(1\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(-2+\beta )q^{7}+q^{11}+(2+\beta )q^{13}+\cdots\)
1296.2.a.q 1296.a 1.a $2$ $10.349$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}-2\beta q^{7}-2q^{11}+(1-2\beta )q^{13}+\cdots\)
1296.2.c.a 1296.c 12.b $2$ $10.349$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{5}-\zeta_{6}q^{7}-3q^{11}-5q^{13}+\cdots\)
1296.2.c.b 1296.c 12.b $2$ $10.349$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\zeta_{6}q^{5}-2\zeta_{6}q^{7}-3q^{11}+4q^{13}+\cdots\)
1296.2.c.c 1296.c 12.b $2$ $10.349$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{5}+\zeta_{6}q^{7}+3q^{11}-5q^{13}+\cdots\)
1296.2.c.d 1296.c 12.b $2$ $10.349$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\zeta_{6}q^{5}+2\zeta_{6}q^{7}+3q^{11}+4q^{13}+\cdots\)
1296.2.c.e 1296.c 12.b $4$ $10.349$ \(\Q(\sqrt{-2}, \sqrt{3})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{5}+(-2+\beta _{3})q^{13}+(\beta _{1}-\beta _{2}+\cdots)q^{17}+\cdots\)
1296.2.c.f 1296.c 12.b $4$ $10.349$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-\zeta_{12}^{3}q^{11}+\cdots\)
1296.2.c.g 1296.c 12.b $8$ $10.349$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}^{3}q^{5}-\zeta_{24}^{4}q^{7}-\zeta_{24}^{2}q^{11}+\cdots\)
1296.2.i.a 1296.i 9.c $2$ $10.349$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-4\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-4\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(4-4\zeta_{6})q^{11}+\cdots\)
1296.2.i.b 1296.i 9.c $2$ $10.349$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-3\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+\zeta_{6}q^{13}+\cdots\)
1296.2.i.c 1296.i 9.c $2$ $10.349$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
1296.2.i.d 1296.i 9.c $2$ $10.349$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-3\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
1296.2.i.e 1296.i 9.c $2$ $10.349$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}+2\zeta_{6}q^{13}+\cdots\)
1296.2.i.f 1296.i 9.c $2$ $10.349$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}+5\zeta_{6}q^{13}+\cdots\)
1296.2.i.g 1296.i 9.c $2$ $10.349$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
1296.2.i.h 1296.i 9.c $2$ $10.349$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{U}(1)[D_{3}]$ \(q+(-4+4\zeta_{6})q^{7}-2\zeta_{6}q^{13}-8q^{19}+\cdots\)
1296.2.i.i 1296.i 9.c $2$ $10.349$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) $\mathrm{U}(1)[D_{3}]$ \(q+(-1+\zeta_{6})q^{7}-5\zeta_{6}q^{13}+7q^{19}+\cdots\)
1296.2.i.j 1296.i 9.c $2$ $10.349$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(5\) $\mathrm{U}(1)[D_{3}]$ \(q+(5-5\zeta_{6})q^{7}+7\zeta_{6}q^{13}+q^{19}+(5+\cdots)q^{25}+\cdots\)
1296.2.i.k 1296.i 9.c $2$ $10.349$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{11}+5\zeta_{6}q^{13}+\cdots\)
1296.2.i.l 1296.i 9.c $2$ $10.349$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+(5-5\zeta_{6})q^{11}+\cdots\)
1296.2.i.m 1296.i 9.c $2$ $10.349$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{5}+(4-4\zeta_{6})q^{11}+2\zeta_{6}q^{13}+\cdots\)
1296.2.i.n 1296.i 9.c $2$ $10.349$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+3\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+\zeta_{6}q^{13}+\cdots\)
1296.2.i.o 1296.i 9.c $2$ $10.349$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
1296.2.i.p 1296.i 9.c $2$ $10.349$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+3\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
1296.2.i.q 1296.i 9.c $2$ $10.349$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(4\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-4+4\zeta_{6})q^{11}+\cdots\)
1296.2.i.r 1296.i 9.c $4$ $10.349$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2\zeta_{12}+\zeta_{12}^{2})q^{5}+(2\zeta_{12}^{2}-2\zeta_{12}^{3})q^{7}+\cdots\)
1296.2.i.s 1296.i 9.c $4$ $10.349$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}^{2}q^{5}+(2-2\zeta_{12})q^{7}+(-2\zeta_{12}^{2}+\cdots)q^{11}+\cdots\)
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