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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
324.1.d.a 324.d 4.b $1$ $0.162$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(1\) \(0\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-q^{13}+\cdots\)
324.1.d.b 324.d 4.b $1$ $0.162$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(-1\) \(0\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-q^{13}+\cdots\)
324.1.f.a 324.f 36.f $2$ $0.162$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(1\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+q^{8}-q^{10}+\cdots\)
324.1.f.b 324.f 36.f $2$ $0.162$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}-q^{8}-q^{10}+\cdots\)
324.1.g.a 324.g 9.d $2$ $0.162$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-\zeta_{6}^{2}q^{7}+\zeta_{6}q^{13}-q^{19}+\zeta_{6}^{2}q^{25}+\cdots\)
324.2.a.a 324.a 1.a $1$ $2.587$ \(\Q\) None None \(0\) \(0\) \(-3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-3q^{5}-q^{7}-3q^{11}-q^{13}-6q^{17}+\cdots\)
324.2.a.b 324.a 1.a $1$ $2.587$ \(\Q\) None None \(0\) \(0\) \(-3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-3q^{5}+2q^{7}+6q^{11}+5q^{13}+3q^{17}+\cdots\)
324.2.a.c 324.a 1.a $1$ $2.587$ \(\Q\) None None \(0\) \(0\) \(3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{5}-q^{7}+3q^{11}-q^{13}+6q^{17}+\cdots\)
324.2.a.d 324.a 1.a $1$ $2.587$ \(\Q\) None None \(0\) \(0\) \(3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+3q^{5}+2q^{7}-6q^{11}+5q^{13}-3q^{17}+\cdots\)
324.2.b.a 324.b 12.b $4$ $2.587$ \(\Q(\sqrt{-2}, \sqrt{3})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}-2\beta _{1}q^{8}+\cdots\)
324.2.b.b 324.b 12.b $8$ $2.587$ 8.0.170772624.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{2}q^{4}+(\beta _{3}-\beta _{4}+\beta _{7})q^{5}+\cdots\)
324.2.b.c 324.b 12.b $8$ $2.587$ 8.0.5780865024.3 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{3}+\beta _{5})q^{5}+\cdots\)
324.2.e.a 324.e 9.c $2$ $2.587$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-3\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
324.2.e.b 324.e 9.c $2$ $2.587$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-5\) $\mathrm{U}(1)[D_{3}]$ \(q+(-5+5\zeta_{6})q^{7}+7\zeta_{6}q^{13}-q^{19}+\cdots\)
324.2.e.c 324.e 9.c $2$ $2.587$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(4\) $\mathrm{U}(1)[D_{3}]$ \(q+(4-4\zeta_{6})q^{7}-2\zeta_{6}q^{13}+8q^{19}+\cdots\)
324.2.e.d 324.e 9.c $2$ $2.587$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+3\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
324.2.h.a 324.h 36.h $4$ $2.587$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{3}q^{2}-2q^{4}+2\beta _{1}q^{5}+(2-\beta _{2}+\cdots)q^{7}+\cdots\)
324.2.h.b 324.h 36.h $4$ $2.587$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+2\beta _{1}q^{5}+(-2+\cdots)q^{7}+\cdots\)
324.2.h.c 324.h 36.h $4$ $2.587$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(\beta _{1}-\beta _{3})q^{2}+(2-2\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots\)
324.2.h.d 324.h 36.h $8$ $2.587$ 8.0.12960000.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{3}+\beta _{7})q^{2}+(-\beta _{1}-\beta _{2})q^{4}+\cdots\)
324.2.h.e 324.h 36.h $8$ $2.587$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q-\zeta_{24}^{3}q^{2}+(2-2\zeta_{24})q^{4}+(\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
324.2.h.f 324.h 36.h $16$ $2.587$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{15}q^{2}+(-1+\beta _{8}-\beta _{9}-\beta _{11}+\cdots)q^{4}+\cdots\)
324.2.i.a 324.i 27.e $18$ $2.587$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{8}-\beta _{9}-\beta _{10}+\cdots)q^{7}+\cdots\)
324.2.l.a 324.l 108.l $96$ $2.587$ None None \(6\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{18}]$
324.2.m.a 324.m 81.g $162$ $2.587$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{27}]$
324.2.p.a 324.p 324.p $936$ $2.587$ None None \(-18\) \(0\) \(-36\) \(0\) $\mathrm{SU}(2)[C_{54}]$
324.3.c.a 324.c 3.b $4$ $8.828$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}-\beta _{3}q^{11}+\cdots\)
324.3.c.b 324.c 3.b $4$ $8.828$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{5}+(1-\beta _{2})q^{7}+(-\beta _{1}+\beta _{3})q^{11}+\cdots\)
324.3.d.a 324.d 4.b $2$ $8.828$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-1}) \) None \(-4\) \(0\) \(-8\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+4q^{4}+(-4+\beta )q^{5}-8q^{8}+\cdots\)
324.3.d.b 324.d 4.b $2$ $8.828$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{4}+4q^{5}+\cdots\)
324.3.d.c 324.d 4.b $2$ $8.828$ \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{4}-4q^{5}+\cdots\)
324.3.d.d 324.d 4.b $2$ $8.828$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-1}) \) None \(4\) \(0\) \(8\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}+4q^{4}+(4+\beta )q^{5}+8q^{8}+(8+\cdots)q^{10}+\cdots\)
324.3.d.e 324.d 4.b $6$ $8.828$ 6.0.3636603.2 None None \(-1\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{1}q^{4}+(-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
324.3.d.f 324.d 4.b $6$ $8.828$ 6.0.3636603.2 None None \(1\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{2}q^{4}+(-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
324.3.d.g 324.d 4.b $8$ $8.828$ 8.0.\(\cdots\).1 None None \(-3\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{5}-\beta _{6})q^{4}+\cdots\)
324.3.d.h 324.d 4.b $8$ $8.828$ 8.0.\(\cdots\).4 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+(-1-\beta _{6})q^{4}+(-2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
324.3.d.i 324.d 4.b $8$ $8.828$ 8.0.\(\cdots\).1 None None \(3\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{4}+\beta _{6})q^{4}+\cdots\)
324.3.f.a 324.f 36.f $2$ $8.828$ \(\Q(\sqrt{-3}) \) None None \(-4\) \(0\) \(-2\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q-2q^{2}+4q^{4}+(-2+2\zeta_{6})q^{5}+(8+\cdots)q^{7}+\cdots\)
324.3.f.b 324.f 36.f $2$ $8.828$ \(\Q(\sqrt{-3}) \) None None \(-4\) \(0\) \(7\) \(-15\) $\mathrm{SU}(2)[C_{6}]$ \(q-2q^{2}+4q^{4}+(7-7\zeta_{6})q^{5}+(-10+\cdots)q^{7}+\cdots\)
324.3.f.c 324.f 36.f $2$ $8.828$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(-7\) \(15\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(-7+7\zeta_{6})q^{5}+\cdots\)
324.3.f.d 324.f 36.f $2$ $8.828$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(2\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(2-2\zeta_{6})q^{5}+\cdots\)
324.3.f.e 324.f 36.f $2$ $8.828$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(8\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q-2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+(8-8\zeta_{6})q^{5}+\cdots\)
324.3.f.f 324.f 36.f $2$ $8.828$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-8\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+2\zeta_{6}q^{2}+(-4+4\zeta_{6})q^{4}+(-8+8\zeta_{6})q^{5}+\cdots\)
324.3.f.g 324.f 36.f $2$ $8.828$ \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(-2\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{5}+\cdots\)
324.3.f.h 324.f 36.f $2$ $8.828$ \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(7\) \(15\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(7-7\zeta_{6})q^{5}+\cdots\)
324.3.f.i 324.f 36.f $2$ $8.828$ \(\Q(\sqrt{-3}) \) None None \(4\) \(0\) \(-7\) \(-15\) $\mathrm{SU}(2)[C_{6}]$ \(q+2q^{2}+4q^{4}+(-7+7\zeta_{6})q^{5}+(-10+\cdots)q^{7}+\cdots\)
324.3.f.j 324.f 36.f $2$ $8.828$ \(\Q(\sqrt{-3}) \) None None \(4\) \(0\) \(2\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q+2q^{2}+4q^{4}+(2-2\zeta_{6})q^{5}+(8-4\zeta_{6})q^{7}+\cdots\)
324.3.f.k 324.f 36.f $4$ $8.828$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(-4\) \(0\) \(-8\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(-2+2\zeta_{12})q^{2}-4\zeta_{12}q^{4}+(-4\zeta_{12}+\cdots)q^{5}+\cdots\)
324.3.f.l 324.f 36.f $4$ $8.828$ \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(-3\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{1})q^{2}+(-\beta _{1}+3\beta _{2}+\beta _{3})q^{4}+\cdots\)
324.3.f.m 324.f 36.f $4$ $8.828$ \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(3\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{1})q^{2}+(-\beta _{1}+3\beta _{2}+\beta _{3})q^{4}+\cdots\)
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