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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1080.1.c.a 1080.c 15.d $4$ $0.539$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{5}+\zeta_{8}^{2}q^{7}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots\)
1080.1.i.a 1080.i 120.i $1$ $0.539$ \(\Q\) \(\Q(\sqrt{-30}) \) None \(-1\) \(0\) \(-1\) \(0\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+q^{11}+\cdots\)
1080.1.i.b 1080.i 120.i $1$ $0.539$ \(\Q\) \(\Q(\sqrt{-30}) \) None \(-1\) \(0\) \(1\) \(0\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-q^{11}+\cdots\)
1080.1.i.c 1080.i 120.i $1$ $0.539$ \(\Q\) \(\Q(\sqrt{-30}) \) None \(1\) \(0\) \(-1\) \(0\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{11}+\cdots\)
1080.1.i.d 1080.i 120.i $1$ $0.539$ \(\Q\) \(\Q(\sqrt{-30}) \) None \(1\) \(0\) \(1\) \(0\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-q^{11}+\cdots\)
1080.1.i.e 1080.i 120.i $4$ $0.539$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}q^{5}+(\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
1080.1.i.f 1080.i 120.i $4$ $0.539$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots\)
1080.1.p.a 1080.p 40.e $2$ $0.539$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-15}) \) None \(-1\) \(0\) \(-2\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{5}+q^{8}-\zeta_{6}^{2}q^{10}+\cdots\)
1080.1.p.b 1080.p 40.e $2$ $0.539$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-15}) \) None \(1\) \(0\) \(2\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{5}-q^{8}-\zeta_{6}^{2}q^{10}+\cdots\)
1080.1.u.a 1080.u 40.i $8$ $0.539$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{24}^{3}q^{2}+\zeta_{24}^{6}q^{4}-\zeta_{24}q^{5}+(-\zeta_{24}^{2}+\cdots)q^{7}+\cdots\)
1080.2.a.a 1080.a 1.a $1$ $8.624$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}+2q^{11}+4q^{13}+q^{17}+\cdots\)
1080.2.a.b 1080.a 1.a $1$ $8.624$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-6q^{13}+7q^{17}+7q^{19}+\cdots\)
1080.2.a.c 1080.a 1.a $1$ $8.624$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+2q^{11}-5q^{13}+4q^{17}+\cdots\)
1080.2.a.d 1080.a 1.a $1$ $8.624$ \(\Q\) None None \(0\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{11}-3q^{17}-q^{19}-3q^{23}+\cdots\)
1080.2.a.e 1080.a 1.a $1$ $8.624$ \(\Q\) None None \(0\) \(0\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-4q^{11}-2q^{13}-5q^{17}+\cdots\)
1080.2.a.f 1080.a 1.a $1$ $8.624$ \(\Q\) None None \(0\) \(0\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-q^{11}+q^{13}+q^{17}+\cdots\)
1080.2.a.g 1080.a 1.a $1$ $8.624$ \(\Q\) None None \(0\) \(0\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}-2q^{11}+4q^{13}-q^{17}+\cdots\)
1080.2.a.h 1080.a 1.a $1$ $8.624$ \(\Q\) None None \(0\) \(0\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-6q^{13}-7q^{17}+7q^{19}+\cdots\)
1080.2.a.i 1080.a 1.a $1$ $8.624$ \(\Q\) None None \(0\) \(0\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-2q^{11}-5q^{13}-4q^{17}+\cdots\)
1080.2.a.j 1080.a 1.a $1$ $8.624$ \(\Q\) None None \(0\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{11}+3q^{17}-q^{19}+3q^{23}+\cdots\)
1080.2.a.k 1080.a 1.a $1$ $8.624$ \(\Q\) None None \(0\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+q^{11}+q^{13}-q^{17}+\cdots\)
1080.2.a.l 1080.a 1.a $1$ $8.624$ \(\Q\) None None \(0\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+4q^{11}-2q^{13}+5q^{17}+\cdots\)
1080.2.a.m 1080.a 1.a $2$ $8.624$ \(\Q(\sqrt{73}) \) None None \(0\) \(0\) \(-2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}+(1-\beta )q^{11}+3q^{13}+\cdots\)
1080.2.a.n 1080.a 1.a $2$ $8.624$ \(\Q(\sqrt{73}) \) None None \(0\) \(0\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta q^{7}+(-1+\beta )q^{11}+3q^{13}+\cdots\)
1080.2.b.a 1080.b 24.f $16$ $8.624$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-2\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{6}q^{4}+q^{5}-\beta _{4}q^{7}-\beta _{7}q^{8}+\cdots\)
1080.2.b.b 1080.b 24.f $16$ $8.624$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-1\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}+\beta _{4}q^{4}-q^{5}-\beta _{2}q^{7}+\beta _{1}q^{8}+\cdots\)
1080.2.b.c 1080.b 24.f $16$ $8.624$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(1\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{2}+\beta _{4}q^{4}+q^{5}-\beta _{2}q^{7}-\beta _{1}q^{8}+\cdots\)
1080.2.b.d 1080.b 24.f $16$ $8.624$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(2\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{6}q^{4}-q^{5}-\beta _{4}q^{7}+\beta _{7}q^{8}+\cdots\)
1080.2.d.a 1080.d 40.f $4$ $8.624$ \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) None \(-3\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-1+\beta _{3})q^{2}+(\beta _{2}-\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1080.2.d.b 1080.d 40.f $4$ $8.624$ \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-30}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}+2\beta _{1}q^{8}+\cdots\)
1080.2.d.c 1080.d 40.f $4$ $8.624$ \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-30}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}-2\beta _{1}q^{8}+\cdots\)
1080.2.d.d 1080.d 40.f $4$ $8.624$ \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(-6\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{3}q^{2}+2q^{4}+(-2-\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)
1080.2.d.e 1080.d 40.f $4$ $8.624$ \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(6\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{3}q^{2}+2q^{4}+(2+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots\)
1080.2.d.f 1080.d 40.f $4$ $8.624$ \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) None \(3\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(1-\beta _{3})q^{2}+(\beta _{2}-\beta _{3})q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
1080.2.d.g 1080.d 40.f $16$ $8.624$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-2\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{12}q^{2}+(-1+\beta _{3}+\beta _{5})q^{4}-\beta _{10}q^{5}+\cdots\)
1080.2.d.h 1080.d 40.f $16$ $8.624$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(2\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{12}q^{2}+(-1+\beta _{3}+\beta _{5})q^{4}+\beta _{10}q^{5}+\cdots\)
1080.2.d.i 1080.d 40.f $20$ $8.624$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{8}q^{2}+\beta _{11}q^{4}+\beta _{14}q^{5}+(\beta _{12}+\cdots)q^{7}+\cdots\)
1080.2.d.j 1080.d 40.f $20$ $8.624$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{14}q^{5}+(1-\beta _{3}+\cdots)q^{7}+\cdots\)
1080.2.f.a 1080.f 5.b $2$ $8.624$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2+i)q^{5}+2iq^{7}-2q^{11}+2iq^{13}+\cdots\)
1080.2.f.b 1080.f 5.b $2$ $8.624$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-2i)q^{5}+4iq^{7}-q^{11}+iq^{13}+\cdots\)
1080.2.f.c 1080.f 5.b $2$ $8.624$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+2i)q^{5}+4iq^{7}+q^{11}+iq^{13}+\cdots\)
1080.2.f.d 1080.f 5.b $2$ $8.624$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2-i)q^{5}+2iq^{7}+2q^{11}+2iq^{13}+\cdots\)
1080.2.f.e 1080.f 5.b $4$ $8.624$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{2}+\beta _{3})q^{5}-\beta _{2}q^{7}+(2-\beta _{1}+\cdots)q^{11}+\cdots\)
1080.2.f.f 1080.f 5.b $4$ $8.624$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{2}-\beta _{3})q^{5}-\beta _{2}q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots\)
1080.2.f.g 1080.f 5.b $8$ $8.624$ 8.0.2702336256.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{5}-\beta _{1}q^{7}+(-2\beta _{3}-\beta _{6}+2\beta _{7})q^{11}+\cdots\)
1080.2.k.a 1080.k 8.b $12$ $8.624$ 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{9}q^{2}-\beta _{8}q^{4}-\beta _{7}q^{5}+(-\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots\)
1080.2.k.b 1080.k 8.b $16$ $8.624$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{9}q^{2}-\beta _{2}q^{4}-\beta _{7}q^{5}-\beta _{14}q^{7}+\cdots\)
1080.2.k.c 1080.k 8.b $16$ $8.624$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{8}q^{5}-\beta _{11}q^{7}+\cdots\)
1080.2.k.d 1080.k 8.b $20$ $8.624$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+\beta _{4}q^{4}-\beta _{6}q^{5}-\beta _{12}q^{7}+\cdots\)
1080.2.m.a 1080.m 120.m $8$ $8.624$ 8.0.12960000.1 \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{3}q^{2}+\beta _{1}q^{4}+(\beta _{3}+\beta _{6})q^{5}+(-\beta _{2}+\cdots)q^{8}+\cdots\)
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