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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2280.1.t.a 2280.t 2280.t $1$ $1.138$ \(\Q\) \(\Q(\sqrt{-95}) \), \(\Q(\sqrt{-570}) \) \(\Q(\sqrt{6}) \) \(-1\) \(-1\) \(-1\) \(0\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
2280.1.t.b 2280.t 2280.t $1$ $1.138$ \(\Q\) \(\Q(\sqrt{-95}) \), \(\Q(\sqrt{-570}) \) \(\Q(\sqrt{6}) \) \(-1\) \(1\) \(1\) \(0\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
2280.1.t.c 2280.t 2280.t $1$ $1.138$ \(\Q\) \(\Q(\sqrt{-95}) \), \(\Q(\sqrt{-570}) \) \(\Q(\sqrt{6}) \) \(1\) \(-1\) \(1\) \(0\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
2280.1.t.d 2280.t 2280.t $1$ $1.138$ \(\Q\) \(\Q(\sqrt{-95}) \), \(\Q(\sqrt{-570}) \) \(\Q(\sqrt{6}) \) \(1\) \(1\) \(-1\) \(0\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
2280.1.t.e 2280.t 2280.t $2$ $1.138$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-95}) \), \(\Q(\sqrt{-114}) \) \(\Q(\sqrt{30}) \) \(0\) \(0\) \(-2\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{5}-q^{6}+iq^{8}+\cdots\)
2280.1.t.f 2280.t 2280.t $2$ $1.138$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-114}) \) \(\Q(\sqrt{190}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}-iq^{5}+q^{6}+iq^{8}+\cdots\)
2280.1.t.g 2280.t 2280.t $2$ $1.138$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-114}) \) \(\Q(\sqrt{190}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}-iq^{5}+q^{6}-iq^{8}+\cdots\)
2280.1.t.h 2280.t 2280.t $2$ $1.138$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-95}) \), \(\Q(\sqrt{-114}) \) \(\Q(\sqrt{30}) \) \(0\) \(0\) \(2\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}+q^{5}-q^{6}+iq^{8}+\cdots\)
2280.1.t.i 2280.t 2280.t $4$ $1.138$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}-q^{5}+\cdots\)
2280.1.t.j 2280.t 2280.t $4$ $1.138$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+q^{5}-\zeta_{8}^{2}q^{6}+\cdots\)
2280.1.cf.a 2280.cf 2280.bf $4$ $1.138$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{5}q^{3}-q^{4}-\zeta_{12}^{5}q^{5}+\cdots\)
2280.1.cf.b 2280.cf 2280.bf $4$ $1.138$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}+\cdots\)
2280.1.cs.a 2280.cs 2280.bs $4$ $1.138$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}-q^{4}-\zeta_{12}q^{5}+\cdots\)
2280.1.cs.b 2280.cs 2280.bs $4$ $1.138$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}q^{5}+\cdots\)
2280.1.dj.a 2280.dj 2280.cj $8$ $1.138$ \(\Q(\zeta_{24})\) None None \(0\) \(-4\) \(0\) \(0\) \(q+\zeta_{24}q^{2}-\zeta_{24}^{4}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}q^{5}+\cdots\)
2280.1.dj.b 2280.dj 2280.cj $8$ $1.138$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}q^{2}-\zeta_{24}^{10}q^{3}+\zeta_{24}^{2}q^{4}+\cdots\)
2280.1.ea.a 2280.ea 2280.da $12$ $1.138$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{36}^{13}q^{2}+\zeta_{36}^{11}q^{3}-\zeta_{36}^{8}q^{4}+\cdots\)
2280.1.ea.b 2280.ea 2280.da $12$ $1.138$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{36}^{15}q^{2}+\zeta_{36}^{11}q^{3}-\zeta_{36}^{12}q^{4}+\cdots\)
2280.1.el.a 2280.el 2280.dl $12$ $1.138$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{36}^{7}q^{2}+\zeta_{36}^{17}q^{3}+\zeta_{36}^{14}q^{4}+\cdots\)
2280.1.el.b 2280.el 2280.dl $12$ $1.138$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{36}^{15}q^{2}+\zeta_{36}^{17}q^{3}-\zeta_{36}^{12}q^{4}+\cdots\)
2280.2.a.a 2280.a 1.a $1$ $18.206$ \(\Q\) None None \(0\) \(-1\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}-2q^{13}-q^{15}-6q^{17}+\cdots\)
2280.2.a.b 2280.a 1.a $1$ $18.206$ \(\Q\) None None \(0\) \(-1\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
2280.2.a.c 2280.a 1.a $1$ $18.206$ \(\Q\) None None \(0\) \(-1\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
2280.2.a.d 2280.a 1.a $1$ $18.206$ \(\Q\) None None \(0\) \(-1\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots\)
2280.2.a.e 2280.a 1.a $1$ $18.206$ \(\Q\) None None \(0\) \(1\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
2280.2.a.f 2280.a 1.a $1$ $18.206$ \(\Q\) None None \(0\) \(1\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
2280.2.a.g 2280.a 1.a $1$ $18.206$ \(\Q\) None None \(0\) \(1\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
2280.2.a.h 2280.a 1.a $1$ $18.206$ \(\Q\) None None \(0\) \(1\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
2280.2.a.i 2280.a 1.a $1$ $18.206$ \(\Q\) None None \(0\) \(1\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
2280.2.a.j 2280.a 1.a $1$ $18.206$ \(\Q\) None None \(0\) \(1\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+4q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
2280.2.a.k 2280.a 1.a $2$ $18.206$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
2280.2.a.l 2280.a 1.a $2$ $18.206$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
2280.2.a.m 2280.a 1.a $2$ $18.206$ \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
2280.2.a.n 2280.a 1.a $2$ $18.206$ \(\Q(\sqrt{7}) \) None None \(0\) \(-2\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(-1+\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
2280.2.a.o 2280.a 1.a $2$ $18.206$ \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(-2+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
2280.2.a.p 2280.a 1.a $2$ $18.206$ \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(-2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(3+\beta )q^{7}+q^{9}+(1-\beta )q^{11}+\cdots\)
2280.2.a.q 2280.a 1.a $2$ $18.206$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(2\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(-3+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
2280.2.a.r 2280.a 1.a $3$ $18.206$ 3.3.568.1 None None \(0\) \(-3\) \(-3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(-1-\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
2280.2.a.s 2280.a 1.a $3$ $18.206$ 3.3.316.1 None None \(0\) \(-3\) \(3\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(-1+\beta _{1})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
2280.2.a.t 2280.a 1.a $3$ $18.206$ 3.3.1016.1 None None \(0\) \(3\) \(-3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+\beta _{2}q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
2280.2.a.u 2280.a 1.a $3$ $18.206$ 3.3.1772.1 None None \(0\) \(3\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+\beta _{2}q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots\)
2280.2.j.a 2280.j 5.b $2$ $18.206$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-2+i)q^{5}+4iq^{7}-q^{9}+\cdots\)
2280.2.j.b 2280.j 5.b $2$ $18.206$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-1+2i)q^{5}+2iq^{7}-q^{9}+\cdots\)
2280.2.j.c 2280.j 5.b $2$ $18.206$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+(-1-2i)q^{5}+2iq^{7}-q^{9}+\cdots\)
2280.2.j.d 2280.j 5.b $2$ $18.206$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+(-1-2i)q^{5}+2iq^{7}-q^{9}+\cdots\)
2280.2.j.e 2280.j 5.b $2$ $18.206$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-1-2i)q^{5}+4iq^{7}-q^{9}+\cdots\)
2280.2.j.f 2280.j 5.b $6$ $18.206$ 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+(\beta _{1}-\beta _{4})q^{5}+(-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
2280.2.j.g 2280.j 5.b $10$ $18.206$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{3}+(1-\beta _{2}-\beta _{4})q^{5}+(\beta _{6}+\beta _{9})q^{7}+\cdots\)
2280.2.j.h 2280.j 5.b $12$ $18.206$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+\beta _{10}q^{5}+\beta _{2}q^{7}-q^{9}-\beta _{8}q^{11}+\cdots\)
2280.2.j.i 2280.j 5.b $18$ $18.206$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{9}q^{3}+\beta _{2}q^{5}-\beta _{5}q^{7}-q^{9}-\beta _{3}q^{11}+\cdots\)
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