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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
980.1.f.a 980.f 20.d $1$ $0.489$ \(\Q\) \(\Q(\sqrt{-5}) \) None \(-1\) \(-1\) \(-1\) \(0\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
980.1.f.b 980.f 20.d $1$ $0.489$ \(\Q\) \(\Q(\sqrt{-5}) \) None \(-1\) \(1\) \(1\) \(0\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
980.1.f.c 980.f 20.d $1$ $0.489$ \(\Q\) \(\Q(\sqrt{-5}) \) None \(1\) \(-1\) \(1\) \(0\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
980.1.f.d 980.f 20.d $1$ $0.489$ \(\Q\) \(\Q(\sqrt{-5}) \) None \(1\) \(1\) \(-1\) \(0\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
980.1.f.e 980.f 20.d $4$ $0.489$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}q^{5}-\zeta_{8}^{2}q^{8}+\cdots\)
980.1.j.a 980.j 140.j $8$ $0.489$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{4}q^{4}+\zeta_{16}^{5}q^{5}+\cdots\)
980.1.l.a 980.l 5.c $4$ $0.489$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+\zeta_{8}^{3}q^{5}-q^{11}-\zeta_{8}q^{13}+\cdots\)
980.1.n.a 980.n 35.i $2$ $0.489$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-35}) \) None \(0\) \(-1\) \(1\) \(0\) \(q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}+q^{13}+\cdots\)
980.1.n.b 980.n 35.i $2$ $0.489$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-35}) \) None \(0\) \(1\) \(-1\) \(0\) \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}-q^{13}+\cdots\)
980.1.p.a 980.p 140.p $2$ $0.489$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(-1\) \(-1\) \(1\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots\)
980.1.p.b 980.p 140.p $2$ $0.489$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(1\) \(1\) \(1\) \(0\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots\)
980.1.p.c 980.p 140.p $8$ $0.489$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{8}q^{4}-\zeta_{24}^{7}q^{5}+\cdots\)
980.1.w.a 980.w 35.l $8$ $0.489$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{3}+\zeta_{24}^{5}q^{5}+\zeta_{24}^{4}q^{11}+\cdots\)
980.1.y.a 980.y 140.x $16$ $0.489$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{48}^{2}q^{2}+\zeta_{48}^{4}q^{4}+\zeta_{48}^{5}q^{5}+\cdots\)
980.1.ba.a 980.ba 980.aa $6$ $0.489$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-5}) \) None \(-1\) \(5\) \(-1\) \(-1\) \(q-\zeta_{14}q^{2}+(1+\zeta_{14}^{6})q^{3}+\zeta_{14}^{2}q^{4}+\cdots\)
980.1.ba.b 980.ba 980.aa $6$ $0.489$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-5}) \) None \(1\) \(-5\) \(-1\) \(1\) \(q+\zeta_{14}q^{2}+(-1-\zeta_{14}^{6})q^{3}+\zeta_{14}^{2}q^{4}+\cdots\)
980.1.bq.a 980.bq 980.aq $12$ $0.489$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-5}) \) None \(-1\) \(8\) \(1\) \(-1\) \(q-\zeta_{42}^{4}q^{2}+(\zeta_{42}^{3}+\zeta_{42}^{7})q^{3}+\zeta_{42}^{8}q^{4}+\cdots\)
980.1.bq.b 980.bq 980.aq $12$ $0.489$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-5}) \) None \(1\) \(-8\) \(1\) \(1\) \(q+\zeta_{42}^{4}q^{2}+(-\zeta_{42}^{3}-\zeta_{42}^{7})q^{3}+\cdots\)
980.2.a.a 980.a 1.a $1$ $7.825$ \(\Q\) None None \(0\) \(-3\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{5}+6q^{9}-2q^{11}-6q^{13}+\cdots\)
980.2.a.b 980.a 1.a $1$ $7.825$ \(\Q\) None None \(0\) \(-3\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+q^{5}+6q^{9}-5q^{11}+3q^{13}+\cdots\)
980.2.a.c 980.a 1.a $1$ $7.825$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{9}+3q^{11}+q^{13}+\cdots\)
980.2.a.d 980.a 1.a $1$ $7.825$ \(\Q\) None None \(0\) \(-1\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{9}-q^{11}+5q^{13}+\cdots\)
980.2.a.e 980.a 1.a $1$ $7.825$ \(\Q\) None None \(0\) \(-1\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{9}+6q^{11}-2q^{13}+\cdots\)
980.2.a.f 980.a 1.a $1$ $7.825$ \(\Q\) None None \(0\) \(1\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{9}-q^{11}-5q^{13}+\cdots\)
980.2.a.g 980.a 1.a $1$ $7.825$ \(\Q\) None None \(0\) \(1\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{9}+6q^{11}+2q^{13}+\cdots\)
980.2.a.h 980.a 1.a $1$ $7.825$ \(\Q\) None None \(0\) \(2\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
980.2.a.i 980.a 1.a $1$ $7.825$ \(\Q\) None None \(0\) \(3\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{5}+6q^{9}-2q^{11}+6q^{13}+\cdots\)
980.2.a.j 980.a 1.a $2$ $7.825$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}+(-1+\cdots)q^{11}+\cdots\)
980.2.a.k 980.a 1.a $2$ $7.825$ \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}+(-1+2\beta )q^{11}+\cdots\)
980.2.c.a 980.c 140.c $8$ $7.825$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{16}^{2}q^{2}-2q^{4}-\zeta_{16}^{4}q^{5}+2\zeta_{16}^{2}q^{8}+\cdots\)
980.2.c.b 980.c 140.c $8$ $7.825$ 8.0.3317760000.3 \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+2q^{4}+\beta _{6}q^{5}+(-\beta _{5}+\cdots)q^{6}+\cdots\)
980.2.c.c 980.c 140.c $16$ $7.825$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(-\beta _{8}-\beta _{10}-\beta _{12})q^{3}+\cdots\)
980.2.c.d 980.c 140.c $32$ $7.825$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
980.2.c.e 980.c 140.c $48$ $7.825$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
980.2.e.a 980.e 5.b $2$ $7.825$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-i)q^{5}+3q^{9}+2iq^{13}-2iq^{17}+\cdots\)
980.2.e.b 980.e 5.b $2$ $7.825$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+(2+i)q^{5}-6q^{9}+3q^{11}+\cdots\)
980.2.e.c 980.e 5.b $4$ $7.825$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None None \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+\beta _{1}q^{5}+(-2-\beta _{1}-\beta _{3})q^{11}+\cdots\)
980.2.e.d 980.e 5.b $4$ $7.825$ \(\Q(\sqrt{-5}, \sqrt{-21})\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-4+\beta _{3})q^{9}+(1+\cdots)q^{11}+\cdots\)
980.2.e.e 980.e 5.b $4$ $7.825$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}-q^{11}-\beta _{2}q^{13}+\cdots\)
980.2.e.f 980.e 5.b $4$ $7.825$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None None \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}-\beta _{3}q^{5}+(-2-\beta _{1}-\beta _{3})q^{11}+\cdots\)
980.2.g.a 980.g 28.d $32$ $7.825$ None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
980.2.g.b 980.g 28.d $48$ $7.825$ None None \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
980.2.i.a 980.i 7.c $2$ $7.825$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots\)
980.2.i.b 980.i 7.c $2$ $7.825$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots\)
980.2.i.c 980.i 7.c $2$ $7.825$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
980.2.i.d 980.i 7.c $2$ $7.825$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
980.2.i.e 980.i 7.c $2$ $7.825$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots\)
980.2.i.f 980.i 7.c $2$ $7.825$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-6+\cdots)q^{11}+\cdots\)
980.2.i.g 980.i 7.c $2$ $7.825$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(1+\cdots)q^{11}+\cdots\)
980.2.i.h 980.i 7.c $2$ $7.825$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots\)
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