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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
448.1.l.a 448.l 112.l $2$ $0.224$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{7}-iq^{9}+(1+i)q^{11}+iq^{25}+\cdots\)
448.1.r.a 448.r 28.g $4$ $0.224$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(0\) \(q+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}q^{11}+\cdots\)
448.1.bf.a 448.bf 448.af $8$ $0.224$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}q^{2}+\zeta_{16}^{2}q^{4}+\zeta_{16}^{5}q^{7}-\zeta_{16}^{3}q^{8}+\cdots\)
448.2.a.a 448.a 1.a $1$ $3.577$ \(\Q\) None None \(0\) \(-2\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{7}+q^{9}+4q^{13}+6q^{17}+\cdots\)
448.2.a.b 448.a 1.a $1$ $3.577$ \(\Q\) None None \(0\) \(-2\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots\)
448.2.a.c 448.a 1.a $1$ $3.577$ \(\Q\) None None \(0\) \(-2\) \(4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+4q^{5}+q^{7}+q^{9}-8q^{15}+\cdots\)
448.2.a.d 448.a 1.a $1$ $3.577$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-3q^{9}+4q^{11}-2q^{13}+\cdots\)
448.2.a.e 448.a 1.a $1$ $3.577$ \(\Q\) None None \(0\) \(0\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-3q^{9}-4q^{11}-2q^{13}+\cdots\)
448.2.a.f 448.a 1.a $1$ $3.577$ \(\Q\) None None \(0\) \(2\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots\)
448.2.a.g 448.a 1.a $1$ $3.577$ \(\Q\) None None \(0\) \(2\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{7}+q^{9}+4q^{13}+6q^{17}+\cdots\)
448.2.a.h 448.a 1.a $1$ $3.577$ \(\Q\) None None \(0\) \(2\) \(4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+4q^{5}-q^{7}+q^{9}+8q^{15}+\cdots\)
448.2.a.i 448.a 1.a $2$ $3.577$ \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-1+\beta )q^{5}-q^{7}+\cdots\)
448.2.a.j 448.a 1.a $2$ $3.577$ \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-1+\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
448.2.b.a 448.b 8.b $2$ $3.577$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-2iq^{5}-q^{7}-q^{9}-iq^{11}+\cdots\)
448.2.b.b 448.b 8.b $2$ $3.577$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{5}+q^{7}-q^{9}-iq^{11}+\cdots\)
448.2.b.c 448.b 8.b $4$ $3.577$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}q^{3}-\zeta_{12}q^{5}-q^{7}+(-1+\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)
448.2.b.d 448.b 8.b $4$ $3.577$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}q^{3}+\zeta_{12}q^{5}+q^{7}+(-1+\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)
448.2.e.a 448.e 56.e $8$ $3.577$ 8.0.629407744.1 \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{3}q^{3}+\beta _{1}q^{5}-\beta _{4}q^{7}+(-3-\beta _{7})q^{9}+\cdots\)
448.2.e.b 448.e 56.e $8$ $3.577$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{24}^{2}q^{3}+\zeta_{24}^{6}q^{5}-\zeta_{24}^{4}q^{7}+\cdots\)
448.2.f.a 448.f 28.d $2$ $3.577$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{3}-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+q^{9}+\cdots\)
448.2.f.b 448.f 28.d $2$ $3.577$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{7}-3q^{9}-2\beta q^{11}-2\beta q^{23}+\cdots\)
448.2.f.c 448.f 28.d $2$ $3.577$ \(\Q(\sqrt{-3}) \) None None \(0\) \(4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{3}+2\zeta_{6}q^{5}+(2-\zeta_{6})q^{7}+q^{9}+\cdots\)
448.2.f.d 448.f 28.d $8$ $3.577$ \(\Q(\zeta_{16})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{16}^{2}q^{3}-\zeta_{16}^{5}q^{5}-\zeta_{16}^{4}q^{7}+\cdots\)
448.2.i.a 448.i 7.c $2$ $3.577$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
448.2.i.b 448.i 7.c $2$ $3.577$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
448.2.i.c 448.i 7.c $2$ $3.577$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
448.2.i.d 448.i 7.c $2$ $3.577$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
448.2.i.e 448.i 7.c $2$ $3.577$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
448.2.i.f 448.i 7.c $2$ $3.577$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
448.2.i.g 448.i 7.c $4$ $3.577$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(-2\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{3}+(2\beta _{1}-\beta _{2}+2\beta _{3})q^{5}+\cdots\)
448.2.i.h 448.i 7.c $4$ $3.577$ \(\Q(\sqrt{-3}, \sqrt{7})\) None None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}+3\beta _{2}q^{5}+\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots\)
448.2.i.i 448.i 7.c $4$ $3.577$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(1-\zeta_{12}^{2})q^{5}+\cdots\)
448.2.i.j 448.i 7.c $4$ $3.577$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(2\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{3}+(-2\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+\cdots\)
448.2.j.a 448.j 112.j $4$ $3.577$ \(\Q(i, \sqrt{7})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q-\beta _{2}q^{7}+3\beta _{1}q^{9}+(-2+2\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
448.2.j.b 448.j 112.j $4$ $3.577$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{2}+\beta _{3})q^{5}+(1-\beta _{2})q^{7}-3\beta _{1}q^{9}+\cdots\)
448.2.j.c 448.j 112.j $4$ $3.577$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+\cdots\)
448.2.j.d 448.j 112.j $16$ $3.577$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{6}q^{3}+\beta _{5}q^{5}+(-1+\beta _{13})q^{7}+\cdots\)
448.2.m.a 448.m 16.e $2$ $3.577$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2+2i)q^{5}+iq^{7}+3iq^{9}+(-1+\cdots)q^{11}+\cdots\)
448.2.m.b 448.m 16.e $2$ $3.577$ \(\Q(\sqrt{-1}) \) None None \(0\) \(4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2-2i)q^{3}+(-2-2i)q^{5}-iq^{7}+\cdots\)
448.2.m.c 448.m 16.e $8$ $3.577$ 8.0.214798336.3 None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{4}q^{3}+\beta _{1}q^{5}+\beta _{5}q^{7}+(-\beta _{5}-\beta _{7})q^{9}+\cdots\)
448.2.m.d 448.m 16.e $12$ $3.577$ 12.0.\(\cdots\).1 None None \(0\) \(-4\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{6}q^{3}+(1+\beta _{2}+\beta _{3}+\beta _{5})q^{5}-\beta _{3}q^{7}+\cdots\)
448.2.p.a 448.p 28.f $2$ $3.577$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
448.2.p.b 448.p 28.f $2$ $3.577$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-3\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
448.2.p.c 448.p 28.f $4$ $3.577$ \(\Q(\sqrt{-3}, \sqrt{7})\) None None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{3}+(2+\beta _{2})q^{5}+\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots\)
448.2.p.d 448.p 28.f $4$ $3.577$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(1+\zeta_{12}^{2})q^{5}+\cdots\)
448.2.p.e 448.p 28.f $16$ $3.577$ 16.0.\(\cdots\).2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{14}q^{3}+\beta _{13}q^{5}+\beta _{9}q^{7}+(-\beta _{3}+\cdots)q^{9}+\cdots\)
448.2.q.a 448.q 56.m $8$ $3.577$ 8.0.12960000.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}+\beta _{7})q^{3}+\beta _{6}q^{5}+(2\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots\)
448.2.q.b 448.q 56.m $12$ $3.577$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{5}q^{3}+(\beta _{6}-\beta _{7})q^{5}+(\beta _{4}-\beta _{10}+\cdots)q^{7}+\cdots\)
448.2.q.c 448.q 56.m $12$ $3.577$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{5}q^{3}+(-\beta _{6}+\beta _{7})q^{5}+(-\beta _{4}+\beta _{10}+\cdots)q^{7}+\cdots\)
448.2.t.a 448.t 56.p $8$ $3.577$ 8.0.49787136.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{4}q^{3}+\beta _{6}q^{5}+(\beta _{5}-\beta _{7})q^{7}+(-2+\cdots)q^{9}+\cdots\)
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