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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
525.1.k.a 525.k 105.k $4$ $0.262$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{105}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
525.1.p.a 525.p 105.o $4$ $0.262$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
525.1.u.a 525.u 21.h $2$ $0.262$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots\)
525.1.u.b 525.u 21.h $2$ $0.262$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) \(q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots\)
525.1.be.a 525.be 105.w $8$ $0.262$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{11}q^{7}+\cdots\)
525.2.a.a 525.a 1.a $1$ $4.192$ \(\Q\) None None \(-1\) \(-1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}-q^{7}+3q^{8}+\cdots\)
525.2.a.b 525.a 1.a $1$ $4.192$ \(\Q\) None None \(-1\) \(1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}-q^{7}+3q^{8}+\cdots\)
525.2.a.c 525.a 1.a $1$ $4.192$ \(\Q\) None None \(1\) \(-1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}+q^{7}-3q^{8}+\cdots\)
525.2.a.d 525.a 1.a $1$ $4.192$ \(\Q\) None None \(1\) \(-1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}+q^{7}-3q^{8}+\cdots\)
525.2.a.e 525.a 1.a $2$ $4.192$ \(\Q(\sqrt{5}) \) None None \(-3\) \(-2\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots\)
525.2.a.f 525.a 1.a $2$ $4.192$ \(\Q(\sqrt{13}) \) None None \(-1\) \(-2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+\beta q^{6}-q^{7}+\cdots\)
525.2.a.g 525.a 1.a $2$ $4.192$ \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+3q^{4}-\beta q^{6}-q^{7}-\beta q^{8}+\cdots\)
525.2.a.h 525.a 1.a $2$ $4.192$ \(\Q(\sqrt{13}) \) None None \(1\) \(2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(1+\beta )q^{4}+\beta q^{6}+q^{7}+\cdots\)
525.2.a.i 525.a 1.a $2$ $4.192$ \(\Q(\sqrt{5}) \) None None \(3\) \(2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots\)
525.2.a.j 525.a 1.a $3$ $4.192$ 3.3.148.1 None None \(-1\) \(3\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
525.2.a.k 525.a 1.a $3$ $4.192$ 3.3.148.1 None None \(1\) \(-3\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
525.2.b.a 525.b 21.c $2$ $4.192$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{2}-\zeta_{6}q^{3}-q^{4}-3q^{6}+(-2+\cdots)q^{7}+\cdots\)
525.2.b.b 525.b 21.c $2$ $4.192$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}-q^{4}+3q^{6}+(-2+\cdots)q^{7}+\cdots\)
525.2.b.c 525.b 21.c $2$ $4.192$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-5\) $\mathrm{U}(1)[D_{2}]$ \(q+(1-2\zeta_{6})q^{3}+2q^{4}+(-2-\zeta_{6})q^{7}+\cdots\)
525.2.b.d 525.b 21.c $2$ $4.192$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(5\) $\mathrm{U}(1)[D_{2}]$ \(q+(1-2\zeta_{6})q^{3}+2q^{4}+(3-\zeta_{6})q^{7}+\cdots\)
525.2.b.e 525.b 21.c $4$ $4.192$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(-1\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+\beta _{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)
525.2.b.f 525.b 21.c $4$ $4.192$ \(\Q(\sqrt{5}, \sqrt{-7})\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{3}q^{3}+2q^{4}+(\beta _{1}-\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots\)
525.2.b.g 525.b 21.c $4$ $4.192$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(1\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}-\beta _{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)
525.2.b.h 525.b 21.c $8$ $4.192$ 8.0.\(\cdots\).7 None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-\beta _{7}q^{3}+(-2+\beta _{4})q^{4}+\beta _{3}q^{6}+\cdots\)
525.2.b.i 525.b 21.c $8$ $4.192$ 8.0.\(\cdots\).7 None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+\beta _{1}q^{3}+(-2+\beta _{4})q^{4}-\beta _{5}q^{6}+\cdots\)
525.2.b.j 525.b 21.c $8$ $4.192$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}q^{2}-\zeta_{24}^{3}q^{3}-q^{4}+(\zeta_{24}^{2}+\cdots)q^{6}+\cdots\)
525.2.d.a 525.d 5.b $2$ $4.192$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}+q^{4}-q^{6}+iq^{7}+3iq^{8}+\cdots\)
525.2.d.b 525.d 5.b $2$ $4.192$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}+q^{4}+q^{6}+iq^{7}+3iq^{8}+\cdots\)
525.2.d.c 525.d 5.b $4$ $4.192$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-\beta _{1}q^{3}-3q^{4}+\beta _{3}q^{6}-\beta _{1}q^{7}+\cdots\)
525.2.d.d 525.d 5.b $4$ $4.192$ \(\Q(i, \sqrt{13})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-2+\beta _{3})q^{4}+(1+\cdots)q^{6}+\cdots\)
525.2.d.e 525.d 5.b $4$ $4.192$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{3})q^{2}+\beta _{3}q^{3}+3\beta _{2}q^{4}+(1+\cdots)q^{6}+\cdots\)
525.2.g.a 525.g 105.g $4$ $4.192$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{12}q^{3}-2q^{4}+(\zeta_{12}-\zeta_{12}^{2})q^{7}+\cdots\)
525.2.g.b 525.g 105.g $4$ $4.192$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+q^{4}-3q^{6}+(-\zeta_{12}+\cdots)q^{7}+\cdots\)
525.2.g.c 525.g 105.g $4$ $4.192$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}q^{2}-\zeta_{12}q^{3}+q^{4}+3q^{6}+(-\zeta_{12}+\cdots)q^{7}+\cdots\)
525.2.g.d 525.g 105.g $8$ $4.192$ 8.0.303595776.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{4}-\beta _{5})q^{2}-\beta _{1}q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
525.2.g.e 525.g 105.g $8$ $4.192$ 8.0.303595776.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{2}+(-\beta _{2}-\beta _{4}-\beta _{6})q^{3}+(1+\cdots)q^{4}+\cdots\)
525.2.g.f 525.g 105.g $16$ $4.192$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{4}q^{3}+(1-\beta _{5})q^{4}-\beta _{8}q^{6}+\cdots\)
525.2.i.a 525.i 7.c $2$ $4.192$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
525.2.i.b 525.i 7.c $2$ $4.192$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(-1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
525.2.i.c 525.i 7.c $2$ $4.192$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(-2-\zeta_{6})q^{7}+\cdots\)
525.2.i.d 525.i 7.c $2$ $4.192$ \(\Q(\sqrt{-3}) \) None None \(1\) \(1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
525.2.i.e 525.i 7.c $2$ $4.192$ \(\Q(\sqrt{-3}) \) None None \(2\) \(1\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
525.2.i.f 525.i 7.c $4$ $4.192$ \(\Q(\zeta_{12})\) None None \(-2\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
525.2.i.g 525.i 7.c $4$ $4.192$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(-2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{3}q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
525.2.i.h 525.i 7.c $8$ $4.192$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-2\) \(4\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{1}-\beta _{3}+\beta _{4})q^{2}+\beta _{4}q^{3}+\cdots\)
525.2.i.i 525.i 7.c $8$ $4.192$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-1\) \(4\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(\beta _{2}-\beta _{3}+2\beta _{5}+\cdots)q^{4}+\cdots\)
525.2.i.j 525.i 7.c $8$ $4.192$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(1\) \(-4\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(\beta _{2}-\beta _{3}+2\beta _{5}+\cdots)q^{4}+\cdots\)
525.2.i.k 525.i 7.c $8$ $4.192$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(2\) \(-4\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{3}-\beta _{4})q^{2}-\beta _{4}q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
525.2.j.a 525.j 15.e $16$ $4.192$ 16.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta _{10}+\beta _{13}-\beta _{15})q^{2}+\beta _{7}q^{3}+\cdots\)
525.2.j.b 525.j 15.e $24$ $4.192$ None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
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