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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2025.1.i.a 2025.i 45.h $4$ $1.011$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{7}-\zeta_{12}^{5}q^{13}+\cdots\)
2025.1.j.a 2025.j 9.d $2$ $1.011$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{7}-\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+\cdots\)
2025.1.j.b 2025.j 9.d $2$ $1.011$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+\cdots\)
2025.1.j.c 2025.j 9.d $4$ $1.011$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{3}q^{8}-\zeta_{12}^{4}q^{16}+\cdots\)
2025.1.p.a 2025.p 45.k $4$ $1.011$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{4}-\zeta_{12}^{4}q^{16}-\zeta_{12}^{3}q^{19}+\cdots\)
2025.1.p.b 2025.p 45.k $8$ $1.011$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}^{3}-\zeta_{24}^{7})q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{6}+\cdots)q^{4}+\cdots\)
2025.1.p.c 2025.p 45.k $8$ $1.011$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{10}q^{4}+(-\zeta_{24}^{3}-\zeta_{24}^{7})q^{7}+\cdots\)
2025.1.y.a 2025.y 225.t $16$ $1.011$ \(\Q(\zeta_{60})\) None None \(0\) \(0\) \(0\) \(4\) \(q+(\zeta_{60}^{5}-\zeta_{60}^{23})q^{2}+(\zeta_{60}^{10}-\zeta_{60}^{16}+\cdots)q^{4}+\cdots\)
2025.2.a.a 2025.a 1.a $1$ $16.170$ \(\Q\) None None \(-2\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+5q^{11}-4q^{13}-4q^{16}+\cdots\)
2025.2.a.b 2025.a 1.a $1$ $16.170$ \(\Q\) None None \(-1\) \(0\) \(0\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{7}+3q^{8}-2q^{11}+\cdots\)
2025.2.a.c 2025.a 1.a $1$ $16.170$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-2q^{7}-3q^{11}+4q^{13}+4q^{16}+\cdots\)
2025.2.a.d 2025.a 1.a $1$ $16.170$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-2q^{7}+3q^{11}+4q^{13}+4q^{16}+\cdots\)
2025.2.a.e 2025.a 1.a $1$ $16.170$ \(\Q\) None None \(1\) \(0\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+3q^{7}-3q^{8}+2q^{11}+\cdots\)
2025.2.a.f 2025.a 1.a $1$ $16.170$ \(\Q\) None None \(2\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-5q^{11}-4q^{13}-4q^{16}+\cdots\)
2025.2.a.g 2025.a 1.a $2$ $16.170$ \(\Q(\sqrt{3}) \) None None \(-2\) \(0\) \(0\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+(3+\beta )q^{7}+\cdots\)
2025.2.a.h 2025.a 1.a $2$ $16.170$ \(\Q(\sqrt{13}) \) None None \(-1\) \(0\) \(0\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1+\beta )q^{4}+(-2-\beta )q^{7}-3q^{8}+\cdots\)
2025.2.a.i 2025.a 1.a $2$ $16.170$ \(\Q(\sqrt{13}) \) None None \(-1\) \(0\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1+\beta )q^{4}+(2+\beta )q^{7}-3q^{8}+\cdots\)
2025.2.a.j 2025.a 1.a $2$ $16.170$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}-2q^{7}-\beta q^{8}+2\beta q^{11}+\cdots\)
2025.2.a.k 2025.a 1.a $2$ $16.170$ \(\Q(\sqrt{13}) \) None None \(1\) \(0\) \(0\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}+(-2-\beta )q^{7}+3q^{8}+\cdots\)
2025.2.a.l 2025.a 1.a $2$ $16.170$ \(\Q(\sqrt{13}) \) None None \(1\) \(0\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}+(2+\beta )q^{7}+3q^{8}+\cdots\)
2025.2.a.m 2025.a 1.a $2$ $16.170$ \(\Q(\sqrt{3}) \) None None \(2\) \(0\) \(0\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(2+2\beta )q^{4}+(3-\beta )q^{7}+\cdots\)
2025.2.a.n 2025.a 1.a $3$ $16.170$ 3.3.564.1 None None \(-1\) \(0\) \(0\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-2+\beta _{1})q^{7}+\cdots\)
2025.2.a.o 2025.a 1.a $3$ $16.170$ 3.3.564.1 None None \(1\) \(0\) \(0\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-2+\beta _{1})q^{7}+\cdots\)
2025.2.a.p 2025.a 1.a $4$ $16.170$ 4.4.11661.1 None None \(-2\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2025.2.a.q 2025.a 1.a $4$ $16.170$ 4.4.11661.1 None None \(-2\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2025.2.a.r 2025.a 1.a $4$ $16.170$ \(\Q(\zeta_{24})^+\) None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-2\beta _{3})q^{7}+\cdots\)
2025.2.a.s 2025.a 1.a $4$ $16.170$ \(\Q(\zeta_{24})^+\) None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+\beta _{3}q^{7}-2\beta _{2}q^{8}-\beta _{1}q^{11}+\cdots\)
2025.2.a.t 2025.a 1.a $4$ $16.170$ \(\Q(\zeta_{24})^+\) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+2\beta _{3})q^{7}+\beta _{3}q^{8}+\cdots\)
2025.2.a.u 2025.a 1.a $4$ $16.170$ \(\Q(\sqrt{3}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}-\beta _{2}q^{4}+(-1+\beta _{2})q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)
2025.2.a.v 2025.a 1.a $4$ $16.170$ \(\Q(\sqrt{3}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}-\beta _{2}q^{4}+(1-\beta _{2})q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)
2025.2.a.w 2025.a 1.a $4$ $16.170$ \(\Q(\sqrt{3}, \sqrt{11})\) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{7}+\cdots\)
2025.2.a.x 2025.a 1.a $4$ $16.170$ \(\Q(\sqrt{3}, \sqrt{11})\) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}+\beta _{3})q^{7}+\cdots\)
2025.2.a.y 2025.a 1.a $4$ $16.170$ 4.4.11661.1 None None \(2\) \(0\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{7}+\cdots\)
2025.2.a.z 2025.a 1.a $4$ $16.170$ 4.4.11661.1 None None \(2\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{7}+\cdots\)
2025.2.b.a 2025.b 5.b $2$ $16.170$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-2q^{4}-5q^{11}+2iq^{13}-4q^{16}+\cdots\)
2025.2.b.b 2025.b 5.b $2$ $16.170$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-2q^{4}+5q^{11}-2iq^{13}-4q^{16}+\cdots\)
2025.2.b.c 2025.b 5.b $2$ $16.170$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}-3iq^{7}+3iq^{8}-2q^{11}+\cdots\)
2025.2.b.d 2025.b 5.b $2$ $16.170$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+3iq^{7}+3iq^{8}+2q^{11}+\cdots\)
2025.2.b.e 2025.b 5.b $2$ $16.170$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}-iq^{7}-3q^{11}-2iq^{13}+4q^{16}+\cdots\)
2025.2.b.f 2025.b 5.b $2$ $16.170$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}-iq^{7}+3q^{11}-2iq^{13}+4q^{16}+\cdots\)
2025.2.b.g 2025.b 5.b $4$ $16.170$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{3}q^{2}+(-2+2\zeta_{12})q^{4}+(2\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
2025.2.b.h 2025.b 5.b $4$ $16.170$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{3}q^{2}+(-2+2\zeta_{12})q^{4}+(-2\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
2025.2.b.i 2025.b 5.b $4$ $16.170$ \(\Q(i, \sqrt{13})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
2025.2.b.j 2025.b 5.b $4$ $16.170$ \(\Q(i, \sqrt{13})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
2025.2.b.k 2025.b 5.b $4$ $16.170$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}^{2}q^{2}-q^{4}-2\zeta_{12}q^{7}+\zeta_{12}^{2}q^{8}+\cdots\)
2025.2.b.l 2025.b 5.b $6$ $16.170$ 6.0.5089536.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{4}-\beta _{5})q^{7}+\cdots\)
2025.2.b.m 2025.b 5.b $6$ $16.170$ 6.0.5089536.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+(-2+\beta _{3})q^{4}+(\beta _{4}+\beta _{5})q^{7}+\cdots\)
2025.2.b.n 2025.b 5.b $8$ $16.170$ 8.0.\(\cdots\).6 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{4}-\beta _{6})q^{4}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
2025.2.b.o 2025.b 5.b $8$ $16.170$ 8.0.\(\cdots\).6 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{4}-\beta _{6})q^{4}+(\beta _{2}+\cdots)q^{7}+\cdots\)
2025.2.b.p 2025.b 5.b $8$ $16.170$ 8.0.49787136.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{2}+\beta _{4}q^{4}+(-\beta _{1}+2\beta _{3})q^{7}+\cdots\)
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