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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
725.1.g.a 725.g 29.c $2$ $0.362$ \(\Q(\sqrt{-1}) \) None \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{4}-iq^{9}+(-1-i)q^{11}-q^{16}+\cdots\)
725.1.h.a 725.h 145.h $2$ $0.362$ \(\Q(\sqrt{-1}) \) None \(\Q(\sqrt{29}) \) \(0\) \(0\) \(0\) \(2\) \(q-iq^{4}+(1-i)q^{7}+iq^{9}+(-1-i+\cdots)q^{13}+\cdots\)
725.2.a.a 725.a 1.a $1$ $5.789$ \(\Q\) None None \(1\) \(0\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+2q^{7}-3q^{8}-3q^{9}-6q^{11}+\cdots\)
725.2.a.b 725.a 1.a $2$ $5.789$ \(\Q(\sqrt{2}) \) None None \(2\) \(-2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(-1-\beta )q^{3}+(1+2\beta )q^{4}+\cdots\)
725.2.a.c 725.a 1.a $2$ $5.789$ \(\Q(\sqrt{2}) \) None None \(2\) \(4\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+2q^{3}+(1+2\beta )q^{4}+(2+\cdots)q^{6}+\cdots\)
725.2.a.d 725.a 1.a $3$ $5.789$ 3.3.148.1 None None \(-3\) \(2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+\cdots\)
725.2.a.e 725.a 1.a $3$ $5.789$ 3.3.148.1 None None \(-1\) \(-2\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
725.2.a.f 725.a 1.a $4$ $5.789$ \(\Q(\zeta_{24})^+\) None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
725.2.a.g 725.a 1.a $4$ $5.789$ \(\Q(\sqrt{3}, \sqrt{11})\) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+q^{4}+(-2-\beta _{3})q^{6}+\cdots\)
725.2.a.h 725.a 1.a $5$ $5.789$ 5.5.240881.1 None None \(-2\) \(-6\) \(0\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
725.2.a.i 725.a 1.a $5$ $5.789$ 5.5.294577.1 None None \(0\) \(-6\) \(0\) \(-10\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+(1+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
725.2.a.j 725.a 1.a $5$ $5.789$ 5.5.294577.1 None None \(0\) \(6\) \(0\) \(10\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(1+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
725.2.a.k 725.a 1.a $5$ $5.789$ 5.5.240881.1 None None \(2\) \(6\) \(0\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
725.2.a.l 725.a 1.a $6$ $5.789$ 6.6.337383424.1 None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{4})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
725.2.b.a 725.b 5.b $2$ $5.789$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+2iq^{7}+3iq^{8}+3q^{9}+\cdots\)
725.2.b.b 725.b 5.b $4$ $5.789$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(\zeta_{8}+\zeta_{8}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
725.2.b.c 725.b 5.b $4$ $5.789$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}^{3})q^{4}+\cdots\)
725.2.b.d 725.b 5.b $6$ $5.789$ 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+(\beta _{2}-\beta _{4})q^{3}+(-2-\beta _{3}+\cdots)q^{4}+\cdots\)
725.2.b.e 725.b 5.b $6$ $5.789$ 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(\beta _{2}-\beta _{4})q^{3}+\beta _{1}q^{4}+(-1+\cdots)q^{6}+\cdots\)
725.2.b.f 725.b 5.b $10$ $5.789$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{4}+\beta _{7})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
725.2.b.g 725.b 5.b $10$ $5.789$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{2}+\beta _{7})q^{3}+(-1+\beta _{5}+\cdots)q^{4}+\cdots\)
725.2.c.a 725.c 29.b $2$ $5.789$ \(\Q(\sqrt{-5}) \) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-3q^{4}-2q^{7}-\beta q^{8}+3q^{9}+\cdots\)
725.2.c.b 725.c 29.b $2$ $5.789$ \(\Q(\sqrt{-5}) \) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-3q^{4}+2q^{7}-\beta q^{8}+3q^{9}+\cdots\)
725.2.c.c 725.c 29.b $2$ $5.789$ \(\Q(\sqrt{-5}) \) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-\beta q^{3}-3q^{4}+5q^{6}-2q^{7}+\cdots\)
725.2.c.d 725.c 29.b $4$ $5.789$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots\)
725.2.c.e 725.c 29.b $6$ $5.789$ 6.0.16516096.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
725.2.c.f 725.c 29.b $8$ $5.789$ 8.0.1731891456.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{7}q^{2}-\beta _{5}q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots\)
725.2.c.g 725.c 29.b $10$ $5.789$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
725.2.c.h 725.c 29.b $10$ $5.789$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
725.2.d.a 725.d 145.d $4$ $5.789$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{3}q^{3}+3q^{4}+5q^{6}-2\beta _{1}q^{7}+\cdots\)
725.2.d.b 725.d 145.d $8$ $5.789$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{24}^{6}q^{2}+(\zeta_{24}^{3}-\zeta_{24}^{6})q^{3}+\zeta_{24}^{2}q^{4}+\cdots\)
725.2.d.c 725.d 145.d $12$ $5.789$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{7}q^{2}+(\beta _{5}-\beta _{7})q^{3}+(1+\beta _{4})q^{4}+\cdots\)
725.2.d.d 725.d 145.d $20$ $5.789$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+\beta _{16}q^{3}+(1-\beta _{9})q^{4}+(1+\cdots)q^{6}+\cdots\)
725.2.e.a 725.e 145.e $4$ $5.789$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}-3q^{4}+(-\beta _{2}+\beta _{3})q^{7}-\beta _{2}q^{8}+\cdots\)
725.2.e.b 725.e 145.e $16$ $5.789$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{7}q^{2}+\beta _{9}q^{3}-\beta _{2}q^{4}+(\beta _{4}+\beta _{6}+\cdots)q^{6}+\cdots\)
725.2.e.c 725.e 145.e $26$ $5.789$ None None \(0\) \(4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$
725.2.e.d 725.e 145.e $40$ $5.789$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
725.2.j.a 725.j 145.j $4$ $5.789$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{2}+3q^{4}+(\beta _{2}-\beta _{3})q^{7}+\beta _{3}q^{8}+\cdots\)
725.2.j.b 725.j 145.j $16$ $5.789$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+\beta _{2}q^{4}+(\beta _{4}+\beta _{6}+\cdots)q^{6}+\cdots\)
725.2.j.c 725.j 145.j $26$ $5.789$ None None \(6\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$
725.2.j.d 725.j 145.j $40$ $5.789$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
725.2.k.a 725.k 25.d $4$ $5.789$ \(\Q(\zeta_{10})\) None None \(0\) \(-4\) \(-5\) \(-12\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+2\zeta_{10}^{3}q^{4}+\cdots\)
725.2.k.b 725.k 25.d $128$ $5.789$ None None \(0\) \(-2\) \(3\) \(-2\) $\mathrm{SU}(2)[C_{5}]$
725.2.k.c 725.k 25.d $148$ $5.789$ None None \(0\) \(2\) \(8\) \(10\) $\mathrm{SU}(2)[C_{5}]$
725.2.l.a 725.l 29.d $6$ $5.789$ \(\Q(\zeta_{14})\) None None \(-3\) \(-7\) \(0\) \(7\) $\mathrm{SU}(2)[C_{7}]$ \(q+(-\zeta_{14}^{3}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{2}+(-1+\cdots)q^{3}+\cdots\)
725.2.l.b 725.l 29.d $6$ $5.789$ \(\Q(\zeta_{14})\) None None \(2\) \(5\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{7}]$ \(q+(1-\zeta_{14}-\zeta_{14}^{3}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{2}+\cdots\)
725.2.l.c 725.l 29.d $6$ $5.789$ \(\Q(\zeta_{14})\) None None \(3\) \(7\) \(0\) \(-7\) $\mathrm{SU}(2)[C_{7}]$ \(q+(\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+(1-\zeta_{14}^{2}+\cdots)q^{3}+\cdots\)
725.2.l.d 725.l 29.d $24$ $5.789$ None None \(2\) \(-2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{7}]$
725.2.l.e 725.l 29.d $36$ $5.789$ None None \(2\) \(2\) \(0\) \(8\) $\mathrm{SU}(2)[C_{7}]$
725.2.l.f 725.l 29.d $54$ $5.789$ None None \(-1\) \(-7\) \(0\) \(3\) $\mathrm{SU}(2)[C_{7}]$
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