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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
195.1.e.a 195.e 195.e $4$ $0.097$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots\)
195.2.a.a 195.a 1.a $1$ $1.557$ \(\Q\) None None \(-1\) \(1\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots\)
195.2.a.b 195.a 1.a $1$ $1.557$ \(\Q\) None None \(2\) \(-1\) \(1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+3q^{7}+\cdots\)
195.2.a.c 195.a 1.a $1$ $1.557$ \(\Q\) None None \(2\) \(1\) \(-1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-q^{7}+\cdots\)
195.2.a.d 195.a 1.a $1$ $1.557$ \(\Q\) None None \(2\) \(1\) \(1\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-3q^{7}+\cdots\)
195.2.a.e 195.a 1.a $3$ $1.557$ 3.3.316.1 None None \(0\) \(-3\) \(-3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(3+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
195.2.b.a 195.b 13.b $2$ $1.557$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+2q^{4}+iq^{5}+3iq^{7}+q^{9}+\cdots\)
195.2.b.b 195.b 13.b $2$ $1.557$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{3}+q^{4}+iq^{5}+iq^{6}-2iq^{7}+\cdots\)
195.2.b.c 195.b 13.b $4$ $1.557$ \(\Q(i, \sqrt{17})\) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+q^{3}+(-3+\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots\)
195.2.c.a 195.c 5.b $2$ $1.557$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2q^{4}+(-1+2i)q^{5}+iq^{7}+\cdots\)
195.2.c.b 195.c 5.b $10$ $1.557$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
195.2.h.a 195.h 65.d $2$ $1.557$ \(\Q(\sqrt{-1}) \) None None \(-4\) \(0\) \(-4\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{2}+iq^{3}+2q^{4}+(-2-i)q^{5}+\cdots\)
195.2.h.b 195.h 65.d $2$ $1.557$ \(\Q(\sqrt{-1}) \) None None \(4\) \(0\) \(4\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{2}+iq^{3}+2q^{4}+(2+i)q^{5}+2iq^{6}+\cdots\)
195.2.h.c 195.h 65.d $12$ $1.557$ 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{10}q^{2}+\beta _{1}q^{3}+(1+\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
195.2.i.a 195.i 13.c $2$ $1.557$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(-1\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
195.2.i.b 195.i 13.c $2$ $1.557$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{4}-q^{5}+\zeta_{6}q^{7}+\cdots\)
195.2.i.c 195.i 13.c $4$ $1.557$ \(\Q(\zeta_{12})\) None None \(2\) \(-2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}-\zeta_{12}q^{3}+(-2+\cdots)q^{4}+\cdots\)
195.2.i.d 195.i 13.c $6$ $1.557$ 6.0.1714608.1 None None \(0\) \(3\) \(6\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{3}+\beta _{5})q^{2}+(1+\beta _{4})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
195.2.i.e 195.i 13.c $6$ $1.557$ 6.0.591408.1 None None \(0\) \(3\) \(-6\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{5}q^{2}+(1-\beta _{4})q^{3}+(\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
195.2.k.a 195.k 65.f $28$ $1.557$ None None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$
195.2.m.a 195.m 15.e $48$ $1.557$ None None \(0\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$
195.2.n.a 195.n 195.n $48$ $1.557$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
195.2.o.a 195.o 39.f $40$ $1.557$ None None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{4}]$
195.2.s.a 195.s 195.s $16$ $1.557$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(2\beta _{2}+\beta _{12})q^{4}+\cdots\)
195.2.s.b 195.s 195.s $32$ $1.557$ None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
195.2.t.a 195.t 65.k $28$ $1.557$ None None \(-4\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$
195.2.v.a 195.v 65.l $32$ $1.557$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
195.2.ba.a 195.ba 65.n $24$ $1.557$ None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$
195.2.bb.a 195.bb 13.e $4$ $1.557$ \(\Q(\zeta_{12})\) None None \(-6\) \(-2\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
195.2.bb.b 195.bb 13.e $8$ $1.557$ 8.0.191102976.5 None None \(0\) \(4\) \(0\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2\beta _{1}+\beta _{3}-\beta _{5}-\beta _{7})q^{2}+(1-\beta _{4}+\cdots)q^{3}+\cdots\)
195.2.bb.c 195.bb 13.e $8$ $1.557$ 8.0.56070144.2 None None \(6\) \(-4\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{1}-\beta _{2}-\beta _{4}+\beta _{5}+\beta _{6})q^{2}+\cdots\)
195.2.bd.a 195.bd 65.o $56$ $1.557$ None None \(4\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{12}]$
195.2.bf.a 195.bf 195.af $96$ $1.557$ None None \(0\) \(-2\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{12}]$
195.2.bg.a 195.bg 39.k $72$ $1.557$ None None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{12}]$
195.2.bh.a 195.bh 195.ah $96$ $1.557$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
195.2.bl.a 195.bl 195.al $96$ $1.557$ None None \(0\) \(-2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{12}]$
195.2.bm.a 195.bm 65.t $56$ $1.557$ None None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{12}]$
195.3.d.a 195.d 3.b $32$ $5.313$ None None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
195.3.e.a 195.e 195.e $1$ $5.313$ \(\Q\) \(\Q(\sqrt{-195}) \) None \(0\) \(-3\) \(-5\) \(1\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{3}+4q^{4}-5q^{5}+q^{7}+9q^{9}+\cdots\)
195.3.e.b 195.e 195.e $1$ $5.313$ \(\Q\) \(\Q(\sqrt{-195}) \) None \(0\) \(-3\) \(5\) \(-1\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{3}+4q^{4}+5q^{5}-q^{7}+9q^{9}+\cdots\)
195.3.e.c 195.e 195.e $1$ $5.313$ \(\Q\) \(\Q(\sqrt{-195}) \) None \(0\) \(3\) \(-5\) \(-1\) $\mathrm{U}(1)[D_{2}]$ \(q+3q^{3}+4q^{4}-5q^{5}-q^{7}+9q^{9}+\cdots\)
195.3.e.d 195.e 195.e $1$ $5.313$ \(\Q\) \(\Q(\sqrt{-195}) \) None \(0\) \(3\) \(5\) \(1\) $\mathrm{U}(1)[D_{2}]$ \(q+3q^{3}+4q^{4}+5q^{5}+q^{7}+9q^{9}+\cdots\)
195.3.e.e 195.e 195.e $8$ $5.313$ 8.0.\(\cdots\).2 \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{6}q^{2}-3\beta _{1}q^{3}+(-4+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
195.3.e.f 195.e 195.e $40$ $5.313$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
195.3.f.a 195.f 15.d $48$ $5.313$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
195.3.g.a 195.g 39.d $4$ $5.313$ \(\Q(\sqrt{-2}, \sqrt{5})\) None None \(0\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-3q^{3}+q^{4}-\beta _{2}q^{5}+3\beta _{2}q^{6}+\cdots\)
195.3.g.b 195.g 39.d $32$ $5.313$ None None \(0\) \(12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
195.3.j.a 195.j 195.j $2$ $5.313$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+iq^{2}-3q^{3}+3q^{4}+5iq^{5}-3iq^{6}+\cdots\)
195.3.j.b 195.j 195.j $2$ $5.313$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-iq^{2}-3iq^{3}+3q^{4}-5iq^{5}-3q^{6}+\cdots\)
195.3.j.c 195.j 195.j $4$ $5.313$ \(\Q(\zeta_{8})\) None None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2\zeta_{8}+2\zeta_{8}^{3})q^{2}+(2+2\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots\)
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