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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
245.2.a.a 245.a 1.a $1$ $1.956$ \(\Q\) None \(-2\) \(-3\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+2q^{4}+q^{5}+6q^{6}+\cdots\)
245.2.a.b 245.a 1.a $1$ $1.956$ \(\Q\) None \(-2\) \(3\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+2q^{4}-q^{5}-6q^{6}+\cdots\)
245.2.a.c 245.a 1.a $1$ $1.956$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{5}-2q^{9}-3q^{11}+\cdots\)
245.2.a.d 245.a 1.a $2$ $1.956$ \(\Q(\sqrt{17}) \) None \(-1\) \(1\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1-\beta )q^{3}+(2+\beta )q^{4}-q^{5}+\cdots\)
245.2.a.e 245.a 1.a $2$ $1.956$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1-\beta )q^{3}-q^{5}+(-2-\beta )q^{6}+\cdots\)
245.2.a.f 245.a 1.a $2$ $1.956$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{3}+q^{5}+(2+\beta )q^{6}+\cdots\)
245.2.a.g 245.a 1.a $2$ $1.956$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(-1+\beta )q^{3}+(1+2\beta )q^{4}+\cdots\)
245.2.a.h 245.a 1.a $2$ $1.956$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1-\beta )q^{3}+(1+2\beta )q^{4}+\cdots\)
245.2.b.a 245.b 5.b $2$ $1.956$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+iq^{3}-2q^{4}+(2+i)q^{5}+\cdots\)
245.2.b.b 245.b 5.b $2$ $1.956$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}+q^{4}+(-1+2i)q^{5}+\cdots\)
245.2.b.c 245.b 5.b $2$ $1.956$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}+q^{4}+(1-2i)q^{5}-q^{6}+\cdots\)
245.2.b.d 245.b 5.b $2$ $1.956$ \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{3}+2q^{4}+\beta q^{5}-2q^{9}-3q^{11}+\cdots\)
245.2.b.e 245.b 5.b $4$ $1.956$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+\beta _{2}q^{3}-4q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
245.2.b.f 245.b 5.b $4$ $1.956$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{2}+(2\zeta_{8}+2\zeta_{8}^{3})q^{3}+q^{4}+\cdots\)
245.2.e.a 245.e 7.c $2$ $1.956$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots\)
245.2.e.b 245.e 7.c $2$ $1.956$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots\)
245.2.e.c 245.e 7.c $2$ $1.956$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
245.2.e.d 245.e 7.c $2$ $1.956$ \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
245.2.e.e 245.e 7.c $4$ $1.956$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
245.2.e.f 245.e 7.c $4$ $1.956$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-1+\cdots)q^{5}+\cdots\)
245.2.e.g 245.e 7.c $4$ $1.956$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
245.2.e.h 245.e 7.c $4$ $1.956$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(1\) \(-1\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots\)
245.2.e.i 245.e 7.c $4$ $1.956$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(1\) \(1\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots\)
245.2.f.a 245.f 35.f $4$ $1.956$ \(\Q(\zeta_{12})\) None \(2\) \(-2\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}+\cdots)q^{3}+\cdots\)
245.2.f.b 245.f 35.f $4$ $1.956$ \(\Q(\zeta_{12})\) None \(2\) \(2\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-\zeta_{12}+\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
245.2.f.c 245.f 35.f $24$ $1.956$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
245.2.j.a 245.j 35.j $4$ $1.956$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-6\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+(4+4\beta _{2}+\cdots)q^{4}+\cdots\)
245.2.j.b 245.j 35.j $4$ $1.956$ \(\Q(\sqrt{-3}, \sqrt{-5})\) \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{1}q^{3}+(-2+2\beta _{2})q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
245.2.j.c 245.j 35.j $4$ $1.956$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
245.2.j.d 245.j 35.j $4$ $1.956$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+2\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots\)
245.2.j.e 245.j 35.j $4$ $1.956$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+2\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots\)
245.2.j.f 245.j 35.j $4$ $1.956$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(6\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(4+4\beta _{2}+\cdots)q^{4}+\cdots\)
245.2.j.g 245.j 35.j $8$ $1.956$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{24}^{2}-\zeta_{24}^{6})q^{2}+(2\zeta_{24}^{3}+2\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
245.2.k.a 245.k 49.e $54$ $1.956$ None \(1\) \(-2\) \(9\) \(-1\) $\mathrm{SU}(2)[C_{7}]$
245.2.k.b 245.k 49.e $66$ $1.956$ None \(-1\) \(-2\) \(-11\) \(-5\) $\mathrm{SU}(2)[C_{7}]$
245.2.l.a 245.l 35.k $4$ $1.956$ \(\Q(\zeta_{12})\) None \(-4\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12})q^{2}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
245.2.l.b 245.l 35.k $4$ $1.956$ \(\Q(\zeta_{12})\) None \(2\) \(4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1+\zeta_{12}+\cdots)q^{3}+\cdots\)
245.2.l.c 245.l 35.k $8$ $1.956$ 8.0.3317760000.2 None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\beta _{2}-\beta _{4})q^{2}+\beta _{1}q^{3}+\beta _{5}q^{5}+\cdots\)
245.2.l.d 245.l 35.k $48$ $1.956$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
245.2.p.a 245.p 245.p $12$ $1.956$ \(\Q(\zeta_{28})\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{14}]$ \(q-\zeta_{28}^{9}q^{2}+(-2\zeta_{28}^{3}+\zeta_{28}^{5}-\zeta_{28}^{7}+\cdots)q^{3}+\cdots\)
245.2.p.b 245.p 245.p $144$ $1.956$ None \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{14}]$
245.2.q.a 245.q 49.g $96$ $1.956$ None \(-1\) \(1\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{21}]$
245.2.q.b 245.q 49.g $120$ $1.956$ None \(1\) \(1\) \(10\) \(-2\) $\mathrm{SU}(2)[C_{21}]$
245.2.s.a 245.s 245.s $312$ $1.956$ None \(-10\) \(-14\) \(-14\) \(-18\) $\mathrm{SU}(2)[C_{28}]$
245.2.t.a 245.t 245.t $312$ $1.956$ None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{42}]$
245.2.x.a 245.x 245.x $624$ $1.956$ None \(-26\) \(-22\) \(-28\) \(-18\) $\mathrm{SU}(2)[C_{84}]$
245.3.c.a 245.c 35.c $12$ $6.676$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+\beta _{9}q^{3}+(-1+\beta _{1})q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\)
245.3.c.b 245.c 35.c $24$ $6.676$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
245.3.d.a 245.d 7.b $12$ $6.676$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{11}q^{3}+(2-\beta _{5}+\beta _{6})q^{4}+\cdots\)
245.3.d.b 245.d 7.b $16$ $6.676$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{2})q^{2}+\beta _{6}q^{3}+(3-\beta _{1})q^{4}+\cdots\)
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