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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
135.1.d.a 135.d 15.d $1$ $0.067$ \(\Q\) \(\Q(\sqrt{-15}) \) None \(-1\) \(0\) \(1\) \(0\) \(q-q^{2}+q^{5}+q^{8}-q^{10}-q^{16}-q^{17}+\cdots\)
135.1.d.b 135.d 15.d $1$ $0.067$ \(\Q\) \(\Q(\sqrt{-15}) \) None \(1\) \(0\) \(-1\) \(0\) \(q+q^{2}-q^{5}-q^{8}-q^{10}-q^{16}+q^{17}+\cdots\)
135.2.a.a 135.a 1.a $1$ $1.078$ \(\Q\) None None \(-2\) \(0\) \(-1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{5}-3q^{7}+2q^{10}+\cdots\)
135.2.a.b 135.a 1.a $1$ $1.078$ \(\Q\) None None \(2\) \(0\) \(1\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{5}-3q^{7}+2q^{10}+\cdots\)
135.2.a.c 135.a 1.a $2$ $1.078$ \(\Q(\sqrt{13}) \) None None \(-1\) \(0\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1+\beta )q^{4}+q^{5}+(2-2\beta )q^{7}+\cdots\)
135.2.a.d 135.a 1.a $2$ $1.078$ \(\Q(\sqrt{13}) \) None None \(1\) \(0\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}-q^{5}+(2-2\beta )q^{7}+\cdots\)
135.2.b.a 135.b 5.b $4$ $1.078$ \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
135.2.b.b 135.b 5.b $4$ $1.078$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{2}+\zeta_{8}^{3}q^{5}-\zeta_{8}q^{7}+2\zeta_{8}^{2}q^{8}+\cdots\)
135.2.e.a 135.e 9.c $2$ $1.078$ \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(-1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots\)
135.2.e.b 135.e 9.c $6$ $1.078$ 6.0.954288.1 None None \(1\) \(0\) \(3\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{4}+\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
135.2.f.a 135.f 15.e $8$ $1.078$ 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{4}+(-\beta _{3}-\beta _{5}+\cdots)q^{5}+\cdots\)
135.2.f.b 135.f 15.e $8$ $1.078$ 8.0.\(\cdots\).8 None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(2\beta _{2}+\beta _{3}+\beta _{6})q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)
135.2.j.a 135.j 45.j $8$ $1.078$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{24}^{6}q^{2}-\zeta_{24}^{3}q^{4}+(\zeta_{24}-\zeta_{24}^{3}+\cdots)q^{5}+\cdots\)
135.2.k.a 135.k 27.e $30$ $1.078$ None None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
135.2.k.b 135.k 27.e $42$ $1.078$ None None \(0\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
135.2.m.a 135.m 45.l $16$ $1.078$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(6\) \(0\) \(6\) \(-2\) $\mathrm{SU}(2)[C_{12}]$ \(q+\beta _{5}q^{2}+(\beta _{5}+\beta _{8}+\beta _{15})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
135.2.p.a 135.p 135.p $96$ $1.078$ None None \(0\) \(0\) \(-9\) \(0\) $\mathrm{SU}(2)[C_{18}]$
135.2.q.a 135.q 135.q $192$ $1.078$ None None \(-12\) \(-12\) \(-12\) \(-12\) $\mathrm{SU}(2)[C_{36}]$
135.3.c.a 135.c 3.b $2$ $3.678$ \(\Q(\sqrt{-5}) \) None None \(0\) \(0\) \(0\) \(24\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-q^{4}-\beta q^{5}+12q^{7}+3\beta q^{8}+\cdots\)
135.3.c.b 135.c 3.b $4$ $3.678$ \(\Q(\sqrt{-5}, \sqrt{-29})\) None None \(0\) \(0\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-5+\beta _{3})q^{4}+\beta _{2}q^{5}+(-4+\cdots)q^{7}+\cdots\)
135.3.c.c 135.c 3.b $4$ $3.678$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{3}q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
135.3.d.a 135.d 15.d $2$ $3.678$ \(\Q(\sqrt{-11}) \) None None \(-2\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-3q^{4}-\beta q^{5}+(-1+2\beta )q^{7}+\cdots\)
135.3.d.b 135.d 15.d $2$ $3.678$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-3q^{4}+(4+i)q^{5}-2iq^{7}+7q^{8}+\cdots\)
135.3.d.c 135.d 15.d $2$ $3.678$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-15}) \) None \(-1\) \(0\) \(10\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-1-\beta )q^{2}+(8+\beta )q^{4}+5q^{5}+(-15+\cdots)q^{8}+\cdots\)
135.3.d.d 135.d 15.d $2$ $3.678$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-15}) \) None \(1\) \(0\) \(-10\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(1+\beta )q^{2}+(8+\beta )q^{4}-5q^{5}+(15+\cdots)q^{8}+\cdots\)
135.3.d.e 135.d 15.d $2$ $3.678$ \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-3q^{4}+(-4+i)q^{5}+2iq^{7}+\cdots\)
135.3.d.f 135.d 15.d $2$ $3.678$ \(\Q(\sqrt{-11}) \) None None \(2\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-3q^{4}+(1-\beta )q^{5}+(1-2\beta )q^{7}+\cdots\)
135.3.d.g 135.d 15.d $4$ $3.678$ \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+6q^{4}-\beta _{2}q^{5}+\beta _{1}q^{7}-2\beta _{3}q^{8}+\cdots\)
135.3.g.a 135.g 5.c $16$ $3.678$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(2\beta _{4}+\beta _{7})q^{4}-\beta _{13}q^{5}+\cdots\)
135.3.g.b 135.g 5.c $16$ $3.678$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(2\beta _{3}+\beta _{4})q^{4}+\beta _{10}q^{5}+\cdots\)
135.3.h.a 135.h 45.h $20$ $3.678$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{2}+(-2+\beta _{3}-2\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots\)
135.3.i.a 135.i 9.d $16$ $3.678$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{4})q^{2}+(\beta _{1}-\beta _{3}-\beta _{4}+2\beta _{7}+\cdots)q^{4}+\cdots\)
135.3.l.a 135.l 45.k $40$ $3.678$ None None \(2\) \(0\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{12}]$
135.3.n.a 135.n 135.n $204$ $3.678$ None None \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{18}]$
135.3.o.a 135.o 27.f $144$ $3.678$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
135.3.r.a 135.r 135.r $408$ $3.678$ None None \(-12\) \(-12\) \(-12\) \(-12\) $\mathrm{SU}(2)[C_{36}]$
135.4.a.a 135.a 1.a $1$ $7.965$ \(\Q\) None None \(-2\) \(0\) \(5\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-4q^{4}+5q^{5}+24q^{8}-10q^{10}+\cdots\)
135.4.a.b 135.a 1.a $1$ $7.965$ \(\Q\) None None \(-1\) \(0\) \(-5\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-7q^{4}-5q^{5}-6q^{7}+15q^{8}+\cdots\)
135.4.a.c 135.a 1.a $1$ $7.965$ \(\Q\) None None \(1\) \(0\) \(5\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-7q^{4}+5q^{5}-6q^{7}-15q^{8}+\cdots\)
135.4.a.d 135.a 1.a $1$ $7.965$ \(\Q\) None None \(2\) \(0\) \(-5\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-4q^{4}-5q^{5}-24q^{8}-10q^{10}+\cdots\)
135.4.a.e 135.a 1.a $3$ $7.965$ 3.3.1772.1 None None \(-5\) \(0\) \(-15\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{2}+(7-3\beta _{1}+\beta _{2})q^{4}+\cdots\)
135.4.a.f 135.a 1.a $3$ $7.965$ 3.3.5637.1 None None \(-1\) \(0\) \(15\) \(44\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(7+\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots\)
135.4.a.g 135.a 1.a $3$ $7.965$ 3.3.5637.1 None None \(1\) \(0\) \(-15\) \(44\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(7+\beta _{1}+\beta _{2})q^{4}-5q^{5}+\cdots\)
135.4.a.h 135.a 1.a $3$ $7.965$ 3.3.1772.1 None None \(5\) \(0\) \(15\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{2}+(7-3\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots\)
135.4.b.a 135.b 5.b $4$ $7.965$ \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{2}+(-13-\beta _{3})q^{4}-5\beta _{1}q^{5}+\cdots\)
135.4.b.b 135.b 5.b $8$ $7.965$ 8.0.\(\cdots\).7 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{4}-2\beta _{5}+\cdots)q^{5}+\cdots\)
135.4.b.c 135.b 5.b $12$ $7.965$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{7}q^{2}+(-5-\beta _{1})q^{4}-\beta _{3}q^{5}+\beta _{8}q^{7}+\cdots\)
135.4.e.a 135.e 9.c $4$ $7.965$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(-1\) \(0\) \(10\) \(-9\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
135.4.e.b 135.e 9.c $6$ $7.965$ 6.0.15759792.1 None None \(-1\) \(0\) \(15\) \(43\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{4})q^{2}+(-\beta _{2}+3\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
135.4.e.c 135.e 9.c $14$ $7.965$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(-2\) \(0\) \(-35\) \(-22\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{2})q^{2}+(-5-\beta _{3}-5\beta _{5}-\beta _{10}+\cdots)q^{4}+\cdots\)
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