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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
405.1.h.a 405.h 45.h $2$ $0.202$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-15}) \) None \(-1\) \(0\) \(1\) \(0\) \(q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{5}-q^{8}-q^{10}+\zeta_{6}q^{16}+\cdots\)
405.1.h.b 405.h 45.h $2$ $0.202$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-15}) \) None \(1\) \(0\) \(-1\) \(0\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{5}+q^{8}-q^{10}+\zeta_{6}q^{16}+\cdots\)
405.2.a.a 405.a 1.a $1$ $3.234$ \(\Q\) None None \(-2\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{5}+2q^{10}-5q^{11}+\cdots\)
405.2.a.b 405.a 1.a $1$ $3.234$ \(\Q\) None None \(-1\) \(0\) \(1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}-3q^{7}+3q^{8}-q^{10}+\cdots\)
405.2.a.c 405.a 1.a $1$ $3.234$ \(\Q\) None None \(0\) \(0\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-q^{5}+2q^{7}-3q^{11}-4q^{13}+\cdots\)
405.2.a.d 405.a 1.a $1$ $3.234$ \(\Q\) None None \(0\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}+2q^{7}+3q^{11}-4q^{13}+\cdots\)
405.2.a.e 405.a 1.a $1$ $3.234$ \(\Q\) None None \(1\) \(0\) \(-1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}-3q^{7}-3q^{8}-q^{10}+\cdots\)
405.2.a.f 405.a 1.a $1$ $3.234$ \(\Q\) None None \(2\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{5}+2q^{10}+5q^{11}+\cdots\)
405.2.a.g 405.a 1.a $2$ $3.234$ \(\Q(\sqrt{3}) \) None None \(-2\) \(0\) \(2\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+q^{5}+(-3+\cdots)q^{7}+\cdots\)
405.2.a.h 405.a 1.a $2$ $3.234$ \(\Q(\sqrt{3}) \) None None \(2\) \(0\) \(-2\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(2+2\beta )q^{4}-q^{5}+(-3+\cdots)q^{7}+\cdots\)
405.2.a.i 405.a 1.a $3$ $3.234$ 3.3.564.1 None None \(-1\) \(0\) \(-3\) \(5\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
405.2.a.j 405.a 1.a $3$ $3.234$ 3.3.564.1 None None \(1\) \(0\) \(3\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
405.2.b.a 405.b 5.b $4$ $3.234$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(-2+\beta _{1}+\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
405.2.b.b 405.b 5.b $4$ $3.234$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(-2+\beta _{1}+\beta _{3})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
405.2.b.c 405.b 5.b $4$ $3.234$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
405.2.b.d 405.b 5.b $4$ $3.234$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)
405.2.b.e 405.b 5.b $4$ $3.234$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{7}-2\beta _{1}q^{8}+\cdots\)
405.2.e.a 405.e 9.c $2$ $3.234$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
405.2.e.b 405.e 9.c $2$ $3.234$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(-1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
405.2.e.c 405.e 9.c $2$ $3.234$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}-3q^{8}+\cdots\)
405.2.e.d 405.e 9.c $2$ $3.234$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots\)
405.2.e.e 405.e 9.c $2$ $3.234$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots\)
405.2.e.f 405.e 9.c $2$ $3.234$ \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+3q^{8}+\cdots\)
405.2.e.g 405.e 9.c $2$ $3.234$ \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+2q^{10}+\cdots\)
405.2.e.h 405.e 9.c $2$ $3.234$ \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(3+\cdots)q^{7}+\cdots\)
405.2.e.i 405.e 9.c $4$ $3.234$ \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(2\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}+\cdots)q^{4}+\cdots\)
405.2.e.j 405.e 9.c $4$ $3.234$ \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(-1\) \(0\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
405.2.e.k 405.e 9.c $4$ $3.234$ \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(1\) \(0\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
405.2.e.l 405.e 9.c $4$ $3.234$ \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(-2\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
405.2.f.a 405.f 15.e $16$ $3.234$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{2}+(\beta _{6}-\beta _{14})q^{4}-\beta _{4}q^{5}+\beta _{10}q^{7}+\cdots\)
405.2.f.b 405.f 15.e $24$ $3.234$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
405.2.j.a 405.j 45.j $4$ $3.234$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(-3\) \(0\) \(-6\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{3})q^{2}+(2-\beta _{1}-\beta _{2}+2\beta _{3})q^{4}+\cdots\)
405.2.j.b 405.j 45.j $4$ $3.234$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(-3\) \(0\) \(-3\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{3})q^{2}+(2-\beta _{1}-\beta _{2}+2\beta _{3})q^{4}+\cdots\)
405.2.j.c 405.j 45.j $4$ $3.234$ \(\Q(\sqrt{-3}, \sqrt{-5})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{1}q^{2}+3\beta _{2}q^{4}+(\beta _{1}-\beta _{3})q^{5}+\beta _{3}q^{8}+\cdots\)
405.2.j.d 405.j 45.j $4$ $3.234$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(3\) \(0\) \(3\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
405.2.j.e 405.j 45.j $4$ $3.234$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(3\) \(0\) \(6\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
405.2.j.f 405.j 45.j $8$ $3.234$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{24}^{6}q^{2}-\zeta_{24}^{4}q^{5}-\zeta_{24}q^{7}+(2\zeta_{24}^{5}+\cdots)q^{8}+\cdots\)
405.2.j.g 405.j 45.j $8$ $3.234$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{24}^{5}q^{2}+(\zeta_{24}^{2}+\zeta_{24}^{3})q^{5}+\zeta_{24}^{6}q^{7}+\cdots\)
405.2.j.h 405.j 45.j $8$ $3.234$ 8.0.12960000.1 \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q-\beta _{1}q^{2}+(2-\beta _{3}+2\beta _{5}+\beta _{6})q^{4}+\cdots\)
405.2.k.a 405.k 27.e $30$ $3.234$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
405.2.k.b 405.k 27.e $42$ $3.234$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$
405.2.m.a 405.m 45.l $8$ $3.234$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{12}]$ \(q+\zeta_{24}^{7}q^{2}+\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{3}+2\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
405.2.m.b 405.m 45.l $16$ $3.234$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\beta _{9}-\beta _{10})q^{2}+(-2\beta _{1}-\beta _{13}-\beta _{14}+\cdots)q^{4}+\cdots\)
405.2.m.c 405.m 45.l $16$ $3.234$ 16.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{12}]$ \(q-\beta _{10}q^{2}+(-\beta _{9}-\beta _{15})q^{4}+(-\beta _{7}+\cdots)q^{5}+\cdots\)
405.2.m.d 405.m 45.l $24$ $3.234$ None None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{12}]$
405.2.m.e 405.m 45.l $24$ $3.234$ None None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{12}]$
405.2.p.a 405.p 135.p $96$ $3.234$ None None \(0\) \(0\) \(9\) \(0\) $\mathrm{SU}(2)[C_{18}]$
405.2.q.a 405.q 81.g $306$ $3.234$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{27}]$
405.2.q.b 405.q 81.g $342$ $3.234$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{27}]$
405.2.r.a 405.r 135.q $192$ $3.234$ None None \(12\) \(0\) \(12\) \(-12\) $\mathrm{SU}(2)[C_{36}]$
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