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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
378.2.a.a 378.a 1.a $1$ $3.018$ \(\Q\) None \(-1\) \(0\) \(-4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-4q^{5}-q^{7}-q^{8}+4q^{10}+\cdots\)
378.2.a.b 378.a 1.a $1$ $3.018$ \(\Q\) None \(-1\) \(0\) \(-3\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots\)
378.2.a.c 378.a 1.a $1$ $3.018$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
378.2.a.d 378.a 1.a $1$ $3.018$ \(\Q\) None \(-1\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{13}-q^{14}+\cdots\)
378.2.a.e 378.a 1.a $1$ $3.018$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{13}+q^{14}+\cdots\)
378.2.a.f 378.a 1.a $1$ $3.018$ \(\Q\) None \(1\) \(0\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
378.2.a.g 378.a 1.a $1$ $3.018$ \(\Q\) None \(1\) \(0\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots\)
378.2.a.h 378.a 1.a $1$ $3.018$ \(\Q\) None \(1\) \(0\) \(4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{5}-q^{7}+q^{8}+4q^{10}+\cdots\)
378.2.d.a 378.d 21.c $4$ $3.018$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{3}q^{2}-q^{4}+(-2\zeta_{12}+\zeta_{12}^{3})q^{5}+\cdots\)
378.2.d.b 378.d 21.c $4$ $3.018$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}q^{2}-q^{4}-\zeta_{12}^{3}q^{5}+(2-\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
378.2.d.c 378.d 21.c $4$ $3.018$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{2}-q^{4}-2\zeta_{12}^{3}q^{5}+(2-\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
378.2.e.a 378.e 63.h $2$ $3.018$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(-3+3\zeta_{6})q^{5}+(-3+\cdots)q^{7}+\cdots\)
378.2.e.b 378.e 63.h $2$ $3.018$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(3-3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
378.2.e.c 378.e 63.h $6$ $3.018$ 6.0.309123.1 None \(-6\) \(0\) \(5\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(2-2\beta _{4}+\beta _{5})q^{5}+(1+\cdots)q^{7}+\cdots\)
378.2.e.d 378.e 63.h $6$ $3.018$ 6.0.309123.1 None \(6\) \(0\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}-\beta _{2}q^{5}+(\beta _{3}+\beta _{4}-\beta _{5})q^{7}+\cdots\)
378.2.f.a 378.f 9.c $2$ $3.018$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
378.2.f.b 378.f 9.c $2$ $3.018$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots\)
378.2.f.c 378.f 9.c $4$ $3.018$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-2\) \(0\) \(3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1})q^{2}-\beta _{1}q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
378.2.f.d 378.f 9.c $4$ $3.018$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(0\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1})q^{2}-\beta _{1}q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
378.2.g.a 378.g 7.c $2$ $3.018$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
378.2.g.b 378.g 7.c $2$ $3.018$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(-3+2\zeta_{6})q^{7}+\cdots\)
378.2.g.c 378.g 7.c $2$ $3.018$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
378.2.g.d 378.g 7.c $2$ $3.018$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
378.2.g.e 378.g 7.c $2$ $3.018$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(-3+2\zeta_{6})q^{7}+\cdots\)
378.2.g.f 378.g 7.c $2$ $3.018$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots\)
378.2.g.g 378.g 7.c $4$ $3.018$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(-2\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
378.2.g.h 378.g 7.c $4$ $3.018$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
378.2.h.a 378.h 63.g $2$ $3.018$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-6\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3q^{5}+(3+\cdots)q^{7}+\cdots\)
378.2.h.b 378.h 63.g $2$ $3.018$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(6\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
378.2.h.c 378.h 63.g $6$ $3.018$ 6.0.309123.1 None \(-3\) \(0\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{4})q^{2}-\beta _{4}q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots\)
378.2.h.d 378.h 63.g $6$ $3.018$ 6.0.309123.1 None \(3\) \(0\) \(-10\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{2}+(-1+\beta _{4})q^{4}+(-2-\beta _{1}+\cdots)q^{5}+\cdots\)
378.2.k.a 378.k 21.g $4$ $3.018$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-1+3\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
378.2.k.b 378.k 21.g $4$ $3.018$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2\zeta_{12}+4\zeta_{12}^{3})q^{5}+\cdots\)
378.2.k.c 378.k 21.g $4$ $3.018$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(\zeta_{12}-2\zeta_{12}^{3})q^{5}+\cdots\)
378.2.k.d 378.k 21.g $8$ $3.018$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(\zeta_{24}^{5}-\zeta_{24}^{6}+\cdots)q^{5}+\cdots\)
378.2.l.a 378.l 63.i $16$ $3.018$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}+\beta _{7})q^{2}-q^{4}+(-\beta _{5}-\beta _{10}+\cdots)q^{5}+\cdots\)
378.2.m.a 378.m 63.o $16$ $3.018$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{7}q^{2}+(1+\beta _{5})q^{4}+(\beta _{6}+\beta _{8}-\beta _{15})q^{5}+\cdots\)
378.2.t.a 378.t 63.s $16$ $3.018$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{2}+(1-\beta _{8})q^{4}+(-\beta _{12}-\beta _{14}+\cdots)q^{5}+\cdots\)
378.2.u.a 378.u 27.e $6$ $3.018$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q-\zeta_{18}q^{2}+(\zeta_{18}-2\zeta_{18}^{4})q^{3}+\zeta_{18}^{2}q^{4}+\cdots\)
378.2.u.b 378.u 27.e $12$ $3.018$ 12.0.\(\cdots\).1 None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+\beta _{7}q^{2}+(-\beta _{2}+\beta _{4}+\beta _{5}-\beta _{10}+\cdots)q^{3}+\cdots\)
378.2.u.c 378.u 27.e $24$ $3.018$ None \(0\) \(-3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{9}]$
378.2.u.d 378.u 27.e $30$ $3.018$ None \(0\) \(-3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{9}]$
378.2.u.e 378.u 27.e $36$ $3.018$ None \(0\) \(3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{9}]$
378.2.v.a 378.v 189.u $72$ $3.018$ None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{9}]$
378.2.v.b 378.v 189.u $72$ $3.018$ None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{9}]$
378.2.w.a 378.w 189.w $72$ $3.018$ None \(0\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{9}]$
378.2.w.b 378.w 189.w $72$ $3.018$ None \(0\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{9}]$
378.2.z.a 378.z 189.ae $144$ $3.018$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
378.2.ba.a 378.ba 189.ad $144$ $3.018$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
378.2.bf.a 378.bf 189.aa $144$ $3.018$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$
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