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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
370.2.a.a 370.a 1.a $1$ $2.954$ \(\Q\) None \(-1\) \(-2\) \(-1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}-q^{5}+2q^{6}-q^{7}+\cdots\)
370.2.a.b 370.a 1.a $1$ $2.954$ \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{8}-3q^{9}+q^{10}+\cdots\)
370.2.a.c 370.a 1.a $1$ $2.954$ \(\Q\) None \(-1\) \(2\) \(1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
370.2.a.d 370.a 1.a $1$ $2.954$ \(\Q\) None \(1\) \(-2\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots\)
370.2.a.e 370.a 1.a $2$ $2.954$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(2\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots\)
370.2.a.f 370.a 1.a $2$ $2.954$ \(\Q(\sqrt{33}) \) None \(2\) \(4\) \(2\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}+(-1+\cdots)q^{7}+\cdots\)
370.2.a.g 370.a 1.a $3$ $2.954$ 3.3.892.1 None \(3\) \(0\) \(-3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{2}q^{3}+q^{4}-q^{5}-\beta _{2}q^{6}+\cdots\)
370.2.b.a 370.b 5.b $2$ $2.954$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(-2-i)q^{5}-2iq^{7}+\cdots\)
370.2.b.b 370.b 5.b $2$ $2.954$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(1+2i)q^{5}+iq^{7}-iq^{8}+\cdots\)
370.2.b.c 370.b 5.b $4$ $2.954$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}-q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
370.2.b.d 370.b 5.b $10$ $2.954$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(\beta _{4}-\beta _{5})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
370.2.c.a 370.c 185.d $10$ $2.954$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-10\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)
370.2.c.b 370.c 185.d $10$ $2.954$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(10\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)
370.2.d.a 370.d 37.b $2$ $2.954$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{5}-2q^{7}-iq^{8}+\cdots\)
370.2.d.b 370.d 37.b $2$ $2.954$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{5}+5q^{7}-iq^{8}+\cdots\)
370.2.d.c 370.d 37.b $6$ $2.954$ 6.0.399424.1 None \(0\) \(-4\) \(0\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(-1-\beta _{1}-\beta _{3})q^{3}-q^{4}+\cdots\)
370.2.e.a 370.e 37.c $2$ $2.954$ \(\Q(\sqrt{-3}) \) None \(1\) \(-2\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-2\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
370.2.e.b 370.e 37.c $2$ $2.954$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
370.2.e.c 370.e 37.c $2$ $2.954$ \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+3\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
370.2.e.d 370.e 37.c $4$ $2.954$ \(\Q(\zeta_{12})\) None \(-2\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{12})q^{2}+\zeta_{12}q^{3}-\zeta_{12}q^{4}+\cdots\)
370.2.e.e 370.e 37.c $4$ $2.954$ \(\Q(\sqrt{-3}, \sqrt{10})\) None \(2\) \(2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
370.2.e.f 370.e 37.c $6$ $2.954$ 6.0.2696112.1 None \(-3\) \(0\) \(3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}+\beta _{5}q^{3}+(-1+\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots\)
370.2.g.a 370.g 185.f $2$ $2.954$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(4\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+iq^{2}+(-1-i)q^{3}-q^{4}+(2+i)q^{5}+\cdots\)
370.2.g.b 370.g 185.f $2$ $2.954$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+iq^{2}-q^{4}+(-2+i)q^{5}+(-2-2i)q^{7}+\cdots\)
370.2.g.c 370.g 185.f $4$ $2.954$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}^{2}q^{2}+2\zeta_{8}q^{3}-q^{4}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
370.2.g.d 370.g 185.f $10$ $2.954$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(-2\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{6}q^{2}+(-\beta _{2}-\beta _{3}-\beta _{8})q^{3}-q^{4}+\cdots\)
370.2.g.e 370.g 185.f $20$ $2.954$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(-4\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{10}q^{2}-\beta _{1}q^{3}-q^{4}-\beta _{8}q^{5}+\beta _{4}q^{6}+\cdots\)
370.2.h.a 370.h 185.k $2$ $2.954$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+q^{2}+q^{4}+(-1+2i)q^{5}+(-2+2i)q^{7}+\cdots\)
370.2.h.b 370.h 185.k $2$ $2.954$ \(\Q(\sqrt{-1}) \) None \(2\) \(2\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+q^{2}+(1-i)q^{3}+q^{4}+(-1-2i)q^{5}+\cdots\)
370.2.h.c 370.h 185.k $4$ $2.954$ \(\Q(\zeta_{8})\) None \(4\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+q^{2}+2\zeta_{8}q^{3}+q^{4}+(-\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots\)
370.2.h.d 370.h 185.k $10$ $2.954$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(10\) \(2\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+q^{2}+(\beta _{1}-\beta _{4})q^{3}+q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
370.2.h.e 370.h 185.k $20$ $2.954$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-20\) \(4\) \(-4\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q-q^{2}-\beta _{4}q^{3}+q^{4}+\beta _{13}q^{5}+\beta _{4}q^{6}+\cdots\)
370.2.l.a 370.l 37.e $4$ $2.954$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
370.2.l.b 370.l 37.e $4$ $2.954$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
370.2.l.c 370.l 37.e $12$ $2.954$ 12.0.\(\cdots\).2 None \(0\) \(4\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{2}+(1-\beta _{6}+\beta _{10})q^{3}+(1-\beta _{6}+\cdots)q^{4}+\cdots\)
370.2.m.a 370.m 185.l $4$ $2.954$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-2\) \(-3\) \(-6\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{2}+(-1+\beta _{1})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
370.2.m.b 370.m 185.l $4$ $2.954$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(3\) \(-3\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{2}+(1-\beta _{1})q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
370.2.m.c 370.m 185.l $16$ $2.954$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-8\) \(3\) \(6\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{1})q^{2}+\beta _{10}q^{3}+\beta _{1}q^{4}+\cdots\)
370.2.m.d 370.m 185.l $16$ $2.954$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(8\) \(-3\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{1})q^{2}-\beta _{10}q^{3}+\beta _{1}q^{4}+\beta _{8}q^{5}+\cdots\)
370.2.n.a 370.n 185.n $4$ $2.954$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-8\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2+\zeta_{12}^{3})q^{5}+\cdots\)
370.2.n.b 370.n 185.n $4$ $2.954$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
370.2.n.c 370.n 185.n $4$ $2.954$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2-\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
370.2.n.d 370.n 185.n $4$ $2.954$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(3\zeta_{12}-3\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
370.2.n.e 370.n 185.n $8$ $2.954$ 8.0.303595776.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{3}q^{2}-2\beta _{5}q^{3}-\beta _{4}q^{4}+(\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots\)
370.2.n.f 370.n 185.n $12$ $2.954$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}+(\beta _{5}-\beta _{6}-\beta _{7}+\beta _{9})q^{3}+\cdots\)
370.2.o.a 370.o 37.f $18$ $2.954$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{7}q^{2}+(-\beta _{2}+\beta _{8}-\beta _{17})q^{3}+\beta _{6}q^{4}+\cdots\)
370.2.o.b 370.o 37.f $18$ $2.954$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{9}]$ \(q+\beta _{4}q^{2}+\beta _{8}q^{3}+(-\beta _{10}+\beta _{11})q^{4}+\cdots\)
370.2.o.c 370.o 37.f $24$ $2.954$ None \(0\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{9}]$
370.2.o.d 370.o 37.f $24$ $2.954$ None \(0\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{9}]$
370.2.q.a 370.q 185.p $4$ $2.954$ \(\Q(\zeta_{12})\) None \(-2\) \(4\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{12}]$ \(q-\zeta_{12}^{2}q^{2}+(1+\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
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