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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
360.1.p.a $1$ $0.180$ \(\Q\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{6}) \) \(-1\) \(0\) \(1\) \(0\) $-$ \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{16}+\cdots\)
360.1.p.b $1$ $0.180$ \(\Q\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{6}) \) \(1\) \(0\) \(-1\) \(0\) $-$ \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{16}+\cdots\)
360.1.u.a $4$ $0.180$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-4\) $-$ \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+(-1+\cdots)q^{7}+\cdots\)
360.2.a.a $1$ $2.875$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-4\) $+$ \(q-q^{5}-4q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
360.2.a.b $1$ $2.875$ \(\Q\) None None \(0\) \(0\) \(-1\) \(0\) $-$ \(q-q^{5}+4q^{11}+6q^{13}+6q^{17}-4q^{19}+\cdots\)
360.2.a.c $1$ $2.875$ \(\Q\) None None \(0\) \(0\) \(-1\) \(2\) $-$ \(q-q^{5}+2q^{7}+2q^{11}+4q^{13}-2q^{17}+\cdots\)
360.2.a.d $1$ $2.875$ \(\Q\) None None \(0\) \(0\) \(1\) \(2\) $-$ \(q+q^{5}+2q^{7}-2q^{11}+4q^{13}+2q^{17}+\cdots\)
360.2.a.e $1$ $2.875$ \(\Q\) None None \(0\) \(0\) \(1\) \(4\) $-$ \(q+q^{5}+4q^{7}-6q^{13}+2q^{17}+4q^{19}+\cdots\)
360.2.b.a $2$ $2.875$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(-2\) \(0\) $-$ \(q+\beta q^{2}-2q^{4}-q^{5}-3\beta q^{7}-2\beta q^{8}+\cdots\)
360.2.b.b $2$ $2.875$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(2\) \(0\) $-$ \(q+\beta q^{2}-2q^{4}+q^{5}+3\beta q^{7}-2\beta q^{8}+\cdots\)
360.2.b.c $6$ $2.875$ 6.0.2580992.1 None None \(-2\) \(0\) \(-6\) \(0\) $-$ \(q+\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{4}-q^{5}+\beta _{2}q^{7}+\cdots\)
360.2.b.d $6$ $2.875$ 6.0.2580992.1 None None \(2\) \(0\) \(6\) \(0\) $-$ \(q-\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{4}+q^{5}+\beta _{2}q^{7}+\cdots\)
360.2.d.a $4$ $2.875$ \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-30}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+2\beta _{1}q^{8}+\cdots\)
360.2.d.b $4$ $2.875$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{2}+(-1+\beta _{3})q^{4}+(-\beta _{2}+\beta _{3})q^{5}+\cdots\)
360.2.d.c $4$ $2.875$ \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{2}q^{2}+\beta _{3}q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
360.2.d.d $4$ $2.875$ \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{1}q^{2}+2q^{4}+(\beta _{1}+\beta _{2})q^{5}+2\beta _{3}q^{7}+\cdots\)
360.2.d.e $6$ $2.875$ 6.0.839056.1 None None \(-1\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{3}q^{2}+(-\beta _{1}-\beta _{2})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
360.2.d.f $6$ $2.875$ 6.0.839056.1 None None \(1\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{3})q^{4}+(\beta _{2}-\beta _{3})q^{5}+\cdots\)
360.2.f.a $2$ $2.875$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-4\) \(0\) $-$ \(q+(-2+i)q^{5}+2iq^{7}-2q^{11}+2iq^{13}+\cdots\)
360.2.f.b $2$ $2.875$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-4\) \(0\) $-$ \(q+(-2+i)q^{5}-4iq^{7}+4q^{11}-4iq^{13}+\cdots\)
360.2.f.c $2$ $2.875$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) $-$ \(q+(1+i)q^{5}-iq^{7}+4q^{11}+2iq^{13}+\cdots\)
360.2.f.d $2$ $2.875$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) $-$ \(q+(2+i)q^{5}+4iq^{7}-4q^{11}+4iq^{13}+\cdots\)
360.2.k.a $2$ $2.875$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(0\) \(-8\) $-$ \(q+(-1+i)q^{2}-2iq^{4}+iq^{5}-4q^{7}+\cdots\)
360.2.k.b $2$ $2.875$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(0\) \(4\) $-$ \(q+(-1+i)q^{2}-2iq^{4}+iq^{5}+2q^{7}+\cdots\)
360.2.k.c $2$ $2.875$ \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(-8\) $-$ \(q+(1+i)q^{2}+2iq^{4}+iq^{5}-4q^{7}+\cdots\)
360.2.k.d $4$ $2.875$ \(\Q(i, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(8\) $-$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+2q^{7}+\cdots\)
360.2.k.e $4$ $2.875$ \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(0\) \(-4\) $-$ \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{4}+\cdots\)
360.2.k.f $6$ $2.875$ 6.0.399424.1 None None \(-2\) \(0\) \(0\) \(4\) $-$ \(q-\beta _{1}q^{2}+(\beta _{2}-\beta _{3})q^{4}+\beta _{3}q^{5}+(1+\cdots)q^{7}+\cdots\)
360.2.m.a $4$ $2.875$ \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(-8\) $-$ \(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(-2+\beta _{3})q^{7}+\cdots\)
360.2.m.b $4$ $2.875$ \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(8\) $-$ \(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(2-\beta _{3})q^{7}+\cdots\)
360.2.m.c $16$ $2.875$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{1}q^{2}+(1-\beta _{2})q^{4}-\beta _{12}q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots\)
360.2.q.a $2$ $2.875$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(1\) \(0\) $-$ \(q+(-1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+3\zeta_{6}q^{9}+\cdots\)
360.2.q.b $4$ $2.875$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(-4\) $-$ \(q-\zeta_{12}^{2}q^{3}+\zeta_{12}q^{5}+(-2+2\zeta_{12}+\cdots)q^{7}+\cdots\)
360.2.q.c $4$ $2.875$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(2\) \(2\) \(-2\) $-$ \(q+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
360.2.q.d $6$ $2.875$ 6.0.954288.1 None None \(0\) \(-1\) \(-3\) \(5\) $-$ \(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
360.2.q.e $8$ $2.875$ 8.0.856615824.2 None None \(0\) \(0\) \(-4\) \(1\) $-$ \(q-\beta _{4}q^{3}-\beta _{1}q^{5}+(-\beta _{2}+\beta _{4})q^{7}+\cdots\)
360.2.s.a $4$ $2.875$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(4\zeta_{8}+4\zeta_{8}^{3})q^{11}+\cdots\)
360.2.s.b $8$ $2.875$ 8.0.40960000.1 None None \(0\) \(0\) \(0\) \(-8\) $-$ \(q+\beta _{7}q^{5}+(-1-\beta _{2}-\beta _{5})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)
360.2.w.a $4$ $2.875$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(4\) $-$ \(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
360.2.w.b $4$ $2.875$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(-4\) $-$ \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(-2\zeta_{8}+\cdots)q^{5}+\cdots\)
360.2.w.c $8$ $2.875$ \(\Q(\zeta_{20})\) None None \(2\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{20}^{7}q^{2}+\zeta_{20}q^{4}+(1+\zeta_{20}^{2}-\zeta_{20}^{5}+\cdots)q^{5}+\cdots\)
360.2.w.d $16$ $2.875$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{15}q^{2}-\beta _{2}q^{4}+(\beta _{10}-\beta _{15})q^{5}+\cdots\)
360.2.w.e $24$ $2.875$ None None \(0\) \(0\) \(0\) \(0\) $-$
360.2.x.a $48$ $2.875$ None None \(0\) \(0\) \(0\) \(0\) $-$
360.2.bd.a $8$ $2.875$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+(-\zeta_{24}+\zeta_{24}^{6})q^{2}+(-\zeta_{24}^{3}+\zeta_{24}^{4}+\cdots)q^{3}+\cdots\)
360.2.bd.b $128$ $2.875$ None None \(0\) \(0\) \(0\) \(0\) $-$
360.2.bf.a $4$ $2.875$ \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(0\) \(8\) $-$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
360.2.bf.b $92$ $2.875$ None None \(2\) \(0\) \(0\) \(-8\) $-$
360.2.bi.a $4$ $2.875$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(0\) $-$ \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
360.2.bi.b $32$ $2.875$ None None \(0\) \(0\) \(-2\) \(0\) $-$
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