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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
368.1.f.a $1$ $0.184$ \(\Q\) \(\Q(\sqrt{-23}) \) None \(0\) \(1\) \(0\) \(0\) $-$ \(q+q^{3}-q^{13}-q^{23}+q^{25}-q^{27}+\cdots\)
368.1.k.a $2$ $0.184$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-23}) \) None \(0\) \(2\) \(0\) \(0\) $-$ \(q-iq^{2}+(1-i)q^{3}-q^{4}+(-1-i+\cdots)q^{6}+\cdots\)
368.1.k.b $4$ $0.184$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-23}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ \(q+\zeta_{12}^{5}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
368.2.a.a $1$ $2.938$ \(\Q\) None None \(0\) \(-3\) \(0\) \(2\) $+$ \(q-3q^{3}+2q^{7}+6q^{9}-5q^{13}-6q^{17}+\cdots\)
368.2.a.b $1$ $2.938$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) $+$ \(q-q^{3}-2q^{7}-2q^{9}-q^{13}-6q^{17}+\cdots\)
368.2.a.c $1$ $2.938$ \(\Q\) None None \(0\) \(0\) \(0\) \(-4\) $+$ \(q-4q^{7}-3q^{9}-6q^{11}-2q^{13}+6q^{17}+\cdots\)
368.2.a.d $1$ $2.938$ \(\Q\) None None \(0\) \(0\) \(4\) \(4\) $-$ \(q+4q^{5}+4q^{7}-3q^{9}-2q^{11}-2q^{13}+\cdots\)
368.2.a.e $1$ $2.938$ \(\Q\) None None \(0\) \(1\) \(-4\) \(-2\) $+$ \(q+q^{3}-4q^{5}-2q^{7}-2q^{9}+4q^{11}+\cdots\)
368.2.a.f $1$ $2.938$ \(\Q\) None None \(0\) \(1\) \(-2\) \(4\) $-$ \(q+q^{3}-2q^{5}+4q^{7}-2q^{9}+2q^{11}+\cdots\)
368.2.a.g $1$ $2.938$ \(\Q\) None None \(0\) \(3\) \(-2\) \(4\) $-$ \(q+3q^{3}-2q^{5}+4q^{7}+6q^{9}-2q^{11}+\cdots\)
368.2.a.h $2$ $2.938$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(-2\) \(-2\) $-$ \(q-\beta q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
368.2.a.i $2$ $2.938$ \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(4\) \(0\) $-$ \(q+\beta q^{3}+2q^{5}+(1+\beta )q^{9}-2\beta q^{11}+\cdots\)
368.2.c.a $4$ $2.938$ \(\Q(\sqrt{2}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{3}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}-2q^{9}+3\beta _{1}q^{11}+\cdots\)
368.2.c.b $8$ $2.938$ 8.0.303595776.1 None None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{1}q^{3}-\beta _{4}q^{5}+\beta _{6}q^{7}+\beta _{7}q^{9}+\cdots\)
368.2.i.a $12$ $2.938$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{2}+(-\beta _{7}+\beta _{9}+\beta _{10})q^{3}+\beta _{2}q^{4}+\cdots\)
368.2.i.b $80$ $2.938$ None None \(-4\) \(-4\) \(0\) \(0\) $-$
368.2.j.a $2$ $2.938$ \(\Q(\sqrt{-1}) \) None None \(2\) \(2\) \(0\) \(0\) $-$ \(q+(1-i)q^{2}+(1-i)q^{3}-2iq^{4}-2iq^{6}+\cdots\)
368.2.j.b $4$ $2.938$ \(\Q(\zeta_{12})\) None None \(-2\) \(-6\) \(-4\) \(0\) $-$ \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
368.2.j.c $12$ $2.938$ 12.0.\(\cdots\).1 None None \(2\) \(2\) \(-4\) \(0\) $-$ \(q-\beta _{5}q^{2}+\beta _{10}q^{3}+(\beta _{2}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
368.2.j.d $24$ $2.938$ None None \(-4\) \(-4\) \(4\) \(0\) $-$
368.2.j.e $46$ $2.938$ None None \(2\) \(6\) \(4\) \(0\) $-$
368.2.m.a $10$ $2.938$ \(\Q(\zeta_{22})\) None None \(0\) \(0\) \(-4\) \(7\) $-$ \(q+(-\zeta_{22}^{3}-\zeta_{22}^{4}+\zeta_{22}^{5}+\zeta_{22}^{6}+\cdots)q^{3}+\cdots\)
368.2.m.b $10$ $2.938$ \(\Q(\zeta_{22})\) None None \(0\) \(4\) \(-6\) \(-3\) $-$ \(q+(\zeta_{22}^{3}-\zeta_{22}^{4}+\zeta_{22}^{5}-\zeta_{22}^{6})q^{3}+\cdots\)
368.2.m.c $10$ $2.938$ \(\Q(\zeta_{22})\) None None \(0\) \(7\) \(-3\) \(5\) $-$ \(q+(1+\zeta_{22}^{4}-\zeta_{22}^{5}-\zeta_{22}^{9})q^{3}+(-1+\cdots)q^{5}+\cdots\)
368.2.m.d $20$ $2.938$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(-2\) \(2\) \(-2\) $-$ \(q+(-1+\beta _{6}-\beta _{8}+\beta _{9}+\beta _{10}+\beta _{11}+\cdots)q^{3}+\cdots\)
368.2.m.e $30$ $2.938$ None None \(0\) \(-2\) \(0\) \(13\) $-$
368.2.m.f $30$ $2.938$ None None \(0\) \(2\) \(2\) \(-13\) $-$
368.2.s.a $40$ $2.938$ None None \(0\) \(0\) \(0\) \(0\) $-$
368.2.s.b $80$ $2.938$ None None \(0\) \(0\) \(0\) \(0\) $-$
368.2.w.a $920$ $2.938$ None None \(-18\) \(-18\) \(-18\) \(0\) $-$
368.2.x.a $920$ $2.938$ None None \(-18\) \(-18\) \(-22\) \(-44\) $-$
368.3.d.a $2$ $10.027$ \(\Q(\sqrt{-23}) \) None None \(0\) \(0\) \(-12\) \(0\) $-$ \(q-\beta q^{3}-6q^{5}-14q^{9}+2\beta q^{11}-13q^{13}+\cdots\)
368.3.d.b $4$ $10.027$ \(\Q(\sqrt{-7}, \sqrt{-23})\) None None \(0\) \(0\) \(16\) \(0\) $-$ \(q+(\beta _{1}+\beta _{2})q^{3}+4q^{5}+(2\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
368.3.d.c $16$ $10.027$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(8\) \(0\) $-$ \(q+\beta _{1}q^{3}+(1+\beta _{4})q^{5}-\beta _{9}q^{7}+(-5+\cdots)q^{9}+\cdots\)
368.3.f.a $3$ $10.027$ 3.3.621.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{3}+(9+2\beta _{1}+\beta _{2})q^{9}+(\beta _{1}-2\beta _{2})q^{13}+\cdots\)
368.3.f.b $4$ $10.027$ 4.0.53792.1 None None \(0\) \(-2\) \(0\) \(0\) $-$ \(q-\beta _{3}q^{3}+\beta _{2}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
368.3.f.c $4$ $10.027$ 4.0.613376.1 None None \(0\) \(4\) \(0\) \(0\) $-$ \(q+(1-\beta _{2})q^{3}+\beta _{1}q^{5}+\beta _{3}q^{7}+(-6+\cdots)q^{9}+\cdots\)
368.3.f.d $12$ $10.027$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{3}-\beta _{6}q^{5}-\beta _{9}q^{7}+(4-\beta _{1}+\cdots)q^{9}+\cdots\)
368.3.k.a $12$ $10.027$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{1}q^{2}+(\beta _{4}-\beta _{9}-2\beta _{10}+\beta _{11})q^{3}+\cdots\)
368.3.k.b $176$ $10.027$ None None \(-4\) \(-4\) \(0\) \(0\) $-$
368.3.l.a $176$ $10.027$ None None \(0\) \(0\) \(0\) \(0\) $-$
368.3.p.a $30$ $10.027$ None None \(0\) \(11\) \(-11\) \(11\) $-$
368.3.p.b $40$ $10.027$ None None \(0\) \(-4\) \(0\) \(0\) $-$
368.3.p.c $40$ $10.027$ None None \(0\) \(2\) \(0\) \(0\) $-$
368.3.p.d $120$ $10.027$ None None \(0\) \(0\) \(0\) \(0\) $-$
368.3.r.a $80$ $10.027$ None None \(0\) \(0\) \(8\) \(0\) $-$
368.3.r.b $160$ $10.027$ None None \(0\) \(0\) \(-8\) \(0\) $-$
368.3.u.a $1880$ $10.027$ None None \(-18\) \(-18\) \(-18\) \(-36\) $-$
368.3.v.a $1880$ $10.027$ None None \(-18\) \(-18\) \(-22\) \(0\) $-$
368.4.a.a $1$ $21.713$ \(\Q\) None None \(0\) \(-8\) \(-4\) \(4\) $-$ \(q-8q^{3}-4q^{5}+4q^{7}+37q^{9}-26q^{11}+\cdots\)
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