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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
304.1.e.a $1$ $0.152$ \(\Q\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(1\) $-$ \(q-q^{5}+q^{7}+q^{9}+q^{11}-q^{17}-q^{19}+\cdots\)
304.2.a.a $1$ $2.427$ \(\Q\) None None \(0\) \(-2\) \(-1\) \(3\) $+$ \(q-2q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}+\cdots\)
304.2.a.b $1$ $2.427$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-3\) $+$ \(q-q^{3}-3q^{7}-2q^{9}-2q^{11}+q^{13}+\cdots\)
304.2.a.c $1$ $2.427$ \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) $-$ \(q-q^{3}+q^{7}-2q^{9}+6q^{11}+5q^{13}+\cdots\)
304.2.a.d $1$ $2.427$ \(\Q\) None None \(0\) \(1\) \(-4\) \(-3\) $+$ \(q+q^{3}-4q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots\)
304.2.a.e $1$ $2.427$ \(\Q\) None None \(0\) \(2\) \(-1\) \(3\) $-$ \(q+2q^{3}-q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots\)
304.2.a.f $1$ $2.427$ \(\Q\) None None \(0\) \(2\) \(3\) \(1\) $-$ \(q+2q^{3}+3q^{5}+q^{7}+q^{9}-3q^{11}+\cdots\)
304.2.a.g $3$ $2.427$ 3.3.961.1 None None \(0\) \(-1\) \(1\) \(-4\) $-$ \(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
304.2.h.a $2$ $2.427$ \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ \(q-q^{5}-\beta q^{7}-3q^{9}-\beta q^{11}+7q^{17}+\cdots\)
304.2.h.b $4$ $2.427$ \(\Q(\sqrt{-3}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta _{1}q^{3}-\beta _{2}q^{7}+4q^{9}+2\beta _{2}q^{11}+\cdots\)
304.2.h.c $4$ $2.427$ \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(0\) $-$ \(q+(1-\beta _{2})q^{5}+(2\beta _{1}+\beta _{3})q^{7}-3q^{9}+\cdots\)
304.2.i.a $2$ $2.427$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(1\) \(0\) $-$ \(q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.b $2$ $2.427$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-3\) \(0\) $-$ \(q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.c $2$ $2.427$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(0\) \(8\) $-$ \(q+(1-\zeta_{6})q^{3}+4q^{7}+2\zeta_{6}q^{9}-3q^{11}+\cdots\)
304.2.i.d $2$ $2.427$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(4\) \(0\) $-$ \(q+(1-\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.e $4$ $2.427$ \(\Q(\sqrt{-3}, \sqrt{7})\) None None \(0\) \(0\) \(-2\) \(-4\) $-$ \(q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
304.2.i.f $6$ $2.427$ 6.0.2696112.1 None None \(0\) \(1\) \(-1\) \(4\) $-$ \(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
304.2.k.a $4$ $2.427$ \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(-8\) \(0\) $-$ \(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots\)
304.2.k.b $68$ $2.427$ None None \(0\) \(4\) \(8\) \(0\) $-$
304.2.m.a $76$ $2.427$ None None \(0\) \(0\) \(-4\) \(-8\) $-$
304.2.n.a $2$ $2.427$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-3\) \(0\) $-$ \(q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(2+\cdots)q^{7}+\cdots\)
304.2.n.b $2$ $2.427$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-3\) \(0\) $-$ \(q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
304.2.n.c $4$ $2.427$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(0\) $-$ \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{5}-2\zeta_{12}^{3}q^{7}+\cdots\)
304.2.n.d $6$ $2.427$ 6.0.31726512.1 None None \(0\) \(-1\) \(2\) \(0\) $-$ \(q-\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
304.2.n.e $6$ $2.427$ 6.0.31726512.1 None None \(0\) \(1\) \(2\) \(0\) $-$ \(q+\beta _{1}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(\beta _{4}-\beta _{5})q^{7}+\cdots\)
304.2.u.a $6$ $2.427$ \(\Q(\zeta_{18})\) None None \(0\) \(-9\) \(-6\) \(-6\) $-$ \(q+(-1+\zeta_{18}-2\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+\cdots\)
304.2.u.b $6$ $2.427$ \(\Q(\zeta_{18})\) None None \(0\) \(3\) \(-6\) \(0\) $-$ \(q+(1-\zeta_{18}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+(-1+\cdots)q^{5}+\cdots\)
304.2.u.c $6$ $2.427$ \(\Q(\zeta_{18})\) None None \(0\) \(3\) \(0\) \(6\) $-$ \(q+(\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+2\zeta_{18}^{4}q^{5}+\cdots\)
304.2.u.d $6$ $2.427$ \(\Q(\zeta_{18})\) None None \(0\) \(6\) \(6\) \(-3\) $-$ \(q+(1+\zeta_{18}^{2})q^{3}+(1-\zeta_{18}^{2}+\zeta_{18}^{5})q^{5}+\cdots\)
304.2.u.e $12$ $2.427$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(3\) \(0\) \(-3\) $-$ \(q+(1+\beta _{5}-\beta _{7}-\beta _{9}-\beta _{11})q^{3}+(\beta _{1}+\cdots)q^{5}+\cdots\)
304.2.u.f $18$ $2.427$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(0\) \(0\) \(9\) $-$ \(q+(-\beta _{2}+\beta _{4})q^{3}+(-\beta _{6}+\beta _{7}-\beta _{10}+\cdots)q^{5}+\cdots\)
304.2.v.a $152$ $2.427$ None None \(-2\) \(-2\) \(-2\) \(0\) $-$
304.2.x.a $4$ $2.427$ \(\Q(\zeta_{12})\) None None \(-2\) \(2\) \(-2\) \(-4\) $-$ \(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
304.2.x.b $4$ $2.427$ \(\Q(\zeta_{12})\) None None \(2\) \(4\) \(-2\) \(-4\) $-$ \(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
304.2.x.c $144$ $2.427$ None None \(-6\) \(-12\) \(2\) \(-8\) $-$
304.2.be.a $12$ $2.427$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+(-\beta _{1}+\beta _{7})q^{3}+(1+2\beta _{4}-\beta _{6}-\beta _{9}+\cdots)q^{5}+\cdots\)
304.2.be.b $12$ $2.427$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+(\beta _{3}-\beta _{5}-\beta _{8})q^{3}+(1+\beta _{2}-2\beta _{4}+\cdots)q^{5}+\cdots\)
304.2.be.c $18$ $2.427$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(0\) \(0\) \(-9\) $-$ \(q-\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots\)
304.2.be.d $18$ $2.427$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(0\) \(0\) \(9\) $-$ \(q+\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots\)
304.2.bg.a $456$ $2.427$ None None \(-12\) \(-12\) \(-12\) \(-12\) $-$
304.2.bi.a $456$ $2.427$ None None \(-12\) \(-12\) \(-12\) \(0\) $-$
304.3.d.a $6$ $8.283$ 6.0.210056875.1 None None \(0\) \(0\) \(14\) \(0\) $-$ \(q+\beta _{1}q^{3}+(2-\beta _{2})q^{5}+(-\beta _{1}-2\beta _{4}+\cdots)q^{7}+\cdots\)
304.3.d.b $12$ $8.283$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(-2\) \(0\) $-$ \(q-\beta _{1}q^{3}+\beta _{5}q^{5}+(\beta _{8}-\beta _{9})q^{7}+(-1+\cdots)q^{9}+\cdots\)
304.3.e.a $1$ $8.283$ \(\Q\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-9\) \(5\) $-$ \(q-9q^{5}+5q^{7}+9q^{9}-3q^{11}+15q^{17}+\cdots\)
304.3.e.b $2$ $8.283$ \(\Q(\sqrt{-29}) \) None None \(0\) \(0\) \(-8\) \(2\) $-$ \(q+\beta q^{3}-4q^{5}+q^{7}-20q^{9}-14q^{11}+\cdots\)
304.3.e.c $2$ $8.283$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(-2\) \(-10\) $-$ \(q+\beta q^{3}-q^{5}-5q^{7}+q^{9}-5q^{11}+\cdots\)
304.3.e.d $2$ $8.283$ \(\Q(\sqrt{-13}) \) None None \(0\) \(0\) \(8\) \(10\) $-$ \(q+\beta q^{3}+4q^{5}+5q^{7}-4q^{9}+10q^{11}+\cdots\)
304.3.e.e $2$ $8.283$ \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(9\) \(-5\) $-$ \(q+(5-\beta )q^{5}+(-1-3\beta )q^{7}+9q^{9}+\cdots\)
304.3.e.f $2$ $8.283$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(14\) \(-22\) $-$ \(q+\beta q^{3}+7q^{5}-11q^{7}-23q^{9}-3q^{11}+\cdots\)
304.3.e.g $8$ $8.283$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(-14\) \(6\) $-$ \(q+\beta _{1}q^{3}+(-2-\beta _{4})q^{5}+(1-\beta _{3})q^{7}+\cdots\)
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