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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
572.1.ba.a \(4\) \(0.285\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-13}) \) None \(-1\) \(0\) \(0\) \(-2\) \(q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
572.1.ba.b \(4\) \(0.285\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-13}) \) None \(1\) \(0\) \(0\) \(2\) \(q-\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
572.2.a.a \(1\) \(4.567\) \(\Q\) None None \(0\) \(1\) \(3\) \(2\) \(-\) \(q+q^{3}+3q^{5}+2q^{7}-2q^{9}+q^{11}+\cdots\)
572.2.a.b \(2\) \(4.567\) \(\Q(\sqrt{13}) \) None None \(0\) \(-3\) \(0\) \(-3\) \(+\) \(q+(-1-\beta )q^{3}+(-2+\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
572.2.a.c \(2\) \(4.567\) \(\Q(\sqrt{21}) \) None None \(0\) \(1\) \(-4\) \(3\) \(-\) \(q+\beta q^{3}-2q^{5}+(1+\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
572.2.a.d \(2\) \(4.567\) \(\Q(\sqrt{21}) \) None None \(0\) \(1\) \(4\) \(5\) \(-\) \(q+\beta q^{3}+2q^{5}+(3-\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
572.2.a.e \(3\) \(4.567\) 3.3.229.1 None None \(0\) \(-2\) \(-1\) \(-7\) \(+\) \(q+(-1-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)
572.2.b.a \(4\) \(4.567\) \(\Q(\sqrt{-2}, \sqrt{-13})\) \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-2q^{4}+\beta _{2}q^{7}+2\beta _{2}q^{8}+\cdots\)
572.2.b.b \(20\) \(4.567\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) \(\Q(\sqrt{-143}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{14}q^{2}-\beta _{9}q^{3}+\beta _{12}q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots\)
572.2.b.c \(56\) \(4.567\) None None \(0\) \(0\) \(0\) \(0\)
572.2.e.a \(8\) \(4.567\) 8.0.342102016.5 None None \(0\) \(0\) \(-12\) \(0\) \(q-\beta _{4}q^{2}+(-\beta _{3}-\beta _{5}+\beta _{7})q^{4}+(-2+\cdots)q^{5}+\cdots\)
572.2.e.b \(64\) \(4.567\) None None \(0\) \(0\) \(12\) \(0\)
572.2.f.a \(2\) \(4.567\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+4iq^{7}-3q^{9}-iq^{11}+(-3+2i)q^{13}+\cdots\)
572.2.f.b \(4\) \(4.567\) \(\Q(i, \sqrt{21})\) None None \(0\) \(2\) \(0\) \(0\) \(q+(1-\beta _{3})q^{3}+(\beta _{1}-\beta _{2})q^{7}+(3-\beta _{3})q^{9}+\cdots\)
572.2.f.c \(8\) \(4.567\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(-2\) \(0\) \(0\) \(q-\beta _{2}q^{3}+(\beta _{1}+\beta _{5}+\beta _{6}-\beta _{7})q^{5}+\cdots\)
572.2.i.a \(4\) \(4.567\) \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(-4\) \(-2\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{5}+(-1+\zeta_{12}+\cdots)q^{7}+\cdots\)
572.2.i.b \(6\) \(4.567\) 6.0.309123.1 None None \(0\) \(-1\) \(6\) \(-5\) \(q+(\beta _{1}-\beta _{5})q^{3}+(1+\beta _{1}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
572.2.i.c \(10\) \(4.567\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(1\) \(2\) \(1\) \(q+\beta _{1}q^{3}+(-\beta _{2}-\beta _{3}-\beta _{5})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
572.2.j.a \(140\) \(4.567\) None None \(0\) \(0\) \(4\) \(0\)
572.2.m.a \(28\) \(4.567\) None None \(0\) \(0\) \(0\) \(0\)
572.2.n.a \(20\) \(4.567\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(1\) \(1\) \(3\) \(q+\beta _{5}q^{3}+(-\beta _{9}-\beta _{10})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
572.2.n.b \(28\) \(4.567\) None None \(0\) \(1\) \(-7\) \(11\)
572.2.p.a \(24\) \(4.567\) None None \(0\) \(-2\) \(0\) \(6\)
572.2.s.a \(160\) \(4.567\) None None \(0\) \(0\) \(0\) \(0\)
572.2.t.a \(160\) \(4.567\) None None \(0\) \(0\) \(-16\) \(0\)
572.2.x.a \(56\) \(4.567\) None None \(0\) \(0\) \(0\) \(0\)
572.2.y.a \(288\) \(4.567\) None None \(0\) \(0\) \(0\) \(0\)
572.2.bb.a \(16\) \(4.567\) 16.0.\(\cdots\).9 \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{8}q^{2}+(2+2\beta _{2}-2\beta _{7}-2\beta _{9})q^{4}+\cdots\)
572.2.bb.b \(304\) \(4.567\) None None \(0\) \(0\) \(0\) \(0\)
572.2.bc.a \(56\) \(4.567\) None None \(0\) \(0\) \(0\) \(0\)
572.2.bf.a \(280\) \(4.567\) None None \(0\) \(0\) \(-4\) \(0\)
572.2.bg.a \(112\) \(4.567\) None None \(0\) \(0\) \(0\) \(0\)
572.2.bh.a \(112\) \(4.567\) None None \(0\) \(0\) \(0\) \(0\)
572.2.bk.a \(640\) \(4.567\) None None \(-6\) \(0\) \(-12\) \(0\)
572.2.bm.a \(640\) \(4.567\) None None \(-5\) \(0\) \(-24\) \(0\)
572.2.bn.a \(640\) \(4.567\) None None \(-15\) \(0\) \(0\) \(0\)
572.2.bq.a \(112\) \(4.567\) None None \(0\) \(0\) \(0\) \(0\)
572.2.bs.a \(1280\) \(4.567\) None None \(-12\) \(0\) \(-24\) \(0\)
572.2.bv.a \(224\) \(4.567\) None None \(0\) \(0\) \(0\) \(0\)
572.3.g.a \(28\) \(15.586\) None None \(0\) \(0\) \(0\) \(0\)
572.3.h.a \(24\) \(15.586\) None None \(0\) \(-10\) \(-2\) \(0\)
572.3.l.a \(44\) \(15.586\) None None \(0\) \(0\) \(12\) \(-12\)
572.3.o.a \(56\) \(15.586\) None None \(0\) \(0\) \(0\) \(0\)
572.3.q.a \(56\) \(15.586\) None None \(0\) \(0\) \(0\) \(0\)
572.3.v.a \(96\) \(15.586\) None None \(0\) \(10\) \(2\) \(-30\)
572.3.bd.a \(96\) \(15.586\) None None \(0\) \(0\) \(-12\) \(-8\)
572.4.a.a \(1\) \(33.749\) \(\Q\) None None \(0\) \(7\) \(-15\) \(-1\) \(-\) \(q+7q^{3}-15q^{5}-q^{7}+22q^{9}+11q^{11}+\cdots\)
572.4.a.b \(1\) \(33.749\) \(\Q\) None None \(0\) \(10\) \(13\) \(-11\) \(+\) \(q+10q^{3}+13q^{5}-11q^{7}+73q^{9}+\cdots\)
572.4.a.c \(6\) \(33.749\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(-19\) \(-14\) \(-45\) \(-\) \(q+(-3-\beta _{1})q^{3}+(-2-\beta _{1}-\beta _{3})q^{5}+\cdots\)
572.4.a.d \(7\) \(33.749\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(0\) \(0\) \(-3\) \(38\) \(+\) \(q-\beta _{1}q^{3}+\beta _{3}q^{5}+(5-\beta _{1}+\beta _{2})q^{7}+\cdots\)
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