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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
135.1.d.a \(1\) \(0.067\) \(\Q\) \(\Q(\sqrt{-15}) \) None \(-1\) \(0\) \(1\) \(0\) \(q-q^{2}+q^{5}+q^{8}-q^{10}-q^{16}-q^{17}+\cdots\)
135.1.d.b \(1\) \(0.067\) \(\Q\) \(\Q(\sqrt{-15}) \) None \(1\) \(0\) \(-1\) \(0\) \(q+q^{2}-q^{5}-q^{8}-q^{10}-q^{16}+q^{17}+\cdots\)
135.2.a.a \(1\) \(1.078\) \(\Q\) None None \(-2\) \(0\) \(-1\) \(-3\) \(+\) \(q-2q^{2}+2q^{4}-q^{5}-3q^{7}+2q^{10}+\cdots\)
135.2.a.b \(1\) \(1.078\) \(\Q\) None None \(2\) \(0\) \(1\) \(-3\) \(-\) \(q+2q^{2}+2q^{4}+q^{5}-3q^{7}+2q^{10}+\cdots\)
135.2.a.c \(2\) \(1.078\) \(\Q(\sqrt{13}) \) None None \(-1\) \(0\) \(2\) \(2\) \(-\) \(q-\beta q^{2}+(1+\beta )q^{4}+q^{5}+(2-2\beta )q^{7}+\cdots\)
135.2.a.d \(2\) \(1.078\) \(\Q(\sqrt{13}) \) None None \(1\) \(0\) \(-2\) \(2\) \(-\) \(q+\beta q^{2}+(1+\beta )q^{4}-q^{5}+(2-2\beta )q^{7}+\cdots\)
135.2.b.a \(4\) \(1.078\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
135.2.b.b \(4\) \(1.078\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}+\zeta_{8}^{3}q^{5}-\zeta_{8}q^{7}+2\zeta_{8}^{2}q^{8}+\cdots\)
135.2.e.a \(2\) \(1.078\) \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(-1\) \(3\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots\)
135.2.e.b \(6\) \(1.078\) 6.0.954288.1 None None \(1\) \(0\) \(3\) \(-5\) \(q+(-\beta _{4}+\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
135.2.f.a \(8\) \(1.078\) 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{4}+(-\beta _{3}-\beta _{5}+\cdots)q^{5}+\cdots\)
135.2.f.b \(8\) \(1.078\) 8.0.\(\cdots\).8 None None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{1}q^{2}+(2\beta _{2}+\beta _{3}+\beta _{6})q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)
135.2.j.a \(8\) \(1.078\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{6}q^{2}-\zeta_{24}^{3}q^{4}+(\zeta_{24}-\zeta_{24}^{3}+\cdots)q^{5}+\cdots\)
135.2.k.a \(30\) \(1.078\) None None \(0\) \(3\) \(0\) \(0\)
135.2.k.b \(42\) \(1.078\) None None \(0\) \(-3\) \(0\) \(0\)
135.2.m.a \(16\) \(1.078\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(6\) \(0\) \(6\) \(-2\) \(q+\beta _{5}q^{2}+(\beta _{5}+\beta _{8}+\beta _{15})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
135.2.p.a \(96\) \(1.078\) None None \(0\) \(0\) \(-9\) \(0\)
135.2.q.a \(192\) \(1.078\) None None \(-12\) \(-12\) \(-12\) \(-12\)
135.3.c.a \(2\) \(3.678\) \(\Q(\sqrt{-5}) \) None None \(0\) \(0\) \(0\) \(24\) \(q+\beta q^{2}-q^{4}-\beta q^{5}+12q^{7}+3\beta q^{8}+\cdots\)
135.3.c.b \(4\) \(3.678\) \(\Q(\sqrt{-5}, \sqrt{-29})\) None None \(0\) \(0\) \(0\) \(-14\) \(q+\beta _{1}q^{2}+(-5+\beta _{3})q^{4}+\beta _{2}q^{5}+(-4+\cdots)q^{7}+\cdots\)
135.3.c.c \(4\) \(3.678\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(-12\) \(q-\beta _{1}q^{2}+\beta _{3}q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
135.3.d.a \(2\) \(3.678\) \(\Q(\sqrt{-11}) \) None None \(-2\) \(0\) \(-1\) \(0\) \(q-q^{2}-3q^{4}-\beta q^{5}+(-1+2\beta )q^{7}+\cdots\)
135.3.d.b \(2\) \(3.678\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(8\) \(0\) \(q-q^{2}-3q^{4}+(4+i)q^{5}-2iq^{7}+7q^{8}+\cdots\)
135.3.d.c \(2\) \(3.678\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-15}) \) None \(-1\) \(0\) \(10\) \(0\) \(q+(-1-\beta )q^{2}+(8+\beta )q^{4}+5q^{5}+(-15+\cdots)q^{8}+\cdots\)
135.3.d.d \(2\) \(3.678\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-15}) \) None \(1\) \(0\) \(-10\) \(0\) \(q+(1+\beta )q^{2}+(8+\beta )q^{4}-5q^{5}+(15+\cdots)q^{8}+\cdots\)
135.3.d.e \(2\) \(3.678\) \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(-8\) \(0\) \(q+q^{2}-3q^{4}+(-4+i)q^{5}+2iq^{7}+\cdots\)
135.3.d.f \(2\) \(3.678\) \(\Q(\sqrt{-11}) \) None None \(2\) \(0\) \(1\) \(0\) \(q+q^{2}-3q^{4}+(1-\beta )q^{5}+(1-2\beta )q^{7}+\cdots\)
135.3.d.g \(4\) \(3.678\) \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+6q^{4}-\beta _{2}q^{5}+\beta _{1}q^{7}-2\beta _{3}q^{8}+\cdots\)
135.3.g.a \(16\) \(3.678\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(-8\) \(q+\beta _{1}q^{2}+(2\beta _{4}+\beta _{7})q^{4}-\beta _{13}q^{5}+\cdots\)
135.3.g.b \(16\) \(3.678\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(16\) \(q+\beta _{1}q^{2}+(2\beta _{3}+\beta _{4})q^{4}+\beta _{10}q^{5}+\cdots\)
135.3.h.a \(20\) \(3.678\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(12\) \(0\) \(q+\beta _{2}q^{2}+(-2+\beta _{3}-2\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots\)
135.3.i.a \(16\) \(3.678\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(2\) \(q+(\beta _{1}-\beta _{4})q^{2}+(\beta _{1}-\beta _{3}-\beta _{4}+2\beta _{7}+\cdots)q^{4}+\cdots\)
135.3.l.a \(40\) \(3.678\) None None \(2\) \(0\) \(2\) \(-2\)
135.3.n.a \(204\) \(3.678\) None None \(0\) \(0\) \(3\) \(0\)
135.3.o.a \(144\) \(3.678\) None None \(0\) \(0\) \(0\) \(0\)
135.3.r.a \(408\) \(3.678\) None None \(-12\) \(-12\) \(-12\) \(-12\)
135.4.a.a \(1\) \(7.965\) \(\Q\) None None \(-2\) \(0\) \(5\) \(0\) \(-\) \(q-2q^{2}-4q^{4}+5q^{5}+24q^{8}-10q^{10}+\cdots\)
135.4.a.b \(1\) \(7.965\) \(\Q\) None None \(-1\) \(0\) \(-5\) \(-6\) \(+\) \(q-q^{2}-7q^{4}-5q^{5}-6q^{7}+15q^{8}+\cdots\)
135.4.a.c \(1\) \(7.965\) \(\Q\) None None \(1\) \(0\) \(5\) \(-6\) \(-\) \(q+q^{2}-7q^{4}+5q^{5}-6q^{7}-15q^{8}+\cdots\)
135.4.a.d \(1\) \(7.965\) \(\Q\) None None \(2\) \(0\) \(-5\) \(0\) \(-\) \(q+2q^{2}-4q^{4}-5q^{5}-24q^{8}-10q^{10}+\cdots\)
135.4.a.e \(3\) \(7.965\) 3.3.1772.1 None None \(-5\) \(0\) \(-15\) \(-4\) \(-\) \(q+(-2+\beta _{1})q^{2}+(7-3\beta _{1}+\beta _{2})q^{4}+\cdots\)
135.4.a.f \(3\) \(7.965\) 3.3.5637.1 None None \(-1\) \(0\) \(15\) \(44\) \(+\) \(q-\beta _{1}q^{2}+(7+\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots\)
135.4.a.g \(3\) \(7.965\) 3.3.5637.1 None None \(1\) \(0\) \(-15\) \(44\) \(+\) \(q+\beta _{1}q^{2}+(7+\beta _{1}+\beta _{2})q^{4}-5q^{5}+\cdots\)
135.4.a.h \(3\) \(7.965\) 3.3.1772.1 None None \(5\) \(0\) \(15\) \(-4\) \(+\) \(q+(2-\beta _{1})q^{2}+(7-3\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots\)
135.4.b.a \(4\) \(7.965\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(-13-\beta _{3})q^{4}-5\beta _{1}q^{5}+\cdots\)
135.4.b.b \(8\) \(7.965\) 8.0.\(\cdots\).7 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{4}-2\beta _{5}+\cdots)q^{5}+\cdots\)
135.4.b.c \(12\) \(7.965\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{2}+(-5-\beta _{1})q^{4}-\beta _{3}q^{5}+\beta _{8}q^{7}+\cdots\)
135.4.e.a \(4\) \(7.965\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(-1\) \(0\) \(10\) \(-9\) \(q+(-\beta _{1}+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
135.4.e.b \(6\) \(7.965\) 6.0.15759792.1 None None \(-1\) \(0\) \(15\) \(43\) \(q+(-\beta _{1}-\beta _{4})q^{2}+(-\beta _{2}+3\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
135.4.e.c \(14\) \(7.965\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(-2\) \(0\) \(-35\) \(-22\) \(q+(\beta _{1}-\beta _{2})q^{2}+(-5-\beta _{3}-5\beta _{5}-\beta _{10}+\cdots)q^{4}+\cdots\)
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