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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
30.2.a.a \(1\) \(0.240\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-4\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots\)
30.2.c.a \(2\) \(0.240\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+(-2+i)q^{5}+\cdots\)
30.2.e.a \(4\) \(0.240\) \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(-4\) \(q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
30.3.b.a \(4\) \(0.817\) \(\Q(\sqrt{2}, \sqrt{-17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+2q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots\)
30.3.d.a \(4\) \(0.817\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(4\) \(0\) \(8\) \(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{3}-2q^{4}+\cdots\)
30.3.f.a \(4\) \(0.817\) \(\Q(i, \sqrt{6})\) None \(4\) \(0\) \(0\) \(-16\) \(q+(1-\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
30.4.a.a \(1\) \(1.770\) \(\Q\) None \(-2\) \(3\) \(5\) \(32\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots\)
30.4.a.b \(1\) \(1.770\) \(\Q\) None \(2\) \(3\) \(-5\) \(-4\) \(+\) \(q+2q^{2}+3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)
30.4.c.a \(2\) \(1.770\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+2iq^{2}+3iq^{3}-4q^{4}+(2+11i)q^{5}+\cdots\)
30.4.e.a \(12\) \(1.770\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(8\) \(0\) \(12\) \(q+\beta _{1}q^{2}+(1-\beta _{3}-\beta _{9})q^{3}-4\beta _{3}q^{4}+\cdots\)
30.5.b.a \(8\) \(3.101\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+8q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots\)
30.5.d.a \(4\) \(3.101\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(-8\) \(0\) \(-184\) \(q-\beta _{1}q^{2}+(-2-2\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots\)
30.5.f.a \(4\) \(3.101\) \(\Q(i, \sqrt{6})\) None \(-8\) \(0\) \(84\) \(-28\) \(q+(-2+2\beta _{2})q^{2}-\beta _{1}q^{3}-8\beta _{2}q^{4}+\cdots\)
30.5.f.b \(4\) \(3.101\) \(\Q(i, \sqrt{6})\) None \(8\) \(0\) \(36\) \(68\) \(q+(2-2\beta _{2})q^{2}+3\beta _{1}q^{3}-8\beta _{2}q^{4}+\cdots\)
30.6.a.a \(1\) \(4.812\) \(\Q\) None \(-4\) \(9\) \(-25\) \(164\) \(-\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}-5^{2}q^{5}-6^{2}q^{6}+\cdots\)
30.6.a.b \(1\) \(4.812\) \(\Q\) None \(4\) \(9\) \(25\) \(32\) \(-\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}+5^{2}q^{5}+6^{2}q^{6}+\cdots\)
30.6.c.a \(2\) \(4.812\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-110\) \(0\) \(q+4iq^{2}+9iq^{3}-2^{4}q^{4}+(-55+10i)q^{5}+\cdots\)
30.6.c.b \(4\) \(4.812\) \(\Q(i, \sqrt{1249})\) None \(0\) \(0\) \(6\) \(0\) \(q-4\beta _{1}q^{2}+9\beta _{1}q^{3}-2^{4}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
30.6.e.a \(20\) \(4.812\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(-4\) \(0\) \(76\) \(q+\beta _{1}q^{2}+\beta _{9}q^{3}+2^{4}\beta _{5}q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots\)
30.7.b.a \(12\) \(6.902\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+2^{5}q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
30.7.d.a \(8\) \(6.902\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-20\) \(0\) \(400\) \(q+\beta _{3}q^{2}+(-2-\beta _{2}-\beta _{3})q^{3}-2^{5}q^{4}+\cdots\)
30.7.f.a \(4\) \(6.902\) \(\Q(i, \sqrt{6})\) None \(16\) \(0\) \(-420\) \(596\) \(q+(4-4\beta _{2})q^{2}+3\beta _{1}q^{3}-2^{5}\beta _{2}q^{4}+\cdots\)
30.7.f.b \(8\) \(6.902\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(-32\) \(0\) \(60\) \(388\) \(q+(-4-4\beta _{1})q^{2}-\beta _{3}q^{3}+2^{5}\beta _{1}q^{4}+\cdots\)
30.8.a.a \(1\) \(9.372\) \(\Q\) None \(-8\) \(-27\) \(-125\) \(-1084\) \(+\) \(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}-5^{3}q^{5}+6^{3}q^{6}+\cdots\)
30.8.a.b \(1\) \(9.372\) \(\Q\) None \(-8\) \(-27\) \(125\) \(416\) \(-\) \(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+5^{3}q^{5}+6^{3}q^{6}+\cdots\)
30.8.a.c \(1\) \(9.372\) \(\Q\) None \(-8\) \(27\) \(125\) \(-232\) \(+\) \(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}+5^{3}q^{5}-6^{3}q^{6}+\cdots\)
30.8.a.d \(1\) \(9.372\) \(\Q\) None \(8\) \(-27\) \(-125\) \(-988\) \(-\) \(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}-5^{3}q^{5}-6^{3}q^{6}+\cdots\)
30.8.a.e \(1\) \(9.372\) \(\Q\) None \(8\) \(-27\) \(125\) \(512\) \(+\) \(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+5^{3}q^{5}-6^{3}q^{6}+\cdots\)
30.8.a.f \(1\) \(9.372\) \(\Q\) None \(8\) \(27\) \(-125\) \(1604\) \(+\) \(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}-5^{3}q^{5}+6^{3}q^{6}+\cdots\)
30.8.c.a \(2\) \(9.372\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-100\) \(0\) \(q+8iq^{2}-3^{3}iq^{3}-2^{6}q^{4}+(-50+\cdots)q^{5}+\cdots\)
30.8.c.b \(4\) \(9.372\) \(\Q(i, \sqrt{2641})\) None \(0\) \(0\) \(264\) \(0\) \(q-8\beta _{1}q^{2}-3^{3}\beta _{1}q^{3}-2^{6}q^{4}+(66+\cdots)q^{5}+\cdots\)
30.8.e.a \(28\) \(9.372\) None \(0\) \(-52\) \(0\) \(-1348\)
30.9.b.a \(16\) \(12.221\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-\beta _{1}q^{3}+2^{7}q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
30.9.d.a \(12\) \(12.221\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(112\) \(0\) \(-11304\) \(q+\beta _{1}q^{2}+(9-\beta _{1}-\beta _{2})q^{3}-2^{7}q^{4}+\cdots\)
30.9.f.a \(8\) \(12.221\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(-64\) \(0\) \(636\) \(-1484\) \(q+(-8+8\beta _{1})q^{2}-\beta _{5}q^{3}-2^{7}\beta _{1}q^{4}+\cdots\)
30.9.f.b \(8\) \(12.221\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(64\) \(0\) \(924\) \(-7436\) \(q+(8-8\beta _{1})q^{2}-\beta _{7}q^{3}-2^{7}\beta _{1}q^{4}+\cdots\)
30.10.a.a \(1\) \(15.451\) \(\Q\) None \(-16\) \(-81\) \(-625\) \(6332\) \(+\) \(q-2^{4}q^{2}-3^{4}q^{3}+2^{8}q^{4}-5^{4}q^{5}+\cdots\)
30.10.a.b \(1\) \(15.451\) \(\Q\) None \(-16\) \(-81\) \(625\) \(-7168\) \(-\) \(q-2^{4}q^{2}-3^{4}q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots\)
30.10.a.c \(1\) \(15.451\) \(\Q\) None \(-16\) \(81\) \(-625\) \(7196\) \(-\) \(q-2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}-5^{4}q^{5}+\cdots\)
30.10.a.d \(1\) \(15.451\) \(\Q\) None \(16\) \(-81\) \(-625\) \(3164\) \(-\) \(q+2^{4}q^{2}-3^{4}q^{3}+2^{8}q^{4}-5^{4}q^{5}+\cdots\)
30.10.a.e \(1\) \(15.451\) \(\Q\) None \(16\) \(-81\) \(625\) \(-10336\) \(+\) \(q+2^{4}q^{2}-3^{4}q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots\)
30.10.a.f \(1\) \(15.451\) \(\Q\) None \(16\) \(81\) \(625\) \(2408\) \(-\) \(q+2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots\)
30.10.c.a \(4\) \(15.451\) \(\Q(i, \sqrt{889})\) None \(0\) \(0\) \(1710\) \(0\) \(q-2^{4}\beta _{1}q^{2}-3^{4}\beta _{1}q^{3}-2^{8}q^{4}+(421+\cdots)q^{5}+\cdots\)
30.10.c.b \(6\) \(15.451\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(266\) \(0\) \(q+2^{4}\beta _{1}q^{2}-3^{4}\beta _{1}q^{3}-2^{8}q^{4}+(44+\cdots)q^{5}+\cdots\)
30.10.e.a \(36\) \(15.451\) None \(0\) \(296\) \(0\) \(9756\)
30.11.b.a \(20\) \(19.061\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+2^{9}q^{4}+\cdots\)
30.11.d.a \(12\) \(19.061\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-44\) \(0\) \(71832\) \(q+\beta _{2}q^{2}+(-4+\beta _{2}+\beta _{3})q^{3}-2^{9}q^{4}+\cdots\)
30.11.f.a \(8\) \(19.061\) 8.0.\(\cdots\).1 None \(-128\) \(0\) \(-9240\) \(-14168\) \(q+(-2^{4}+2^{4}\beta _{1})q^{2}+3\beta _{2}q^{3}-2^{9}\beta _{1}q^{4}+\cdots\)
30.11.f.b \(12\) \(19.061\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(192\) \(0\) \(-5880\) \(11352\) \(q+(2^{4}+2^{4}\beta _{1})q^{2}+\beta _{2}q^{3}+2^{9}\beta _{1}q^{4}+\cdots\)
30.12.a.a \(1\) \(23.050\) \(\Q\) None \(-32\) \(-243\) \(-3125\) \(-22876\) \(+\) \(q-2^{5}q^{2}-3^{5}q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots\)
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