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Results (displaying matches 1-50 of 65) Next

Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
47.1.b.a \(2\) \(0.023\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-47}) \) None \(-1\) \(-1\) \(0\) \(-1\) \(q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots\)
47.2.a.a \(4\) \(0.375\) 4.4.1957.1 None None \(1\) \(0\) \(-2\) \(4\) \(-\) \(q+\beta _{3}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
47.2.c.a \(66\) \(0.375\) None None \(-21\) \(-19\) \(-15\) \(-19\)
47.3.b.a \(2\) \(1.281\) \(\Q(\sqrt{-78}) \) None None \(-2\) \(-4\) \(0\) \(-8\) \(q-q^{2}-2q^{3}-3q^{4}+\beta q^{5}+2q^{6}+\cdots\)
47.3.b.b \(5\) \(1.281\) 5.5.6903125.1 \(\Q(\sqrt{-47}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(4+2\beta _{1}+\cdots)q^{4}+\cdots\)
47.3.d.a \(154\) \(1.281\) None None \(-21\) \(-19\) \(-23\) \(-15\)
47.4.a.a \(3\) \(2.773\) 3.3.1101.1 None None \(-5\) \(-5\) \(-6\) \(-45\) \(-\) \(q+(-2-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+\cdots\)
47.4.a.b \(8\) \(2.773\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(3\) \(7\) \(14\) \(39\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{5})q^{3}+(5+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
47.4.c.a \(242\) \(2.773\) None None \(-21\) \(-25\) \(-31\) \(-17\)
47.5.b.a \(5\) \(4.858\) 5.5.6903125.1 \(\Q(\sqrt{-47}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(2\beta _{1}+\beta _{4})q^{2}+(-2\beta _{2}+5\beta _{3})q^{3}+\cdots\)
47.5.b.b \(10\) \(4.858\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(-2\) \(8\) \(0\) \(28\) \(q-\beta _{3}q^{2}+(1+\beta _{9})q^{3}+(2\beta _{3}+\beta _{4}-\beta _{9})q^{4}+\cdots\)
47.5.d.a \(330\) \(4.858\) None None \(-21\) \(-31\) \(-23\) \(-51\)
47.6.a.a \(7\) \(7.538\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(-9\) \(-20\) \(-58\) \(-236\) \(+\) \(q+(-1-\beta _{1})q^{2}+(-3+\beta _{3})q^{3}+(7+\cdots)q^{4}+\cdots\)
47.6.a.b \(12\) \(7.538\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(7\) \(16\) \(42\) \(352\) \(-\) \(q+(1-\beta _{1})q^{2}+(1+\beta _{4})q^{3}+(18-\beta _{1}+\cdots)q^{4}+\cdots\)
47.6.c.a \(418\) \(7.538\) None None \(-21\) \(-19\) \(-7\) \(-139\)
47.7.b.a \(5\) \(10.813\) 5.5.6903125.1 \(\Q(\sqrt{-47}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-2\beta _{3})q^{2}+(5\beta _{2}-4\beta _{4})q^{3}+(2^{6}+\cdots)q^{4}+\cdots\)
47.7.b.b \(18\) \(10.813\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(-2\) \(-34\) \(0\) \(142\) \(q-\beta _{3}q^{2}+(-2+\beta _{2})q^{3}+(29+\beta _{2}+\cdots)q^{4}+\cdots\)
47.7.d.a \(506\) \(10.813\) None None \(-21\) \(11\) \(-23\) \(-165\)
47.8.a.a \(11\) \(14.682\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(-17\) \(-68\) \(-56\) \(-2256\) \(-\) \(q+(-2+\beta _{1})q^{2}+(-6-\beta _{1}-\beta _{5})q^{3}+\cdots\)
47.8.a.b \(16\) \(14.682\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(15\) \(40\) \(444\) \(1860\) \(+\) \(q+(1-\beta _{1})q^{2}+(3+\beta _{3})q^{3}+(70-\beta _{1}+\cdots)q^{4}+\cdots\)
47.8.c.a \(594\) \(14.682\) None None \(-21\) \(5\) \(-411\) \(373\)
47.9.b.a \(5\) \(19.147\) 5.5.6903125.1 \(\Q(\sqrt{-47}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{2}+9\beta _{3})q^{2}+(-57\beta _{1}-\beta _{4})q^{3}+\cdots\)
47.9.b.b \(26\) \(19.147\) None None \(-2\) \(68\) \(0\) \(-2192\)
47.9.d.a \(682\) \(19.147\) None None \(-21\) \(-91\) \(-23\) \(2169\)
47.10.a.a \(15\) \(24.207\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None None \(-33\) \(-89\) \(-2388\) \(-16313\) \(+\) \(q+(-2-\beta _{1})q^{2}+(-6-\beta _{3})q^{3}+(227+\cdots)q^{4}+\cdots\)
47.10.a.b \(20\) \(24.207\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(31\) \(235\) \(112\) \(12499\) \(-\) \(q+(2-\beta _{1})q^{2}+(12-\beta _{2})q^{3}+(300-2\beta _{1}+\cdots)q^{4}+\cdots\)
47.10.c.a \(770\) \(24.207\) None None \(-21\) \(-169\) \(2253\) \(3791\)
47.11.b.a \(1\) \(29.862\) \(\Q\) \(\Q(\sqrt{-47}) \) None \(17\) \(298\) \(0\) \(31922\) \(q+17q^{2}+298q^{3}-735q^{4}+5066q^{6}+\cdots\)
47.11.b.b \(4\) \(29.862\) 4.4.276125.1 \(\Q(\sqrt{-47}) \) None \(-17\) \(-298\) \(0\) \(-31922\) \(q+(-9\beta _{1}+4\beta _{2})q^{2}+(-11^{2}-11^{2}\beta _{2}+\cdots)q^{3}+\cdots\)
47.11.b.c \(34\) \(29.862\) None None \(-2\) \(-64\) \(0\) \(3892\)
47.11.d.a \(858\) \(29.862\) None None \(-21\) \(41\) \(-23\) \(-3915\)
47.12.a.a \(18\) \(36.112\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-41\) \(-992\) \(-11466\) \(-64916\) \(-\) \(q+(-2-\beta _{1})q^{2}+(-55+\beta _{2})q^{3}+(881+\cdots)q^{4}+\cdots\)
47.12.a.b \(23\) \(36.112\) None None \(87\) \(-20\) \(1034\) \(136768\) \(+\)
47.12.c.a \(946\) \(36.112\) None None \(-21\) \(485\) \(749\) \(-38387\)
47.13.b.a \(5\) \(42.958\) 5.5.6903125.1 \(\Q(\sqrt{-47}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{2}-5\beta _{4})q^{2}+(33\beta _{1}+38\beta _{3})q^{3}+\cdots\)
47.13.b.b \(42\) \(42.958\) None None \(-2\) \(-322\) \(0\) \(87838\)
47.14.a.a \(23\) \(50.399\) None None \(-129\) \(-860\) \(-10318\) \(-708416\) \(+\)
47.14.a.b \(28\) \(50.399\) None None \(127\) \(2056\) \(52182\) \(703372\) \(-\)
47.15.b.a \(5\) \(58.435\) 5.5.6903125.1 \(\Q(\sqrt{-47}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-33\beta _{1}+4\beta _{4})q^{2}+(-533\beta _{2}-2^{4}\beta _{3}+\cdots)q^{3}+\cdots\)
47.15.b.b \(50\) \(58.435\) None None \(-2\) \(2156\) \(0\) \(-630008\)
47.16.a.a \(26\) \(67.066\) None None \(-473\) \(-1745\) \(-204476\) \(-8691077\) \(-\)
47.16.a.b \(31\) \(67.066\) None None \(39\) \(7003\) \(108024\) \(1191439\) \(+\)
47.17.b.a \(5\) \(76.293\) 5.5.6903125.1 \(\Q(\sqrt{-47}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-43\beta _{1}-98\beta _{4})q^{2}+(3246\beta _{2}+229\beta _{3}+\cdots)q^{3}+\cdots\)
47.17.b.b \(58\) \(76.293\) None None \(-2\) \(-7912\) \(0\) \(-1154132\)
47.18.a.a \(30\) \(86.114\) None None \(15\) \(-10640\) \(-363048\) \(-33054460\) \(+\)
47.18.a.b \(35\) \(86.114\) None None \(1039\) \(15604\) \(1199452\) \(36123152\) \(-\)
47.19.b.a \(5\) \(96.531\) 5.5.6903125.1 \(\Q(\sqrt{-47}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-65\beta _{2}-109\beta _{4})q^{2}+(-2085\beta _{1}+\cdots)q^{3}+\cdots\)
47.19.b.b \(66\) \(96.531\) None None \(-2\) \(20126\) \(0\) \(36640942\)
47.20.a.a \(34\) \(107.544\) None None \(-1481\) \(-74552\) \(28914\) \(-203565056\) \(-\)
47.20.a.b \(39\) \(107.544\) None None \(567\) \(4180\) \(7841414\) \(280678228\) \(+\)
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