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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
23.1.b.a \(1\) \(0.011\) \(\Q\) \(\Q(\sqrt{-23}) \) None \(-1\) \(-1\) \(0\) \(0\) \(q-q^{2}-q^{3}+q^{6}+q^{8}-q^{13}-q^{16}+\cdots\)
23.2.a.a \(2\) \(0.184\) \(\Q(\sqrt{5}) \) None None \(-1\) \(0\) \(-2\) \(2\) \(-\) \(q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
23.2.c.a \(10\) \(0.184\) \(\Q(\zeta_{22})\) None None \(-7\) \(-7\) \(-3\) \(-5\) \(q+(-\zeta_{22}+\zeta_{22}^{4}-\zeta_{22}^{5}+\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
23.3.b.a \(3\) \(0.627\) 3.3.621.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+(4+\cdots)q^{4}+\cdots\)
23.3.d.a \(30\) \(0.627\) None None \(-11\) \(-11\) \(-11\) \(-11\)
23.4.a.a \(1\) \(1.357\) \(\Q\) None None \(-2\) \(-5\) \(-6\) \(-8\) \(-\) \(q-2q^{2}-5q^{3}-4q^{4}-6q^{5}+10q^{6}+\cdots\)
23.4.a.b \(4\) \(1.357\) 4.4.334189.1 None None \(2\) \(7\) \(14\) \(16\) \(+\) \(q+(1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(6+\cdots)q^{4}+\cdots\)
23.4.c.a \(50\) \(1.357\) None None \(-11\) \(-13\) \(-19\) \(-19\)
23.5.b.a \(3\) \(2.378\) 3.3.621.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-2\beta _{2})q^{2}+(6\beta _{1}-\beta _{2})q^{3}+(2^{4}+\cdots)q^{4}+\cdots\)
23.5.b.b \(4\) \(2.378\) \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None None \(-8\) \(-12\) \(0\) \(0\) \(q+(-2-\beta _{3})q^{2}+(-3+3\beta _{3})q^{3}+(-6+\cdots)q^{4}+\cdots\)
23.5.d.a \(70\) \(2.378\) None None \(-3\) \(1\) \(-11\) \(-11\)
23.6.a.a \(3\) \(3.689\) 3.3.7925.1 None None \(-4\) \(-20\) \(-58\) \(-282\) \(+\) \(q+(-1+\beta _{1})q^{2}+(-7-2\beta _{1}-\beta _{2})q^{3}+\cdots\)
23.6.a.b \(6\) \(3.689\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(4\) \(16\) \(42\) \(300\) \(-\) \(q+(1-\beta _{1})q^{2}+(3-\beta _{1}+\beta _{4})q^{3}+(19+\cdots)q^{4}+\cdots\)
23.6.c.a \(90\) \(3.689\) None None \(-11\) \(-7\) \(5\) \(-29\)
23.7.b.a \(1\) \(5.291\) \(\Q\) \(\Q(\sqrt{-23}) \) None \(-7\) \(-38\) \(0\) \(0\) \(q-7q^{2}-38q^{3}-15q^{4}+266q^{6}+\cdots\)
23.7.b.b \(2\) \(5.291\) \(\Q(\sqrt{69}) \) \(\Q(\sqrt{-23}) \) None \(7\) \(38\) \(0\) \(0\) \(q+(2+3\beta )q^{2}+(23-8\beta )q^{3}+(93+21\beta )q^{4}+\cdots\)
23.7.b.c \(8\) \(5.291\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(8\) \(30\) \(0\) \(0\) \(q+(1+\beta _{1})q^{2}+(4+\beta _{3})q^{3}+(21-3\beta _{1}+\cdots)q^{4}+\cdots\)
23.7.d.a \(110\) \(5.291\) None None \(-19\) \(-41\) \(-11\) \(-11\)
23.8.a.a \(5\) \(7.185\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(-16\) \(-68\) \(-56\) \(-1156\) \(-\) \(q+(-3+\beta _{1})q^{2}+(-14+\beta _{2})q^{3}+(51+\cdots)q^{4}+\cdots\)
23.8.a.b \(8\) \(7.185\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(40\) \(444\) \(1446\) \(+\) \(q+\beta _{1}q^{2}+(5-\beta _{1}+\beta _{2})q^{3}+(80+2\beta _{1}+\cdots)q^{4}+\cdots\)
23.8.c.a \(130\) \(7.185\) None None \(5\) \(17\) \(-399\) \(-301\)
23.9.b.a \(3\) \(9.370\) 3.3.621.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-3\beta _{1}-2\beta _{2})q^{2}+(13\beta _{1}-17\beta _{2})q^{3}+\cdots\)
23.9.b.b \(12\) \(9.370\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(-8\) \(-72\) \(0\) \(0\) \(q+(-1+\beta _{2})q^{2}+(-6+\beta _{3})q^{3}+(30+\cdots)q^{4}+\cdots\)
23.9.d.a \(150\) \(9.370\) None None \(-3\) \(61\) \(-11\) \(-11\)
23.10.a.a \(7\) \(11.846\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(0\) \(-89\) \(-2388\) \(-9896\) \(+\) \(q+\beta _{1}q^{2}+(-13-2\beta _{1}-\beta _{4})q^{3}+(220+\cdots)q^{4}+\cdots\)
23.10.a.b \(10\) \(11.846\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(32\) \(235\) \(112\) \(1280\) \(-\) \(q+(3+\beta _{1})q^{2}+(23+\beta _{1}+\beta _{3})q^{3}+(307+\cdots)q^{4}+\cdots\)
23.10.c.a \(170\) \(11.846\) None None \(-43\) \(-157\) \(2265\) \(8605\)
23.11.b.a \(3\) \(14.613\) 3.3.621.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-23\beta _{1}-2\beta _{2})q^{2}+(-66\beta _{1}+119\beta _{2})q^{3}+\cdots\)
23.11.b.b \(16\) \(14.613\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(-24\) \(60\) \(0\) \(0\) \(q+(-2+\beta _{2})q^{2}+(4-\beta _{2}-\beta _{3})q^{3}+\cdots\)
23.11.d.a \(190\) \(14.613\) None None \(13\) \(-71\) \(-11\) \(-11\)
23.12.a.a \(8\) \(17.672\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-32\) \(-992\) \(-11466\) \(-54118\) \(-\) \(q+(-4-\beta _{1})q^{2}+(-124-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
23.12.a.b \(11\) \(17.672\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(32\) \(-20\) \(1034\) \(159584\) \(+\) \(q+(3-\beta _{1})q^{2}+(-2+\beta _{1}-\beta _{2})q^{3}+\cdots\)
23.12.c.a \(210\) \(17.672\) None None \(37\) \(497\) \(761\) \(-71989\)
23.13.b.a \(1\) \(21.022\) \(\Q\) \(\Q(\sqrt{-23}) \) None \(-79\) \(-14\) \(0\) \(0\) \(q-79q^{2}-14q^{3}+2145q^{4}+1106q^{6}+\cdots\)
23.13.b.b \(2\) \(21.022\) \(\Q(\sqrt{69}) \) \(\Q(\sqrt{-23}) \) None \(79\) \(14\) \(0\) \(0\) \(q+(29+21\beta )q^{2}+(159-304\beta )q^{3}+\cdots\)
23.13.b.c \(20\) \(21.022\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(88\) \(318\) \(0\) \(0\) \(q+(4+\beta _{1})q^{2}+(15+2\beta _{1}-\beta _{3})q^{3}+\cdots\)
23.13.d.a \(230\) \(21.022\) None None \(-99\) \(-329\) \(-11\) \(-11\)
23.14.a.a \(11\) \(24.663\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(-64\) \(-860\) \(-10318\) \(-430944\) \(+\) \(q+(-6+\beta _{1})q^{2}+(-78-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
23.14.a.b \(14\) \(24.663\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(64\) \(2056\) \(52182\) \(190602\) \(-\) \(q+(5-\beta _{1})q^{2}+(148-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
23.14.c.a \(250\) \(24.663\) None None \(-11\) \(-1207\) \(-41875\) \(240331\)
23.15.b.a \(3\) \(28.596\) 3.3.621.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(13\beta _{1}-71\beta _{2})q^{2}+(622\beta _{1}-1057\beta _{2})q^{3}+\cdots\)
23.15.b.b \(24\) \(28.596\) None None \(-184\) \(-2160\) \(0\) \(0\)
23.15.d.a \(270\) \(28.596\) None None \(173\) \(2149\) \(-11\) \(-11\)
23.16.a.a \(12\) \(32.820\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-256\) \(-1745\) \(-204476\) \(-5717328\) \(-\) \(q+(-21+\beta _{1})q^{2}+(-145+\beta _{2})q^{3}+\cdots\)
23.16.a.b \(15\) \(32.820\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None None \(0\) \(7003\) \(108024\) \(-135224\) \(+\) \(q-\beta _{1}q^{2}+(467-\beta _{1}-\beta _{2})q^{3}+(17476+\cdots)q^{4}+\cdots\)
23.16.c.a \(290\) \(32.820\) None None \(-187\) \(1427\) \(-7779\) \(207629\)
23.17.b.a \(3\) \(37.335\) 3.3.621.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(48\beta _{1}-47\beta _{2})q^{2}+(-1075\beta _{1}+1359\beta _{2})q^{3}+\cdots\)
23.17.b.b \(28\) \(37.335\) None None \(184\) \(7908\) \(0\) \(0\)
23.17.d.a \(310\) \(37.335\) None None \(-195\) \(-7919\) \(-11\) \(-11\)
23.18.a.a \(14\) \(42.141\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(-10640\) \(-363048\) \(-39649066\) \(+\) \(q-\beta _{1}q^{2}+(-760+\beta _{1}+\beta _{2})q^{3}+(56174+\cdots)q^{4}+\cdots\)
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