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Results (displaying all 48 matches)

Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
83.1.b.a \(1\) \(0.041\) \(\Q\) \(\Q(\sqrt{-83}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots\)
83.2.a.a \(1\) \(0.663\) \(\Q\) None None \(-1\) \(-1\) \(-2\) \(-3\) \(+\) \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}-3q^{7}+\cdots\)
83.2.a.b \(6\) \(0.663\) 6.6.9059636.1 None None \(1\) \(1\) \(2\) \(3\) \(-\) \(q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{3}q^{3}+(1-\beta _{5})q^{4}+\cdots\)
83.2.c.a \(240\) \(0.663\) None None \(-38\) \(-37\) \(-35\) \(-33\)
83.3.b.a \(3\) \(2.262\) 3.3.2241.1 \(\Q(\sqrt{-83}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{2})q^{3}+4q^{4}+(-3\beta _{1}-2\beta _{2})q^{7}+\cdots\)
83.3.b.b \(10\) \(2.262\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(-6\) \(0\) \(12\) \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(-3+\beta _{7}+\cdots)q^{4}+\cdots\)
83.3.d.a \(520\) \(2.262\) None None \(-41\) \(-35\) \(-41\) \(-53\)
83.4.a.a \(7\) \(4.897\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(-5\) \(-11\) \(-17\) \(-46\) \(-\) \(q+(-1-\beta _{4})q^{2}+(-1+\beta _{1}+\beta _{4})q^{3}+\cdots\)
83.4.a.b \(13\) \(4.897\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(5\) \(7\) \(33\) \(52\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{8})q^{3}+(6+\beta _{2})q^{4}+\cdots\)
83.4.c.a \(800\) \(4.897\) None None \(-41\) \(-37\) \(-57\) \(-47\)
83.5.b.a \(3\) \(8.580\) 3.3.2241.1 \(\Q(\sqrt{-83}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(2\beta _{1}-3\beta _{2})q^{3}+2^{4}q^{4}+(21\beta _{1}-11\beta _{2})q^{7}+\cdots\)
83.5.b.b \(24\) \(8.580\) None None \(0\) \(6\) \(0\) \(-112\)
83.5.d.a \(1080\) \(8.580\) None None \(-41\) \(-47\) \(-41\) \(71\)
83.6.a.a \(14\) \(13.312\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(-13\) \(-17\) \(-162\) \(-247\) \(+\) \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{7})q^{3}+(10+\cdots)q^{4}+\cdots\)
83.6.a.b \(20\) \(13.312\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(7\) \(37\) \(88\) \(439\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{5})q^{3}+(19+\beta _{2})q^{4}+\cdots\)
83.6.c.a \(1360\) \(13.312\) None None \(-35\) \(-61\) \(33\) \(-233\)
83.7.b.a \(1\) \(19.094\) \(\Q\) \(\Q(\sqrt{-83}) \) None \(0\) \(-29\) \(0\) \(-61\) \(q-29q^{3}+2^{6}q^{4}-61q^{7}+112q^{9}+\cdots\)
83.7.b.b \(2\) \(19.094\) \(\Q(\sqrt{249}) \) \(\Q(\sqrt{-83}) \) None \(0\) \(29\) \(0\) \(61\) \(q+(15+\beta )q^{3}+2^{6}q^{4}+(23-15\beta )q^{7}+\cdots\)
83.7.b.c \(38\) \(19.094\) None None \(0\) \(18\) \(0\) \(262\)
83.7.d.a \(1640\) \(19.094\) None None \(-41\) \(-59\) \(-41\) \(-303\)
83.8.a.a \(21\) \(25.928\) None None \(-17\) \(-95\) \(-502\) \(-3273\) \(-\)
83.8.a.b \(27\) \(25.928\) None None \(23\) \(67\) \(748\) \(1529\) \(+\)
83.8.c.a \(1920\) \(25.928\) None None \(-47\) \(-13\) \(-287\) \(1703\)
83.9.b.a \(3\) \(33.812\) 3.3.2241.1 \(\Q(\sqrt{-83}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-47\beta _{1}-2\beta _{2})q^{3}+2^{8}q^{4}+(-846\beta _{1}+\cdots)q^{7}+\cdots\)
83.9.b.b \(52\) \(33.812\) None None \(0\) \(-114\) \(0\) \(2028\)
83.9.d.a \(2200\) \(33.812\) None None \(-41\) \(73\) \(-41\) \(-2069\)
83.10.a.a \(28\) \(42.748\) None None \(-49\) \(-317\) \(-3467\) \(-13836\) \(+\)
83.10.a.b \(34\) \(42.748\) None None \(31\) \(169\) \(2783\) \(19778\) \(-\)
83.10.c.a \(2480\) \(42.748\) None None \(-23\) \(107\) \(643\) \(-5983\)
83.11.b.a \(3\) \(52.735\) 3.3.2241.1 \(\Q(\sqrt{-83}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-139\beta _{1}+6\beta _{2})q^{3}+2^{10}q^{4}+(5922\beta _{1}+\cdots)q^{7}+\cdots\)
83.11.b.b \(66\) \(52.735\) None None \(0\) \(42\) \(0\) \(-22288\)
83.11.d.a \(2760\) \(52.735\) None None \(-41\) \(-83\) \(-41\) \(22247\)
83.12.a.a \(34\) \(63.772\) None None \(-41\) \(-719\) \(-19862\) \(-97477\) \(-\)
83.12.a.b \(40\) \(63.772\) None None \(119\) \(739\) \(11388\) \(137821\) \(+\)
83.12.c.a \(3040\) \(63.772\) None None \(-71\) \(-565\) \(-1227\) \(-6897\)
83.13.b.a \(1\) \(75.861\) \(\Q\) \(\Q(\sqrt{-83}) \) None \(0\) \(-617\) \(0\) \(-231577\) \(q-617q^{3}+2^{12}q^{4}-231577q^{7}+\cdots\)
83.13.b.b \(2\) \(75.861\) \(\Q(\sqrt{249}) \) \(\Q(\sqrt{-83}) \) None \(0\) \(617\) \(0\) \(231577\) \(q+(294-29\beta )q^{3}+2^{12}q^{4}+(116246+\cdots)q^{7}+\cdots\)
83.13.b.c \(80\) \(75.861\) None None \(0\) \(918\) \(0\) \(103918\)
83.14.a.a \(42\) \(89.002\) None None \(-193\) \(-2057\) \(-78072\) \(-907547\) \(+\)
83.14.a.b \(48\) \(89.002\) None None \(127\) \(2317\) \(78178\) \(739539\) \(-\)
83.15.b.a \(3\) \(103.193\) 3.3.2241.1 \(\Q(\sqrt{-83}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-63\beta _{1}+152\beta _{2})q^{3}+2^{14}q^{4}+\cdots\)
83.15.b.b \(94\) \(103.193\) None None \(0\) \(-2238\) \(0\) \(-386388\)
83.16.a.a \(48\) \(118.436\) None None \(-473\) \(-5843\) \(-442447\) \(-7927854\) \(-\)
83.16.a.b \(54\) \(118.436\) None None \(167\) \(7279\) \(338803\) \(3601748\) \(+\)
83.18.a.a \(55\) \(152.074\) None None \(-241\) \(-11321\) \(-1009352\) \(-50694303\) \(+\)
83.18.a.b \(61\) \(152.074\) None None \(1039\) \(28045\) \(2896898\) \(30012911\) \(-\)
83.20.a.a \(62\) \(189.918\) None None \(-1481\) \(-94199\) \(-6266132\) \(-202919777\) \(-\)
83.20.a.b \(68\) \(189.918\) None None \(1079\) \(23899\) \(13265118\) \(362030721\) \(+\)


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