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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
6.4.a.a \(1\) \(0.354\) \(\Q\) None \(-2\) \(-3\) \(6\) \(-16\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}+6q^{5}+6q^{6}+\cdots\)
6.5.b.a \(2\) \(0.620\) \(\Q(\sqrt{-2}) \) None \(0\) \(-6\) \(0\) \(52\) \(q+\beta q^{2}+(-3-3\beta )q^{3}-8q^{4}+6\beta q^{5}+\cdots\)
6.6.a.a \(1\) \(0.962\) \(\Q\) None \(4\) \(-9\) \(-66\) \(176\) \(-\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}-66q^{5}-6^{2}q^{6}+\cdots\)
6.7.b.a \(2\) \(1.380\) \(\Q(\sqrt{-2}) \) None \(0\) \(42\) \(0\) \(4\) \(q+\beta q^{2}+(21+3\beta )q^{3}-2^{5}q^{4}-30\beta q^{5}+\cdots\)
6.8.a.a \(1\) \(1.874\) \(\Q\) None \(8\) \(27\) \(-114\) \(-1576\) \(+\) \(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}-114q^{5}+\cdots\)
6.9.b.a \(2\) \(2.444\) \(\Q(\sqrt{-2}) \) None \(0\) \(-126\) \(0\) \(5572\) \(q+2\beta q^{2}+(-63+9\beta )q^{3}-2^{7}q^{4}+\cdots\)
6.10.a.a \(1\) \(3.090\) \(\Q\) None \(-16\) \(81\) \(2694\) \(-3544\) \(-\) \(q-2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}+2694q^{5}+\cdots\)
6.11.b.a \(4\) \(3.812\) \(\Q(\sqrt{-2}, \sqrt{85})\) None \(0\) \(84\) \(0\) \(-45112\) \(q+\beta _{1}q^{2}+(21-3\beta _{1}+\beta _{2})q^{3}-2^{9}q^{4}+\cdots\)
6.12.a.a \(1\) \(4.610\) \(\Q\) None \(-32\) \(-243\) \(5766\) \(72464\) \(+\) \(q-2^{5}q^{2}-3^{5}q^{3}+2^{10}q^{4}+5766q^{5}+\cdots\)
6.12.a.b \(1\) \(4.610\) \(\Q\) None \(-32\) \(243\) \(-11730\) \(-50008\) \(-\) \(q-2^{5}q^{2}+3^{5}q^{3}+2^{10}q^{4}-11730q^{5}+\cdots\)
6.12.a.c \(1\) \(4.610\) \(\Q\) None \(32\) \(243\) \(3630\) \(32936\) \(+\) \(q+2^{5}q^{2}+3^{5}q^{3}+2^{10}q^{4}+3630q^{5}+\cdots\)
6.13.b.a \(4\) \(5.484\) \(\Q(\sqrt{-2}, \sqrt{1009})\) None \(0\) \(780\) \(0\) \(153080\) \(q-\beta _{1}q^{2}+(195-\beta _{1}-\beta _{3})q^{3}-2^{11}q^{4}+\cdots\)
6.14.a.a \(1\) \(6.434\) \(\Q\) None \(64\) \(-729\) \(54654\) \(176336\) \(-\) \(q+2^{6}q^{2}-3^{6}q^{3}+2^{12}q^{4}+54654q^{5}+\cdots\)
6.15.b.a \(4\) \(7.460\) \(\Q(\sqrt{-2}, \sqrt{-35})\) None \(0\) \(-3276\) \(0\) \(-1654072\) \(q+\beta _{1}q^{2}+(-819-7\beta _{1}-\beta _{2})q^{3}+\cdots\)
6.16.a.a \(1\) \(8.562\) \(\Q\) None \(-128\) \(-2187\) \(-314490\) \(2025056\) \(+\) \(q-2^{7}q^{2}-3^{7}q^{3}+2^{14}q^{4}-314490q^{5}+\cdots\)
6.16.a.b \(1\) \(8.562\) \(\Q\) None \(128\) \(-2187\) \(-114810\) \(-3034528\) \(-\) \(q+2^{7}q^{2}-3^{7}q^{3}+2^{14}q^{4}-114810q^{5}+\cdots\)
6.16.a.c \(1\) \(8.562\) \(\Q\) None \(128\) \(2187\) \(77646\) \(762104\) \(+\) \(q+2^{7}q^{2}+3^{7}q^{3}+2^{14}q^{4}+77646q^{5}+\cdots\)
6.17.b.a \(6\) \(9.739\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(6006\) \(0\) \(-167892\) \(q-\beta _{1}q^{2}+(1001+\beta _{1}-\beta _{2})q^{3}-2^{15}q^{4}+\cdots\)
6.18.a.a \(1\) \(10.993\) \(\Q\) None \(-256\) \(-6561\) \(645150\) \(3974432\) \(+\) \(q-2^{8}q^{2}-3^{8}q^{3}+2^{16}q^{4}+645150q^{5}+\cdots\)
6.18.a.b \(1\) \(10.993\) \(\Q\) None \(-256\) \(6561\) \(-72186\) \(-8640184\) \(-\) \(q-2^{8}q^{2}+3^{8}q^{3}+2^{16}q^{4}-72186q^{5}+\cdots\)
6.18.a.c \(1\) \(10.993\) \(\Q\) None \(256\) \(-6561\) \(-199650\) \(24959264\) \(-\) \(q+2^{8}q^{2}-3^{8}q^{3}+2^{16}q^{4}-199650q^{5}+\cdots\)
6.19.b.a \(6\) \(12.323\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-6258\) \(0\) \(28233804\) \(q+\beta _{1}q^{2}+(-1043+20\beta _{1}-\beta _{2})q^{3}+\cdots\)
6.20.a.a \(1\) \(13.729\) \(\Q\) None \(-512\) \(-19683\) \(-3732474\) \(-149672656\) \(+\) \(q-2^{9}q^{2}-3^{9}q^{3}+2^{18}q^{4}-3732474q^{5}+\cdots\)
6.20.a.b \(1\) \(13.729\) \(\Q\) None \(-512\) \(19683\) \(-5849490\) \(173530952\) \(-\) \(q-2^{9}q^{2}+3^{9}q^{3}+2^{18}q^{4}-5849490q^{5}+\cdots\)
6.20.a.c \(1\) \(13.729\) \(\Q\) None \(512\) \(19683\) \(1953390\) \(40488776\) \(+\) \(q+2^{9}q^{2}+3^{9}q^{3}+2^{18}q^{4}+1953390q^{5}+\cdots\)
6.21.b.a \(6\) \(15.211\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(18846\) \(0\) \(-566671812\) \(q+\beta _{1}q^{2}+(3141-11\beta _{1}-\beta _{2})q^{3}+\cdots\)
6.22.a.a \(1\) \(16.769\) \(\Q\) None \(-1024\) \(59049\) \(26444550\) \(166115864\) \(-\) \(q-2^{10}q^{2}+3^{10}q^{3}+2^{20}q^{4}+26444550q^{5}+\cdots\)
6.22.a.b \(1\) \(16.769\) \(\Q\) None \(1024\) \(-59049\) \(12954174\) \(-479513104\) \(-\) \(q+2^{10}q^{2}-3^{10}q^{3}+2^{20}q^{4}+12954174q^{5}+\cdots\)
6.22.a.c \(1\) \(16.769\) \(\Q\) None \(1024\) \(59049\) \(-23245050\) \(-1322977768\) \(+\) \(q+2^{10}q^{2}+3^{10}q^{3}+2^{20}q^{4}-23245050q^{5}+\cdots\)
6.23.b.a \(8\) \(18.402\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-69720\) \(0\) \(5645581840\) \(q-\beta _{1}q^{2}+(-8715+9\beta _{1}-\beta _{2})q^{3}+\cdots\)
6.24.a.a \(1\) \(20.112\) \(\Q\) None \(-2048\) \(-177147\) \(196251270\) \(-8131131904\) \(+\) \(q-2^{11}q^{2}-3^{11}q^{3}+2^{22}q^{4}+196251270q^{5}+\cdots\)
6.24.a.b \(1\) \(20.112\) \(\Q\) None \(-2048\) \(177147\) \(-35483250\) \(-2385847912\) \(-\) \(q-2^{11}q^{2}+3^{11}q^{3}+2^{22}q^{4}-35483250q^{5}+\cdots\)
6.24.a.c \(1\) \(20.112\) \(\Q\) None \(2048\) \(-177147\) \(-9019770\) \(515282432\) \(-\) \(q+2^{11}q^{2}-3^{11}q^{3}+2^{22}q^{4}-9019770q^{5}+\cdots\)
6.24.a.d \(2\) \(20.112\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(4096\) \(354294\) \(25248156\) \(5764462768\) \(+\) \(q+2^{11}q^{2}+3^{11}q^{3}+2^{22}q^{4}+(12624078+\cdots)q^{5}+\cdots\)
6.25.b.a \(8\) \(21.898\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-131880\) \(0\) \(-10160794640\) \(q+\beta _{1}q^{2}+(-16485-\beta _{1}-\beta _{2})q^{3}+\cdots\)
6.26.a.a \(1\) \(23.760\) \(\Q\) None \(-4096\) \(-531441\) \(-292754850\) \(3580644032\) \(+\) \(q-2^{12}q^{2}-3^{12}q^{3}+2^{24}q^{4}-292754850q^{5}+\cdots\)
6.26.a.b \(1\) \(23.760\) \(\Q\) None \(-4096\) \(531441\) \(590425734\) \(57857417576\) \(-\) \(q-2^{12}q^{2}+3^{12}q^{3}+2^{24}q^{4}+590425734q^{5}+\cdots\)
6.26.a.c \(1\) \(23.760\) \(\Q\) None \(4096\) \(-531441\) \(-799327650\) \(7962409664\) \(-\) \(q+2^{12}q^{2}-3^{12}q^{3}+2^{24}q^{4}-799327650q^{5}+\cdots\)
6.27.b.a \(8\) \(25.698\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(2194920\) \(0\) \(183211263760\) \(q+\beta _{1}q^{2}+(274365-33\beta _{1}+\beta _{2})q^{3}+\cdots\)
6.28.a.a \(1\) \(27.711\) \(\Q\) None \(-8192\) \(1594323\) \(1992850350\) \(-321751224088\) \(-\) \(q-2^{13}q^{2}+3^{13}q^{3}+2^{26}q^{4}+1992850350q^{5}+\cdots\)
6.28.a.b \(1\) \(27.711\) \(\Q\) None \(8192\) \(-1594323\) \(2904255750\) \(-493494294832\) \(-\) \(q+2^{13}q^{2}-3^{13}q^{3}+2^{26}q^{4}+2904255750q^{5}+\cdots\)
6.28.a.c \(1\) \(27.711\) \(\Q\) None \(8192\) \(1594323\) \(1220703150\) \(96889207016\) \(+\) \(q+2^{13}q^{2}+3^{13}q^{3}+2^{26}q^{4}+1220703150q^{5}+\cdots\)
6.28.a.d \(2\) \(27.711\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(-16384\) \(-3188646\) \(291441036\) \(121646295328\) \(+\) \(q-2^{13}q^{2}-3^{13}q^{3}+2^{26}q^{4}+(145720518+\cdots)q^{5}+\cdots\)
6.29.b.a \(10\) \(29.801\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(-8805966\) \(0\) \(-640581497308\) \(q-\beta _{1}q^{2}+(-880597-78\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
6.30.a.a \(1\) \(31.967\) \(\Q\) None \(-16384\) \(-4782969\) \(1951578750\) \(-1\!\cdots\!92\) \(+\) \(q-2^{14}q^{2}-3^{14}q^{3}+2^{28}q^{4}+1951578750q^{5}+\cdots\)
6.30.a.b \(1\) \(31.967\) \(\Q\) None \(-16384\) \(4782969\) \(-13482080250\) \(-517740139336\) \(-\) \(q-2^{14}q^{2}+3^{14}q^{3}+2^{28}q^{4}-13482080250q^{5}+\cdots\)
6.30.a.c \(1\) \(31.967\) \(\Q\) None \(16384\) \(4782969\) \(-21003872250\) \(15\!\cdots\!32\) \(+\) \(q+2^{14}q^{2}+3^{14}q^{3}+2^{28}q^{4}-21003872250q^{5}+\cdots\)
6.30.a.d \(2\) \(31.967\) \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None \(32768\) \(-9565938\) \(-6557946756\) \(-1\!\cdots\!48\) \(-\) \(q+2^{14}q^{2}-3^{14}q^{3}+2^{28}q^{4}+(-3278973378+\cdots)q^{5}+\cdots\)
6.31.b.a \(10\) \(34.209\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(14139762\) \(0\) \(-1\!\cdots\!96\) \(q-\beta _{1}q^{2}+(1413976-3^{3}\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
6.32.a.a \(1\) \(36.526\) \(\Q\) None \(-32768\) \(-14348907\) \(21436113030\) \(14\!\cdots\!36\) \(+\) \(q-2^{15}q^{2}-3^{15}q^{3}+2^{30}q^{4}+21436113030q^{5}+\cdots\)
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