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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.12.a.a \(1\) \(0.768\) \(\Q\) None \(-24\) \(252\) \(4830\) \(-16744\) \(+\) \(q-24q^{2}+252q^{3}-1472q^{4}+4830q^{5}+\cdots\)
3.12.a.a \(1\) \(2.305\) \(\Q\) None \(78\) \(-243\) \(-5370\) \(-27760\) \(+\) \(q+78q^{2}-3^{5}q^{3}+4036q^{4}-5370q^{5}+\cdots\)
4.12.a.a \(1\) \(3.073\) \(\Q\) None \(0\) \(-516\) \(-10530\) \(49304\) \(-\) \(q-516q^{3}-10530q^{5}+49304q^{7}+\cdots\)
5.12.a.a \(1\) \(3.842\) \(\Q\) None \(34\) \(-792\) \(3125\) \(-17556\) \(-\) \(q+34q^{2}-792q^{3}-892q^{4}+5^{5}q^{5}+\cdots\)
5.12.a.b \(2\) \(3.842\) \(\Q(\sqrt{151}) \) None \(-20\) \(-220\) \(-6250\) \(57900\) \(+\) \(q+(-10+3\beta )q^{2}+(-110+2^{4}\beta )q^{3}+\cdots\)
5.12.b.a \(4\) \(3.842\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(0\) \(-300\) \(0\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-18-\beta _{2})q^{4}+\cdots\)
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 \(32\) \(243\) \(3630\) \(32936\) \(+\) \(q+2^{5}q^{2}+3^{5}q^{3}+2^{10}q^{4}+3630q^{5}+\cdots\)
7.12.a.a \(2\) \(5.378\) \(\Q(\sqrt{3369}) \) None \(-54\) \(120\) \(-13500\) \(33614\) \(-\) \(q+(-3^{3}-\beta )q^{2}+(60+6\beta )q^{3}+(2050+\cdots)q^{4}+\cdots\)
7.12.a.b \(3\) \(5.378\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(77\) \(-140\) \(5026\) \(-50421\) \(+\) \(q+(26+\beta _{2})q^{2}+(-47-11\beta _{1}+10\beta _{2})q^{3}+\cdots\)
7.12.c.a \(12\) \(5.378\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(22\) \(-244\) \(-8782\) \(-504\) \(q+(4-\beta _{1}-4\beta _{2})q^{2}+(\beta _{1}-40\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)
8.12.a.a \(1\) \(6.147\) \(\Q\) None \(0\) \(-36\) \(-3490\) \(-55464\) \(-\) \(q-6^{2}q^{3}-3490q^{5}-55464q^{7}-175851q^{9}+\cdots\)
8.12.a.b \(2\) \(6.147\) \(\Q(\sqrt{109}) \) None \(0\) \(56\) \(7868\) \(91056\) \(+\) \(q+(28+\beta )q^{3}+(3934-12\beta )q^{5}+(45528+\cdots)q^{7}+\cdots\)
8.12.b.a \(10\) \(6.147\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(22\) \(0\) \(0\) \(-33616\) \(q+(2+\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(43+2\beta _{1}+\cdots)q^{4}+\cdots\)
9.12.a.a \(1\) \(6.915\) \(\Q\) None \(-78\) \(0\) \(5370\) \(-27760\) \(-\) \(q-78q^{2}+4036q^{4}+5370q^{5}-27760q^{7}+\cdots\)
9.12.a.b \(1\) \(6.915\) \(\Q\) None \(24\) \(0\) \(-4830\) \(-16744\) \(-\) \(q+24q^{2}-1472q^{4}-4830q^{5}-16744q^{7}+\cdots\)
9.12.a.c \(2\) \(6.915\) \(\Q(\sqrt{70}) \) None \(0\) \(0\) \(0\) \(116200\) \(+\) \(q+\beta q^{2}+472q^{4}+224\beta q^{5}+58100q^{7}+\cdots\)
9.12.c.a \(20\) \(6.915\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-33\) \(-12\) \(-7230\) \(8512\) \(q+(\beta _{1}-3\beta _{3})q^{2}+(24-51\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
10.12.a.a \(1\) \(7.683\) \(\Q\) None \(-32\) \(-12\) \(3125\) \(-14176\) \(-\) \(q-2^{5}q^{2}-12q^{3}+2^{10}q^{4}+5^{5}q^{5}+\cdots\)
10.12.a.b \(1\) \(7.683\) \(\Q\) None \(-32\) \(738\) \(-3125\) \(25574\) \(+\) \(q-2^{5}q^{2}+738q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots\)
10.12.a.c \(1\) \(7.683\) \(\Q\) None \(32\) \(-318\) \(-3125\) \(-70714\) \(-\) \(q+2^{5}q^{2}-318q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots\)
10.12.a.d \(2\) \(7.683\) \(\Q(\sqrt{1969}) \) None \(64\) \(604\) \(6250\) \(14092\) \(+\) \(q+2^{5}q^{2}+(302-\beta )q^{3}+2^{10}q^{4}+5^{5}q^{5}+\cdots\)
10.12.b.a \(6\) \(7.683\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(530\) \(0\) \(q-\beta _{2}q^{2}+(\beta _{1}+3\beta _{2})q^{3}-2^{10}q^{4}+\cdots\)
11.12.a.a \(3\) \(8.452\) 3.3.202533.1 None \(0\) \(-393\) \(-7305\) \(-5082\) \(-\) \(q-\beta _{1}q^{2}+(-131-2\beta _{1}-4\beta _{2})q^{3}+\cdots\)
11.12.a.b \(5\) \(8.452\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(32\) \(160\) \(-8398\) \(79040\) \(+\) \(q+(6+\beta _{1})q^{2}+(2^{5}-\beta _{3})q^{3}+(1239+\cdots)q^{4}+\cdots\)
11.12.c.a \(40\) \(8.452\) None \(11\) \(-276\) \(6038\) \(55440\)
12.12.a.a \(1\) \(9.220\) \(\Q\) None \(0\) \(-243\) \(9990\) \(-86128\) \(-\) \(q-3^{5}q^{3}+9990q^{5}-86128q^{7}+3^{10}q^{9}+\cdots\)
12.12.a.b \(1\) \(9.220\) \(\Q\) None \(0\) \(243\) \(2862\) \(9128\) \(+\) \(q+3^{5}q^{3}+2862q^{5}+9128q^{7}+3^{10}q^{9}+\cdots\)
12.12.b.a \(20\) \(9.220\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(99+\beta _{2})q^{4}+(-5\beta _{1}+\cdots)q^{5}+\cdots\)
13.12.a.a \(5\) \(9.988\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-41\) \(-496\) \(-2542\) \(-36296\) \(-\) \(q+(-8-\beta _{1})q^{2}+(-99-2\beta _{1}-\beta _{4})q^{3}+\cdots\)
13.12.a.b \(6\) \(9.988\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(55\) \(476\) \(3312\) \(-4176\) \(+\) \(q+(9+\beta _{1})q^{2}+(80-2\beta _{1}+\beta _{4})q^{3}+\cdots\)
13.12.b.a \(12\) \(9.988\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-488\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-41-\beta _{2})q^{3}+(-2^{10}+\cdots)q^{4}+\cdots\)
13.12.c.a \(24\) \(9.988\) None \(31\) \(-244\) \(-10436\) \(-2928\)
13.12.e.a \(22\) \(9.988\) None \(-3\) \(242\) \(0\) \(128496\)
14.12.a.a \(1\) \(10.757\) \(\Q\) None \(-32\) \(-396\) \(7350\) \(16807\) \(-\) \(q-2^{5}q^{2}-396q^{3}+2^{10}q^{4}+7350q^{5}+\cdots\)
14.12.a.b \(1\) \(10.757\) \(\Q\) None \(32\) \(-90\) \(-7480\) \(-16807\) \(-\) \(q+2^{5}q^{2}-90q^{3}+2^{10}q^{4}-7480q^{5}+\cdots\)
14.12.a.c \(2\) \(10.757\) \(\Q(\sqrt{153169}) \) None \(-64\) \(350\) \(266\) \(-33614\) \(+\) \(q-2^{5}q^{2}+(175-\beta )q^{3}+2^{10}q^{4}+(133+\cdots)q^{5}+\cdots\)
14.12.a.d \(2\) \(10.757\) \(\Q(\sqrt{352969}) \) None \(64\) \(-350\) \(3738\) \(33614\) \(+\) \(q+2^{5}q^{2}+(-175-\beta )q^{3}+2^{10}q^{4}+\cdots\)
14.12.c.a \(8\) \(10.757\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-128\) \(266\) \(7504\) \(-42224\) \(q+(-2^{5}+2^{5}\beta _{2})q^{2}+(67\beta _{2}-\beta _{3})q^{3}+\cdots\)
14.12.c.b \(8\) \(10.757\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(128\) \(-266\) \(3808\) \(110328\) \(q+2^{5}\beta _{2}q^{2}+(-67+\beta _{1}+67\beta _{2})q^{3}+\cdots\)
15.12.a.a \(1\) \(11.525\) \(\Q\) None \(-56\) \(-243\) \(3125\) \(27984\) \(-\) \(q-56q^{2}-3^{5}q^{3}+1088q^{4}+5^{5}q^{5}+\cdots\)
15.12.a.b \(2\) \(11.525\) \(\Q(\sqrt{1609}) \) None \(-22\) \(486\) \(-6250\) \(-10864\) \(-\) \(q+(-11-\beta )q^{2}+3^{5}q^{3}+(-318+22\beta )q^{4}+\cdots\)
15.12.a.c \(2\) \(11.525\) \(\Q(\sqrt{1801}) \) None \(-13\) \(-486\) \(-6250\) \(7784\) \(+\) \(q+(-6-\beta )q^{2}-3^{5}q^{3}+(-1562+13\beta )q^{4}+\cdots\)
15.12.a.d \(3\) \(11.525\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-1\) \(729\) \(9375\) \(-14608\) \(+\) \(q-\beta _{1}q^{2}+3^{5}q^{3}+(1585+3\beta _{1}+\beta _{2})q^{4}+\cdots\)
15.12.b.a \(12\) \(11.525\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(2556\) \(0\) \(q+\beta _{3}q^{2}-\beta _{4}q^{3}+(-1359+\beta _{1})q^{4}+\cdots\)
15.12.e.a \(40\) \(11.525\) None \(0\) \(504\) \(0\) \(31504\)
16.12.a.a \(1\) \(12.293\) \(\Q\) None \(0\) \(-252\) \(4830\) \(16744\) \(-\) \(q-252q^{3}+4830q^{5}+16744q^{7}+\cdots\)
16.12.a.b \(1\) \(12.293\) \(\Q\) None \(0\) \(36\) \(-3490\) \(55464\) \(+\) \(q+6^{2}q^{3}-3490q^{5}+55464q^{7}-175851q^{9}+\cdots\)
16.12.a.c \(1\) \(12.293\) \(\Q\) None \(0\) \(516\) \(-10530\) \(-49304\) \(-\) \(q+516q^{3}-10530q^{5}-49304q^{7}+\cdots\)
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