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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
309.1.h.a \(4\) \(0.154\) \(\Q(\zeta_{12})\) None None \(0\) \(-4\) \(0\) \(2\) \(q-\zeta_{12}q^{2}-q^{3}+\zeta_{12}^{5}q^{5}+\zeta_{12}q^{6}+\cdots\)
309.1.l.a \(16\) \(0.154\) \(\Q(\zeta_{34})\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) \(q+\zeta_{34}^{6}q^{3}-\zeta_{34}^{7}q^{4}+(\zeta_{34}^{4}-\zeta_{34}^{9}+\cdots)q^{7}+\cdots\)
309.2.a.a \(1\) \(2.467\) \(\Q\) None None \(-1\) \(1\) \(-1\) \(-2\) \(+\) \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
309.2.a.b \(3\) \(2.467\) 3.3.148.1 None None \(1\) \(-3\) \(1\) \(-2\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots\)
309.2.a.c \(5\) \(2.467\) 5.5.81509.1 None None \(-2\) \(-5\) \(-5\) \(-2\) \(+\) \(q+\beta _{3}q^{2}-q^{3}+(-\beta _{3}-\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
309.2.a.d \(8\) \(2.467\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-1\) \(8\) \(-1\) \(6\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots\)
309.2.c.a \(32\) \(2.467\) None None \(0\) \(0\) \(0\) \(-16\)
309.2.e.a \(2\) \(2.467\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(2\) \(4\) \(-1\) \(q-2\zeta_{6}q^{2}+q^{3}+(-2+2\zeta_{6})q^{4}+(4+\cdots)q^{5}+\cdots\)
309.2.e.b \(16\) \(2.467\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(1\) \(-16\) \(1\) \(4\) \(q+\beta _{1}q^{2}-q^{3}+(-\beta _{3}+\beta _{13})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
309.2.e.c \(16\) \(2.467\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(1\) \(16\) \(-5\) \(0\) \(q-\beta _{13}q^{2}+q^{3}+(\beta _{1}+2\beta _{6}+\beta _{12}+\cdots)q^{4}+\cdots\)
309.2.g.a \(2\) \(2.467\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-5\) \(q+(1-2\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(-5+\cdots)q^{7}+\cdots\)
309.2.g.b \(8\) \(2.467\) 8.0.1568160000.5 None None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{3}q^{2}+(-1-2\beta _{2})q^{3}+(-\beta _{2}-\beta _{5}+\cdots)q^{4}+\cdots\)
309.2.g.c \(56\) \(2.467\) None None \(0\) \(0\) \(0\) \(-10\)
309.2.i.a \(128\) \(2.467\) None None \(1\) \(8\) \(4\) \(4\)
309.2.i.b \(160\) \(2.467\) None None \(-1\) \(-10\) \(-4\) \(-12\)
309.2.k.a \(512\) \(2.467\) None None \(0\) \(-17\) \(0\) \(-18\)
309.2.m.a \(256\) \(2.467\) None None \(-1\) \(16\) \(-1\) \(-4\)
309.2.m.b \(288\) \(2.467\) None None \(1\) \(-18\) \(1\) \(1\)
309.2.o.a \(32\) \(2.467\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(5\)
309.2.o.b \(1024\) \(2.467\) None None \(0\) \(-34\) \(0\) \(-66\)
309.3.b.a \(68\) \(8.420\) None None \(0\) \(-4\) \(0\) \(0\)
309.3.d.a \(34\) \(8.420\) None None \(0\) \(0\) \(0\) \(0\)
309.3.f.a \(34\) \(8.420\) None None \(0\) \(0\) \(-9\) \(9\)
309.3.f.b \(36\) \(8.420\) None None \(0\) \(0\) \(9\) \(-14\)
309.3.h.a \(2\) \(8.420\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-6\) \(0\) \(-11\) \(q-3q^{3}-4\zeta_{6}q^{4}-11\zeta_{6}q^{7}+9q^{9}+\cdots\)
309.3.h.b \(132\) \(8.420\) None None \(0\) \(4\) \(0\) \(16\)
309.3.j.a \(544\) \(8.420\) None None \(0\) \(0\) \(0\) \(0\)
309.3.l.a \(1088\) \(8.420\) None None \(0\) \(-13\) \(0\) \(-34\)
309.3.n.a \(32\) \(8.420\) \(\Q(\sqrt{-3}) \) None \(0\) \(6\) \(0\) \(11\)
309.3.n.b \(2112\) \(8.420\) None None \(0\) \(-38\) \(0\) \(-84\)
309.3.p.a \(544\) \(8.420\) None None \(0\) \(0\) \(9\) \(-9\)
309.3.p.b \(576\) \(8.420\) None None \(0\) \(0\) \(-9\) \(14\)
309.4.a.a \(2\) \(18.232\) \(\Q(\sqrt{41}) \) None None \(-3\) \(6\) \(-15\) \(22\) \(-\) \(q+(-1-\beta )q^{2}+3q^{3}+(3+3\beta )q^{4}+\cdots\)
309.4.a.b \(7\) \(18.232\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(-1\) \(21\) \(5\) \(-73\) \(-\) \(q-\beta _{1}q^{2}+3q^{3}+(1+\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
309.4.a.c \(12\) \(18.232\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(4\) \(-36\) \(10\) \(5\) \(+\) \(q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+(1-\beta _{7}+\cdots)q^{5}+\cdots\)
309.4.a.d \(14\) \(18.232\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(-2\) \(-42\) \(-20\) \(5\) \(-\) \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
309.4.a.e \(17\) \(18.232\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None None \(2\) \(51\) \(20\) \(61\) \(+\) \(q+\beta _{1}q^{2}+3q^{3}+(5+\beta _{2})q^{4}+(1+\beta _{7}+\cdots)q^{5}+\cdots\)
309.5.d.a \(70\) \(31.941\) None None \(0\) \(0\) \(0\) \(-56\)
309.6.a.a \(17\) \(49.559\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None None \(2\) \(153\) \(-103\) \(-382\) \(+\) \(q+\beta _{1}q^{2}+9q^{3}+(11+\beta _{2})q^{4}+(-6+\cdots)q^{5}+\cdots\)
309.6.a.b \(20\) \(49.559\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(4\) \(-180\) \(97\) \(10\) \(-\) \(q+\beta _{1}q^{2}-9q^{3}+(2^{4}+\beta _{2})q^{4}+(5+\beta _{9}+\cdots)q^{5}+\cdots\)
309.6.a.c \(22\) \(49.559\) None None \(-8\) \(-198\) \(-53\) \(10\) \(+\)
309.6.a.d \(25\) \(49.559\) None None \(14\) \(225\) \(47\) \(402\) \(-\)
309.8.a.a \(26\) \(96.527\) None None \(-16\) \(702\) \(-445\) \(-2598\) \(-\)
309.8.a.b \(29\) \(96.527\) None None \(10\) \(-783\) \(55\) \(146\) \(+\)
309.8.a.c \(31\) \(96.527\) None None \(-14\) \(-837\) \(-695\) \(146\) \(-\)
309.8.a.d \(34\) \(96.527\) None None \(8\) \(918\) \(305\) \(2890\) \(+\)
309.10.a.a \(34\) \(159.146\) None None \(-34\) \(2754\) \(-1078\) \(-23515\) \(+\)
309.10.a.b \(37\) \(159.146\) None None \(52\) \(-2997\) \(3922\) \(-4307\) \(-\)
309.10.a.c \(39\) \(159.146\) None None \(4\) \(-3159\) \(172\) \(-4307\) \(+\)
309.10.a.d \(42\) \(159.146\) None None \(14\) \(3402\) \(2672\) \(14901\) \(-\)
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