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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
123.2.a.a \(1\) \(0.982\) \(\Q\) None \(-2\) \(1\) \(-4\) \(-2\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}-4q^{5}-2q^{6}+\cdots\)
123.2.a.b \(1\) \(0.982\) \(\Q\) None \(0\) \(-1\) \(-2\) \(-4\) \(+\) \(q-q^{3}-2q^{4}-2q^{5}-4q^{7}+q^{9}+5q^{11}+\cdots\)
123.2.a.c \(2\) \(0.982\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(4\) \(-4\) \(-\) \(q+\beta q^{2}+q^{3}+(2-\beta )q^{5}+\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)
123.2.a.d \(3\) \(0.982\) 3.3.316.1 None \(1\) \(-3\) \(4\) \(2\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
123.2.d.a \(8\) \(0.982\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(2\) \(0\) \(-8\) \(0\) \(q+\beta _{4}q^{2}+\beta _{3}q^{3}+(1-\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
123.2.e.a \(12\) \(0.982\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-1+\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots\)
123.2.g.a \(4\) \(0.982\) \(\Q(\zeta_{10})\) None \(-5\) \(-4\) \(-8\) \(-6\) \(q+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
123.2.g.b \(12\) \(0.982\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(4\) \(-12\) \(1\) \(8\) \(q+(-\beta _{1}+\beta _{4}-\beta _{5})q^{2}-q^{3}+(-1+\cdots)q^{4}+\cdots\)
123.2.g.c \(16\) \(0.982\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-1\) \(16\) \(-1\) \(-2\) \(q+\beta _{12}q^{2}+q^{3}+(-1+\beta _{1}+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
123.2.i.a \(48\) \(0.982\) None \(0\) \(-8\) \(0\) \(-8\)
123.2.j.a \(32\) \(0.982\) None \(-2\) \(0\) \(8\) \(0\)
123.2.n.a \(48\) \(0.982\) None \(0\) \(0\) \(0\) \(0\)
123.2.o.a \(192\) \(0.982\) None \(0\) \(-12\) \(0\) \(-32\)
123.3.b.a \(1\) \(3.352\) \(\Q\) \(\Q(\sqrt{-123}) \) \(0\) \(-3\) \(0\) \(0\) \(q-3q^{3}+4q^{4}+9q^{9}+19q^{11}-12q^{12}+\cdots\)
123.3.b.b \(1\) \(3.352\) \(\Q\) \(\Q(\sqrt{-123}) \) \(0\) \(3\) \(0\) \(0\) \(q+3q^{3}+4q^{4}+9q^{9}-19q^{11}+12q^{12}+\cdots\)
123.3.b.c \(2\) \(3.352\) \(\Q(\sqrt{-5}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+\beta q^{2}+(-2-\beta )q^{3}-q^{4}+\beta q^{5}+\cdots\)
123.3.b.d \(2\) \(3.352\) \(\Q(\sqrt{-5}) \) None \(0\) \(4\) \(0\) \(0\) \(q+\beta q^{2}+(2+\beta )q^{3}-q^{4}+\beta q^{5}+(-5+\cdots)q^{6}+\cdots\)
123.3.b.e \(20\) \(3.352\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{8}q^{3}+(-3-\beta _{6})q^{4}+\beta _{11}q^{5}+\cdots\)
123.3.c.a \(26\) \(3.352\) None \(0\) \(2\) \(0\) \(-4\)
123.3.f.a \(52\) \(3.352\) None \(0\) \(2\) \(0\) \(-4\)
123.3.h.a \(56\) \(3.352\) None \(8\) \(0\) \(0\) \(0\)
123.3.k.a \(104\) \(3.352\) None \(0\) \(-12\) \(0\) \(-6\)
123.3.l.a \(104\) \(3.352\) None \(0\) \(0\) \(0\) \(-10\)
123.3.m.a \(208\) \(3.352\) None \(0\) \(-12\) \(0\) \(-16\)
123.3.p.a \(224\) \(3.352\) None \(-8\) \(0\) \(0\) \(0\)
123.4.a.a \(4\) \(7.257\) 4.4.183064.1 None \(-4\) \(12\) \(-33\) \(-28\) \(-\) \(q+(-1-\beta _{3})q^{2}+3q^{3}+(2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
123.4.a.b \(4\) \(7.257\) 4.4.994300.1 None \(0\) \(-12\) \(-9\) \(-14\) \(-\) \(q-\beta _{1}q^{2}-3q^{3}+(3+\beta _{3})q^{4}+(-3+\cdots)q^{5}+\cdots\)
123.4.a.c \(6\) \(7.257\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(2\) \(-18\) \(21\) \(28\) \(+\) \(q+\beta _{1}q^{2}-3q^{3}+(5+\beta _{1}+\beta _{3}+\beta _{5})q^{4}+\cdots\)
123.4.a.d \(6\) \(7.257\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(6\) \(18\) \(37\) \(14\) \(+\) \(q+(1-\beta _{1})q^{2}+3q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
123.4.d.a \(20\) \(7.257\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(4\) \(0\) \(-16\) \(0\) \(q-\beta _{2}q^{2}+\beta _{5}q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
123.4.e.a \(44\) \(7.257\) None \(0\) \(0\) \(0\) \(0\)
123.4.g.a \(40\) \(7.257\) None \(-2\) \(-120\) \(-2\) \(-14\)
123.4.g.b \(40\) \(7.257\) None \(-2\) \(120\) \(-14\) \(14\)
123.4.i.a \(160\) \(7.257\) None \(0\) \(-8\) \(0\) \(-8\)
123.4.j.a \(80\) \(7.257\) None \(-4\) \(0\) \(16\) \(0\)
123.4.n.a \(176\) \(7.257\) None \(0\) \(0\) \(0\) \(0\)
123.4.o.a \(640\) \(7.257\) None \(0\) \(-12\) \(0\) \(-32\)
123.5.b.a \(1\) \(12.715\) \(\Q\) \(\Q(\sqrt{-123}) \) \(0\) \(-9\) \(0\) \(0\) \(q-9q^{3}+2^{4}q^{4}+3^{4}q^{9}-119q^{11}+\cdots\)
123.5.b.b \(1\) \(12.715\) \(\Q\) \(\Q(\sqrt{-123}) \) \(0\) \(9\) \(0\) \(0\) \(q+9q^{3}+2^{4}q^{4}+3^{4}q^{9}+119q^{11}+\cdots\)
123.5.b.c \(52\) \(12.715\) None \(0\) \(0\) \(0\) \(0\)
123.5.c.a \(54\) \(12.715\) None \(0\) \(-10\) \(0\) \(-4\)
123.5.f.a \(108\) \(12.715\) None \(0\) \(-10\) \(0\) \(-4\)
123.5.h.a \(112\) \(12.715\) None \(0\) \(0\) \(0\) \(0\)
123.5.k.a \(216\) \(12.715\) None \(0\) \(0\) \(0\) \(-6\)
123.5.l.a \(216\) \(12.715\) None \(0\) \(0\) \(0\) \(-10\)
123.5.m.a \(432\) \(12.715\) None \(0\) \(0\) \(0\) \(-16\)
123.5.p.a \(448\) \(12.715\) None \(0\) \(0\) \(0\) \(0\)
123.6.a.a \(7\) \(19.727\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-6\) \(63\) \(-200\) \(-58\) \(+\) \(q+(-1+\beta _{1})q^{2}+9q^{3}+(13-2\beta _{1}+\cdots)q^{4}+\cdots\)
123.6.a.b \(8\) \(19.727\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(-72\) \(-72\) \(-196\) \(+\) \(q+(-1+\beta _{1})q^{2}-9q^{3}+(17+\beta _{2})q^{4}+\cdots\)
123.6.a.c \(9\) \(19.727\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(14\) \(81\) \(150\) \(236\) \(-\) \(q+(2-\beta _{1})q^{2}+9q^{3}+(19-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
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