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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
100.1.j.a \(4\) \(0.050\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(-1\) \(0\) \(q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{8}+\cdots\)
100.2.a.a \(1\) \(0.799\) \(\Q\) None None \(0\) \(2\) \(0\) \(-2\) \(-\) \(q+2q^{3}-2q^{7}+q^{9}-2q^{13}+6q^{17}+\cdots\)
100.2.c.a \(2\) \(0.799\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{7}-q^{9}-iq^{13}-3iq^{17}+\cdots\)
100.2.e.a \(2\) \(0.799\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None \(-2\) \(-2\) \(0\) \(6\) \(q+(-1+i)q^{2}+(-1-i)q^{3}-2iq^{4}+\cdots\)
100.2.e.b \(2\) \(0.799\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(1+i)q^{2}+2iq^{4}+(-2+2i)q^{8}+\cdots\)
100.2.e.c \(2\) \(0.799\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None \(2\) \(2\) \(0\) \(-6\) \(q+(1-i)q^{2}+(1+i)q^{3}-2iq^{4}+2q^{6}+\cdots\)
100.2.e.d \(8\) \(0.799\) 8.0.3317760000.5 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{4}+\beta _{6})q^{3}+\beta _{2}q^{4}+\cdots\)
100.2.g.a \(12\) \(0.799\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(2\) \(-4\) \(-2\) \(q-\beta _{4}q^{3}+(-1-\beta _{4}+\beta _{5}-\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots\)
100.2.i.a \(8\) \(0.799\) 8.0.58140625.2 None None \(0\) \(0\) \(5\) \(0\) \(q+(-\beta _{4}-\beta _{5})q^{3}+(2\beta _{1}+\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)
100.2.l.a \(8\) \(0.799\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(4\) \(0\) \(q+(1-\zeta_{20}^{2}+\zeta_{20}^{3}+\zeta_{20}^{4}-\zeta_{20}^{6}+\cdots)q^{2}+\cdots\)
100.2.l.b \(96\) \(0.799\) None None \(-10\) \(0\) \(-20\) \(0\)
100.3.b.a \(1\) \(2.725\) \(\Q\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-2q^{2}+4q^{4}-8q^{8}+9q^{9}+24q^{13}+\cdots\)
100.3.b.b \(1\) \(2.725\) \(\Q\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+2q^{2}+4q^{4}+8q^{8}+9q^{9}-24q^{13}+\cdots\)
100.3.b.c \(2\) \(2.725\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-4q^{4}-8q^{6}+2iq^{7}+\cdots\)
100.3.b.d \(4\) \(2.725\) 4.0.8405.1 None None \(-1\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
100.3.b.e \(4\) \(2.725\) 4.0.8405.1 None None \(1\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
100.3.b.f \(4\) \(2.725\) \(\Q(\zeta_{10})\) None None \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{3}+(-1+\zeta_{10}+\cdots)q^{4}+\cdots\)
100.3.d.a \(8\) \(2.725\) 8.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
100.3.d.b \(8\) \(2.725\) \(\Q(\zeta_{20})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}q^{2}+\zeta_{20}^{6}q^{3}+(1+\zeta_{20}^{4})q^{4}+\cdots\)
100.3.f.a \(2\) \(2.725\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(14\) \(q+(-1+i)q^{3}+(7+7i)q^{7}+7iq^{9}+\cdots\)
100.3.f.b \(4\) \(2.725\) \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(0\) \(q+3\beta _{1}q^{3}-4\beta _{3}q^{7}+18\beta _{2}q^{9}-15q^{11}+\cdots\)
100.3.h.a \(8\) \(2.725\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-6\) \(0\) \(q+\zeta_{20}q^{2}+4\zeta_{20}^{2}q^{4}+(-3+3\zeta_{20}^{2}+\cdots)q^{5}+\cdots\)
100.3.h.b \(104\) \(2.725\) None None \(-5\) \(0\) \(0\) \(0\)
100.3.j.a \(112\) \(2.725\) None None \(-3\) \(0\) \(-10\) \(0\)
100.3.k.a \(40\) \(2.725\) None None \(0\) \(-2\) \(6\) \(14\)
100.4.a.a \(1\) \(5.900\) \(\Q\) None None \(0\) \(-4\) \(0\) \(16\) \(-\) \(q-4q^{3}+2^{4}q^{7}-11q^{9}-60q^{11}+\cdots\)
100.4.a.b \(1\) \(5.900\) \(\Q\) None None \(0\) \(-1\) \(0\) \(-26\) \(-\) \(q-q^{3}-26q^{7}-26q^{9}+45q^{11}-44q^{13}+\cdots\)
100.4.a.c \(1\) \(5.900\) \(\Q\) None None \(0\) \(1\) \(0\) \(26\) \(+\) \(q+q^{3}+26q^{7}-26q^{9}+45q^{11}+44q^{13}+\cdots\)
100.4.a.d \(2\) \(5.900\) \(\Q(\sqrt{19}) \) None None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta q^{3}+\beta q^{7}+7^{2}q^{9}+20q^{11}-6\beta q^{13}+\cdots\)
100.4.c.a \(2\) \(5.900\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{3}+8iq^{7}+11q^{9}-60q^{11}+\cdots\)
100.4.c.b \(2\) \(5.900\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-26iq^{7}+26q^{9}+45q^{11}+\cdots\)
100.4.e.a \(2\) \(5.900\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(-4\) \(0\) \(0\) \(0\) \(q+(-2-2i)q^{2}+8iq^{4}+(2^{4}-2^{4}i)q^{8}+\cdots\)
100.4.e.b \(2\) \(5.900\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None \(-4\) \(14\) \(0\) \(-18\) \(q+(-2+2i)q^{2}+(7+7i)q^{3}-8iq^{4}+\cdots\)
100.4.e.c \(2\) \(5.900\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None \(4\) \(-14\) \(0\) \(18\) \(q+(2-2i)q^{2}+(-7-7i)q^{3}-8iq^{4}+\cdots\)
100.4.e.d \(8\) \(5.900\) 8.0.2342560000.1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(-\beta _{3}-\beta _{6})q^{3}+(-\beta _{1}-3\beta _{4}+\cdots)q^{4}+\cdots\)
100.4.e.e \(12\) \(5.900\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(6\) \(0\) \(0\) \(0\) \(q+(\beta _{3}+\beta _{5})q^{2}+\beta _{9}q^{3}+(-2\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
100.4.e.f \(24\) \(5.900\) None None \(0\) \(0\) \(0\) \(0\)
100.4.g.a \(28\) \(5.900\) None None \(0\) \(-4\) \(-25\) \(16\)
100.4.i.a \(32\) \(5.900\) None None \(0\) \(0\) \(6\) \(0\)
100.4.l.a \(8\) \(5.900\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(-4\) \(0\) \(4\) \(0\) \(q+(-2+2\zeta_{20}^{2}-2\zeta_{20}^{3}-2\zeta_{20}^{4}+\cdots)q^{2}+\cdots\)
100.4.l.b \(336\) \(5.900\) None None \(-4\) \(0\) \(-20\) \(0\)
100.5.b.a \(1\) \(10.337\) \(\Q\) \(\Q(\sqrt{-1}) \) None \(4\) \(0\) \(0\) \(0\) \(q+4q^{2}+2^{4}q^{4}+2^{6}q^{8}+3^{4}q^{9}+238q^{13}+\cdots\)
100.5.b.b \(2\) \(10.337\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}+iq^{3}-2^{4}q^{4}-8q^{6}-41iq^{7}+\cdots\)
100.5.b.c \(8\) \(10.337\) 8.0.\(\cdots\).1 None None \(-6\) \(0\) \(0\) \(0\) \(q+(-1-\beta _{1})q^{2}+\beta _{3}q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots\)
100.5.b.d \(8\) \(10.337\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-3\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+(-6+\cdots)q^{6}+\cdots\)
100.5.b.e \(8\) \(10.337\) 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(6+\beta _{6})q^{4}+(-\beta _{4}+\cdots)q^{6}+\cdots\)
100.5.b.f \(8\) \(10.337\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(3\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+(-6+\cdots)q^{6}+\cdots\)
100.5.d.a \(2\) \(10.337\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-2^{4}q^{4}-2^{5}iq^{8}-3^{4}q^{9}+\cdots\)
100.5.d.b \(16\) \(10.337\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(-6+\cdots)q^{6}+\cdots\)
100.5.d.c \(16\) \(10.337\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+\beta _{8}q^{3}+(2-\beta _{4})q^{4}+(6+\beta _{5}+\cdots)q^{6}+\cdots\)
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