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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1003.1.b.a \(1\) \(0.501\) \(\Q\) \(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-1003}) \) \(\Q(\sqrt{17}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{4}+q^{9}+q^{16}-q^{17}-2q^{19}+\cdots\)
1003.1.b.b \(2\) \(0.501\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-59}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{5}+\cdots\)
1003.1.f.a \(2\) \(0.501\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-59}) \) None \(0\) \(-2\) \(-2\) \(-2\) \(q+(-1+i)q^{3}-q^{4}+(-1+i)q^{5}+\cdots\)
1003.1.f.b \(4\) \(0.501\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-59}) \) None \(0\) \(2\) \(2\) \(2\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-q^{4}+(-\zeta_{12}^{4}+\cdots)q^{5}+\cdots\)
1003.1.h.a \(4\) \(0.501\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-59}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots\)
1003.1.h.b \(8\) \(0.501\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-59}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}-\zeta_{24}^{2})q^{3}-\zeta_{24}^{6}q^{4}+(\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
1003.2.a.a \(1\) \(8.009\) \(\Q\) None None \(-1\) \(3\) \(1\) \(1\) \(-\) \(q-q^{2}+3q^{3}-q^{4}+q^{5}-3q^{6}+q^{7}+\cdots\)
1003.2.a.b \(1\) \(8.009\) \(\Q\) None None \(0\) \(2\) \(-2\) \(2\) \(+\) \(q+2q^{3}-2q^{4}-2q^{5}+2q^{7}+q^{9}+\cdots\)
1003.2.a.c \(1\) \(8.009\) \(\Q\) None None \(1\) \(1\) \(1\) \(3\) \(-\) \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+3q^{7}+\cdots\)
1003.2.a.d \(1\) \(8.009\) \(\Q\) None None \(2\) \(0\) \(-2\) \(-2\) \(+\) \(q+2q^{2}+2q^{4}-2q^{5}-2q^{7}-3q^{9}+\cdots\)
1003.2.a.e \(3\) \(8.009\) 3.3.229.1 None None \(-3\) \(2\) \(-4\) \(-2\) \(+\) \(q-q^{2}+(1+\beta _{2})q^{3}-q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1003.2.a.f \(4\) \(8.009\) 4.4.2225.1 None None \(-3\) \(-2\) \(1\) \(8\) \(+\) \(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1003.2.a.g \(10\) \(8.009\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(-1\) \(-7\) \(-12\) \(-9\) \(+\) \(q-\beta _{8}q^{2}+(-1+\beta _{1})q^{3}+(2-\beta _{5})q^{4}+\cdots\)
1003.2.a.h \(16\) \(8.009\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-6\) \(-7\) \(-21\) \(-11\) \(+\) \(q-\beta _{1}q^{2}-\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1003.2.a.i \(18\) \(8.009\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(5\) \(1\) \(21\) \(-1\) \(-\) \(q+\beta _{1}q^{2}+\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
1003.2.a.j \(22\) \(8.009\) None None \(5\) \(7\) \(19\) \(3\) \(-\)
1003.2.d.a \(2\) \(8.009\) \(\Q(\sqrt{-2}) \) None None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}-q^{4}-3q^{8}+3q^{9}-\beta q^{11}+\cdots\)
1003.2.d.b \(4\) \(8.009\) \(\Q(i, \sqrt{5})\) None None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-2\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
1003.2.d.c \(38\) \(8.009\) None None \(2\) \(0\) \(0\) \(0\)
1003.2.d.d \(44\) \(8.009\) None None \(-8\) \(0\) \(0\) \(0\)
1003.4.a.a \(3\) \(59.179\) 3.3.75845.1 None None \(-3\) \(-5\) \(17\) \(-2\) \(-\) \(q-q^{2}+(-2-\beta _{2})q^{3}-7q^{4}+(6+\beta _{2})q^{5}+\cdots\)
1003.4.a.b \(52\) \(59.179\) None None \(-8\) \(-19\) \(-95\) \(-50\) \(-\)
1003.4.a.c \(57\) \(59.179\) None None \(-11\) \(-18\) \(-132\) \(-52\) \(-\)
1003.4.a.d \(59\) \(59.179\) None None \(13\) \(12\) \(102\) \(-24\) \(+\)
1003.4.a.e \(61\) \(59.179\) None None \(13\) \(30\) \(128\) \(116\) \(+\)
1003.6.a.a \(94\) \(160.865\) None None \(-23\) \(-99\) \(-759\) \(-929\) \(+\)
1003.6.a.b \(96\) \(160.865\) None None \(-23\) \(-45\) \(-391\) \(51\) \(+\)
1003.6.a.c \(98\) \(160.865\) None None \(25\) \(45\) \(541\) \(247\) \(-\)
1003.6.a.d \(100\) \(160.865\) None None \(25\) \(63\) \(509\) \(247\) \(-\)


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