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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
40.2.a.a \(1\) \(0.319\) \(\Q\) None \(0\) \(0\) \(1\) \(-4\) \(-\) \(q+q^{5}-4q^{7}-3q^{9}+4q^{11}-2q^{13}+\cdots\)
40.2.c.a \(2\) \(0.319\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{3}+(-1-i)q^{5}-iq^{7}-q^{9}+\cdots\)
40.2.d.a \(4\) \(0.319\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(-4\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}+\cdots)q^{3}+\cdots\)
40.2.f.a \(4\) \(0.319\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1+\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
40.2.k.a \(8\) \(0.319\) \(\Q(\zeta_{20})\) None \(-2\) \(-4\) \(0\) \(0\) \(q-\zeta_{20}^{7}q^{2}+(-1+\zeta_{20}^{3}+\zeta_{20}^{5}+\cdots)q^{3}+\cdots\)
40.3.e.a \(1\) \(1.090\) \(\Q\) \(\Q(\sqrt{-10}) \) \(-2\) \(0\) \(5\) \(6\) \(q-2q^{2}+4q^{4}+5q^{5}+6q^{7}-8q^{8}+\cdots\)
40.3.e.b \(1\) \(1.090\) \(\Q\) \(\Q(\sqrt{-10}) \) \(2\) \(0\) \(-5\) \(-6\) \(q+2q^{2}+4q^{4}-5q^{5}-6q^{7}+8q^{8}+\cdots\)
40.3.e.c \(8\) \(1.090\) 8.0.\(\cdots\).2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}-\beta _{7}q^{3}+(-2-\beta _{3}-\beta _{6}+\cdots)q^{4}+\cdots\)
40.3.g.a \(8\) \(1.090\) 8.0.\(\cdots\).1 None \(2\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}-\beta _{6}q^{3}+(-1+\beta _{1}+\beta _{4}+\cdots)q^{4}+\cdots\)
40.3.i.a \(20\) \(1.090\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(0\) \(0\) \(-4\) \(q+\beta _{4}q^{2}+\beta _{16}q^{3}+\beta _{3}q^{4}+\beta _{8}q^{5}+\cdots\)
40.3.l.a \(2\) \(1.090\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(10\) \(-6\) \(q+(1-i)q^{3}+5q^{5}+(-3-3i)q^{7}+\cdots\)
40.3.l.b \(4\) \(1.090\) \(\Q(i, \sqrt{41})\) None \(0\) \(-2\) \(-6\) \(14\) \(q+(-1+\beta _{2})q^{3}+(-1-2\beta _{1}+\beta _{3})q^{5}+\cdots\)
40.4.a.a \(1\) \(2.360\) \(\Q\) None \(0\) \(-6\) \(-5\) \(-34\) \(-\) \(q-6q^{3}-5q^{5}-34q^{7}+9q^{9}+2^{4}q^{11}+\cdots\)
40.4.a.b \(1\) \(2.360\) \(\Q\) None \(0\) \(4\) \(5\) \(16\) \(+\) \(q+4q^{3}+5q^{5}+2^{4}q^{7}-11q^{9}+6^{2}q^{11}+\cdots\)
40.4.a.c \(1\) \(2.360\) \(\Q\) None \(0\) \(10\) \(-5\) \(-18\) \(+\) \(q+10q^{3}-5q^{5}-18q^{7}+73q^{9}-2^{4}q^{11}+\cdots\)
40.4.c.a \(4\) \(2.360\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{3}+(-1-\beta _{2}-\beta _{3})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
40.4.d.a \(12\) \(2.360\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(0\) \(0\) \(28\) \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1-\beta _{4})q^{4}-\beta _{8}q^{5}+\cdots\)
40.4.f.a \(16\) \(2.360\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{13}q^{3}+\beta _{2}q^{4}+\beta _{12}q^{5}+\cdots\)
40.4.k.a \(32\) \(2.360\) None \(-2\) \(-4\) \(0\) \(0\)
40.5.e.a \(1\) \(4.135\) \(\Q\) \(\Q(\sqrt{-10}) \) \(-4\) \(0\) \(-25\) \(62\) \(q-4q^{2}+2^{4}q^{4}-5^{2}q^{5}+62q^{7}-2^{6}q^{8}+\cdots\)
40.5.e.b \(1\) \(4.135\) \(\Q\) \(\Q(\sqrt{-10}) \) \(4\) \(0\) \(25\) \(-62\) \(q+4q^{2}+2^{4}q^{4}+5^{2}q^{5}-62q^{7}+2^{6}q^{8}+\cdots\)
40.5.e.c \(20\) \(4.135\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{11}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
40.5.g.a \(16\) \(4.135\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-6\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}-\beta _{5}q^{5}+\cdots\)
40.5.i.a \(44\) \(4.135\) None \(-2\) \(0\) \(0\) \(-4\)
40.5.l.a \(2\) \(4.135\) \(\Q(\sqrt{-1}) \) None \(0\) \(20\) \(40\) \(-84\) \(q+(10-10i)q^{3}+(20+15i)q^{5}+(-42+\cdots)q^{7}+\cdots\)
40.5.l.b \(4\) \(4.135\) \(\Q(i, \sqrt{29})\) None \(0\) \(-12\) \(-12\) \(44\) \(q+(-3+3\beta _{1})q^{3}+(-3-6\beta _{1}-\beta _{3})q^{5}+\cdots\)
40.5.l.c \(6\) \(4.135\) 6.0.313431616.3 None \(0\) \(-8\) \(-4\) \(-40\) \(q+(-1-\beta _{1}-\beta _{3})q^{3}+(-1+7\beta _{1}+\cdots)q^{5}+\cdots\)
40.6.a.a \(1\) \(6.415\) \(\Q\) None \(0\) \(-18\) \(-25\) \(242\) \(-\) \(q-18q^{3}-5^{2}q^{5}+242q^{7}+3^{4}q^{9}+\cdots\)
40.6.a.b \(1\) \(6.415\) \(\Q\) None \(0\) \(-8\) \(25\) \(-108\) \(+\) \(q-8q^{3}+5^{2}q^{5}-108q^{7}-179q^{9}+\cdots\)
40.6.a.c \(1\) \(6.415\) \(\Q\) None \(0\) \(-2\) \(-25\) \(-62\) \(+\) \(q-2q^{3}-5^{2}q^{5}-62q^{7}-239q^{9}+\cdots\)
40.6.a.d \(2\) \(6.415\) \(\Q(\sqrt{129}) \) None \(0\) \(-12\) \(50\) \(52\) \(-\) \(q+(-6-\beta )q^{3}+5^{2}q^{5}+(26-3\beta )q^{7}+\cdots\)
40.6.c.a \(8\) \(6.415\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(8\) \(0\) \(q-\beta _{1}q^{3}+(1-\beta _{2})q^{5}+(\beta _{2}+\beta _{6})q^{7}+\cdots\)
40.6.d.a \(20\) \(6.415\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(2\) \(0\) \(0\) \(-196\) \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(-2+\beta _{3})q^{4}+\beta _{5}q^{5}+\cdots\)
40.6.f.a \(28\) \(6.415\) None \(0\) \(0\) \(0\) \(0\)
40.6.k.a \(56\) \(6.415\) None \(-2\) \(-4\) \(0\) \(0\)
40.7.e.a \(1\) \(9.202\) \(\Q\) \(\Q(\sqrt{-10}) \) \(-8\) \(0\) \(125\) \(-666\) \(q-8q^{2}+2^{6}q^{4}+5^{3}q^{5}-666q^{7}+\cdots\)
40.7.e.b \(1\) \(9.202\) \(\Q\) \(\Q(\sqrt{-10}) \) \(8\) \(0\) \(-125\) \(666\) \(q+8q^{2}+2^{6}q^{4}-5^{3}q^{5}+666q^{7}+\cdots\)
40.7.e.c \(32\) \(9.202\) None \(0\) \(0\) \(0\) \(0\)
40.7.g.a \(24\) \(9.202\) None \(10\) \(0\) \(0\) \(0\)
40.7.i.a \(68\) \(9.202\) None \(-2\) \(0\) \(0\) \(-4\)
40.7.l.a \(8\) \(9.202\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-14\) \(-50\) \(-46\) \(q+(-2-2\beta _{1}+\beta _{4})q^{3}+(-6+11\beta _{1}+\cdots)q^{5}+\cdots\)
40.7.l.b \(10\) \(9.202\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(14\) \(94\) \(454\) \(q+(1+\beta _{1}-\beta _{3})q^{3}+(9-2^{4}\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
40.8.a.a \(1\) \(12.495\) \(\Q\) None \(0\) \(-36\) \(125\) \(776\) \(-\) \(q-6^{2}q^{3}+5^{3}q^{5}+776q^{7}-891q^{9}+\cdots\)
40.8.a.b \(2\) \(12.495\) \(\Q(\sqrt{46}) \) None \(0\) \(4\) \(-250\) \(844\) \(+\) \(q+(2+\beta )q^{3}-5^{3}q^{5}+(422+17\beta )q^{7}+\cdots\)
40.8.a.c \(2\) \(12.495\) \(\Q(\sqrt{6}) \) None \(0\) \(36\) \(-250\) \(-404\) \(-\) \(q+(18+\beta )q^{3}-5^{3}q^{5}+(-202-63\beta )q^{7}+\cdots\)
40.8.a.d \(2\) \(12.495\) \(\Q(\sqrt{601}) \) None \(0\) \(76\) \(250\) \(796\) \(+\) \(q+(38-\beta )q^{3}+5^{3}q^{5}+(398-7\beta )q^{7}+\cdots\)
40.8.c.a \(2\) \(12.495\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(550\) \(0\) \(q+17iq^{3}+(275+5^{2}i)q^{5}-53iq^{7}+\cdots\)
40.8.c.b \(8\) \(12.495\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(-744\) \(0\) \(q+\beta _{1}q^{3}+(-93-\beta _{1}+\beta _{3})q^{5}+(3\beta _{1}+\cdots)q^{7}+\cdots\)
40.8.d.a \(28\) \(12.495\) None \(-14\) \(0\) \(0\) \(1372\)
40.8.f.a \(40\) \(12.495\) None \(0\) \(0\) \(0\) \(0\)
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