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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
90.2.a.a \(1\) \(0.719\) \(\Q\) None \(-1\) \(0\) \(1\) \(2\) \(-\) \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
90.2.a.b \(1\) \(0.719\) \(\Q\) None \(1\) \(0\) \(-1\) \(2\) \(-\) \(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
90.2.a.c \(1\) \(0.719\) \(\Q\) None \(1\) \(0\) \(1\) \(-4\) \(-\) \(q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots\)
90.2.c.a \(2\) \(0.719\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{2}-q^{4}+(2+i)q^{5}+2iq^{7}-iq^{8}+\cdots\)
90.2.e.a \(2\) \(0.719\) \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(1\) \(1\) \(q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
90.2.e.b \(2\) \(0.719\) \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(-1\) \(4\) \(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
90.2.e.c \(4\) \(0.719\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(2\) \(2\) \(-1\) \(q+\beta _{2}q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
90.2.f.a \(4\) \(0.719\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(8\) \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots\)
90.2.i.a \(4\) \(0.719\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) \(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
90.2.i.b \(8\) \(0.719\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{24}^{2}q^{2}+(\zeta_{24}^{2}+\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
90.2.l.a \(8\) \(0.719\) \(\Q(\zeta_{24})\) None \(0\) \(4\) \(12\) \(-8\) \(q+\zeta_{24}^{7}q^{2}+(1+\zeta_{24}^{2}-\zeta_{24}^{4}+\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
90.2.l.b \(16\) \(0.719\) 16.0.\(\cdots\).9 None \(0\) \(0\) \(-12\) \(8\) \(q-\beta _{11}q^{2}+(-\beta _{3}-\beta _{4}-\beta _{5}+\beta _{8}+\cdots)q^{3}+\cdots\)
90.3.b.a \(4\) \(2.452\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+2q^{4}+5\zeta_{8}q^{5}-4\zeta_{8}^{2}q^{7}+\cdots\)
90.3.g.a \(2\) \(2.452\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(-6\) \(16\) \(q+(-1-i)q^{2}+2iq^{4}+(-3+4i)q^{5}+\cdots\)
90.3.g.b \(2\) \(2.452\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(4\) \(q+(1+i)q^{2}+2iq^{4}+5iq^{5}+(2+2i)q^{7}+\cdots\)
90.3.g.c \(2\) \(2.452\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(6\) \(16\) \(q+(1+i)q^{2}+2iq^{4}+(3-4i)q^{5}+(8+\cdots)q^{7}+\cdots\)
90.3.g.d \(4\) \(2.452\) \(\Q(i, \sqrt{6})\) None \(-4\) \(0\) \(0\) \(-16\) \(q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
90.3.h.a \(16\) \(2.452\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-4\) \(0\) \(-4\) \(q-\beta _{5}q^{2}+(-1-\beta _{2}-\beta _{4}-\beta _{10}+\beta _{12}+\cdots)q^{3}+\cdots\)
90.3.j.a \(8\) \(2.452\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-12\) \(0\) \(q-\zeta_{24}^{4}q^{2}+3\zeta_{24}q^{3}+(-2+2\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
90.3.j.b \(16\) \(2.452\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(30\) \(0\) \(q-\beta _{7}q^{2}+\beta _{13}q^{3}+2\beta _{6}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
90.3.k.a \(24\) \(2.452\) None \(-12\) \(0\) \(0\) \(-6\)
90.3.k.b \(24\) \(2.452\) None \(12\) \(4\) \(0\) \(6\)
90.4.a.a \(1\) \(5.310\) \(\Q\) None \(-2\) \(0\) \(-5\) \(-4\) \(-\) \(q-2q^{2}+4q^{4}-5q^{5}-4q^{7}-8q^{8}+\cdots\)
90.4.a.b \(1\) \(5.310\) \(\Q\) None \(-2\) \(0\) \(-5\) \(14\) \(+\) \(q-2q^{2}+4q^{4}-5q^{5}+14q^{7}-8q^{8}+\cdots\)
90.4.a.c \(1\) \(5.310\) \(\Q\) None \(-2\) \(0\) \(5\) \(-4\) \(+\) \(q-2q^{2}+4q^{4}+5q^{5}-4q^{7}-8q^{8}+\cdots\)
90.4.a.d \(1\) \(5.310\) \(\Q\) None \(2\) \(0\) \(-5\) \(32\) \(+\) \(q+2q^{2}+4q^{4}-5q^{5}+2^{5}q^{7}+8q^{8}+\cdots\)
90.4.a.e \(1\) \(5.310\) \(\Q\) None \(2\) \(0\) \(5\) \(14\) \(+\) \(q+2q^{2}+4q^{4}+5q^{5}+14q^{7}+8q^{8}+\cdots\)
90.4.c.a \(2\) \(5.310\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+2iq^{2}-4q^{4}+(-2+11i)q^{5}+2iq^{7}+\cdots\)
90.4.c.b \(2\) \(5.310\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(10\) \(0\) \(q+iq^{2}-4q^{4}+(5-5i)q^{5}-13iq^{7}+\cdots\)
90.4.c.c \(4\) \(5.310\) \(\Q(i, \sqrt{31})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-4q^{4}-\beta _{1}q^{5}-\beta _{3}q^{7}+4\beta _{2}q^{8}+\cdots\)
90.4.e.a \(2\) \(5.310\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-9\) \(5\) \(16\) \(q+(-2+2\zeta_{6})q^{2}+(-3-3\zeta_{6})q^{3}+\cdots\)
90.4.e.b \(4\) \(5.310\) \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(-4\) \(12\) \(10\) \(-16\) \(q+(-2+2\beta _{1})q^{2}+(4-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
90.4.e.c \(4\) \(5.310\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(4\) \(6\) \(10\) \(2\) \(q+2\beta _{1}q^{2}+(3-3\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)
90.4.e.d \(6\) \(5.310\) 6.0.41783472.1 None \(6\) \(-9\) \(-15\) \(-3\) \(q+(2+2\beta _{1})q^{2}+(-2-\beta _{4})q^{3}+4\beta _{1}q^{4}+\cdots\)
90.4.e.e \(8\) \(5.310\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(2\) \(-20\) \(-23\) \(q+(-2-2\beta _{3})q^{2}-\beta _{1}q^{3}+4\beta _{3}q^{4}+\cdots\)
90.4.f.a \(4\) \(5.310\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-16\) \(q+2\zeta_{8}q^{2}+4\zeta_{8}^{2}q^{4}+(5\zeta_{8}+10\zeta_{8}^{3})q^{5}+\cdots\)
90.4.f.b \(8\) \(5.310\) 8.0.\(\cdots\).8 None \(0\) \(0\) \(0\) \(-8\) \(q+(-\beta _{2}-\beta _{3})q^{2}-4\beta _{1}q^{4}+(3\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
90.4.i.a \(36\) \(5.310\) None \(0\) \(0\) \(-8\) \(0\)
90.4.l.a \(72\) \(5.310\) None \(0\) \(-8\) \(0\) \(0\)
90.5.b.a \(8\) \(9.303\) 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+8q^{4}+(2\beta _{2}-\beta _{3}+\beta _{4})q^{5}+\cdots\)
90.5.d.a \(4\) \(9.303\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(32\) \(q-2\beta _{1}q^{2}-8q^{4}+\beta _{2}q^{5}+(8+3\beta _{3})q^{7}+\cdots\)
90.5.d.b \(4\) \(9.303\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(128\) \(q-2\beta _{1}q^{2}-8q^{4}+\beta _{2}q^{5}+(2^{5}-3\beta _{3})q^{7}+\cdots\)
90.5.g.a \(2\) \(9.303\) \(\Q(\sqrt{-1}) \) None \(-4\) \(0\) \(30\) \(-38\) \(q+(-2-2i)q^{2}+8iq^{4}+(15+20i)q^{5}+\cdots\)
90.5.g.b \(2\) \(9.303\) \(\Q(\sqrt{-1}) \) None \(4\) \(0\) \(30\) \(58\) \(q+(2+2i)q^{2}+8iq^{4}+(15-20i)q^{5}+\cdots\)
90.5.g.c \(4\) \(9.303\) \(\Q(i, \sqrt{6})\) None \(-8\) \(0\) \(-36\) \(68\) \(q+(-2+2\beta _{2})q^{2}-8\beta _{2}q^{4}+(-9-11\beta _{1}+\cdots)q^{5}+\cdots\)
90.5.g.d \(4\) \(9.303\) \(\Q(i, \sqrt{26})\) None \(-8\) \(0\) \(-24\) \(-100\) \(q+(-2-2\beta _{2})q^{2}+8\beta _{2}q^{4}+(-6-2\beta _{1}+\cdots)q^{5}+\cdots\)
90.5.g.e \(4\) \(9.303\) \(\Q(i, \sqrt{6})\) None \(8\) \(0\) \(-84\) \(-28\) \(q+(2-2\beta _{2})q^{2}-8\beta _{2}q^{4}+(-21+\beta _{1}+\cdots)q^{5}+\cdots\)
90.5.g.f \(4\) \(9.303\) \(\Q(i, \sqrt{26})\) None \(8\) \(0\) \(24\) \(-100\) \(q+(2+2\beta _{2})q^{2}+8\beta _{2}q^{4}+(6-2\beta _{1}+\cdots)q^{5}+\cdots\)
90.5.h.a \(32\) \(9.303\) None \(0\) \(8\) \(0\) \(52\)
90.5.j.a \(48\) \(9.303\) None \(0\) \(0\) \(-18\) \(0\)
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