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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
195.1.e.a \(4\) \(0.097\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots\)
195.2.a.a \(1\) \(1.557\) \(\Q\) None None \(-1\) \(1\) \(1\) \(0\) \(-\) \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots\)
195.2.a.b \(1\) \(1.557\) \(\Q\) None None \(2\) \(-1\) \(1\) \(3\) \(-\) \(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+3q^{7}+\cdots\)
195.2.a.c \(1\) \(1.557\) \(\Q\) None None \(2\) \(1\) \(-1\) \(-1\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-q^{7}+\cdots\)
195.2.a.d \(1\) \(1.557\) \(\Q\) None None \(2\) \(1\) \(1\) \(-3\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-3q^{7}+\cdots\)
195.2.a.e \(3\) \(1.557\) 3.3.316.1 None None \(0\) \(-3\) \(-3\) \(1\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(3+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
195.2.b.a \(2\) \(1.557\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}+2q^{4}+iq^{5}+3iq^{7}+q^{9}+\cdots\)
195.2.b.b \(2\) \(1.557\) \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+q^{3}+q^{4}+iq^{5}+iq^{6}-2iq^{7}+\cdots\)
195.2.b.c \(4\) \(1.557\) \(\Q(i, \sqrt{17})\) None None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+q^{3}+(-3+\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots\)
195.2.c.a \(2\) \(1.557\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{3}+2q^{4}+(-1+2i)q^{5}+iq^{7}+\cdots\)
195.2.c.b \(10\) \(1.557\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
195.2.h.a \(2\) \(1.557\) \(\Q(\sqrt{-1}) \) None None \(-4\) \(0\) \(-4\) \(6\) \(q-2q^{2}+iq^{3}+2q^{4}+(-2-i)q^{5}+\cdots\)
195.2.h.b \(2\) \(1.557\) \(\Q(\sqrt{-1}) \) None None \(4\) \(0\) \(4\) \(-6\) \(q+2q^{2}+iq^{3}+2q^{4}+(2+i)q^{5}+2iq^{6}+\cdots\)
195.2.h.c \(12\) \(1.557\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{10}q^{2}+\beta _{1}q^{3}+(1+\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
195.2.i.a \(2\) \(1.557\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(-1\) \(-2\) \(-5\) \(q+(-2+2\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
195.2.i.b \(2\) \(1.557\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(1\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{4}-q^{5}+\zeta_{6}q^{7}+\cdots\)
195.2.i.c \(4\) \(1.557\) \(\Q(\zeta_{12})\) None None \(2\) \(-2\) \(4\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}-\zeta_{12}q^{3}+(-2+\cdots)q^{4}+\cdots\)
195.2.i.d \(6\) \(1.557\) 6.0.1714608.1 None None \(0\) \(3\) \(6\) \(-3\) \(q+(-\beta _{3}+\beta _{5})q^{2}+(1+\beta _{4})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
195.2.i.e \(6\) \(1.557\) 6.0.591408.1 None None \(0\) \(3\) \(-6\) \(5\) \(q-\beta _{5}q^{2}+(1-\beta _{4})q^{3}+(\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
195.2.k.a \(28\) \(1.557\) None None \(0\) \(0\) \(8\) \(0\)
195.2.m.a \(48\) \(1.557\) None None \(0\) \(-4\) \(0\) \(-8\)
195.2.n.a \(48\) \(1.557\) None None \(0\) \(0\) \(0\) \(0\)
195.2.o.a \(40\) \(1.557\) None None \(0\) \(0\) \(0\) \(-16\)
195.2.s.a \(16\) \(1.557\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(2\beta _{2}+\beta _{12})q^{4}+\cdots\)
195.2.s.b \(32\) \(1.557\) None None \(0\) \(-4\) \(0\) \(0\)
195.2.t.a \(28\) \(1.557\) None None \(-4\) \(0\) \(-4\) \(0\)
195.2.v.a \(32\) \(1.557\) None None \(0\) \(0\) \(0\) \(0\)
195.2.ba.a \(24\) \(1.557\) None None \(0\) \(0\) \(4\) \(0\)
195.2.bb.a \(4\) \(1.557\) \(\Q(\zeta_{12})\) None None \(-6\) \(-2\) \(0\) \(-12\) \(q+(-1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
195.2.bb.b \(8\) \(1.557\) 8.0.191102976.5 None None \(0\) \(4\) \(0\) \(12\) \(q+(2\beta _{1}+\beta _{3}-\beta _{5}-\beta _{7})q^{2}+(1-\beta _{4}+\cdots)q^{3}+\cdots\)
195.2.bb.c \(8\) \(1.557\) 8.0.56070144.2 None None \(6\) \(-4\) \(0\) \(6\) \(q+(1-\beta _{1}-\beta _{2}-\beta _{4}+\beta _{5}+\beta _{6})q^{2}+\cdots\)
195.2.bd.a \(56\) \(1.557\) None None \(4\) \(0\) \(4\) \(0\)
195.2.bf.a \(96\) \(1.557\) None None \(0\) \(-2\) \(0\) \(-12\)
195.2.bg.a \(72\) \(1.557\) None None \(0\) \(0\) \(0\) \(12\)
195.2.bh.a \(96\) \(1.557\) None None \(0\) \(0\) \(0\) \(0\)
195.2.bl.a \(96\) \(1.557\) None None \(0\) \(-2\) \(0\) \(-4\)
195.2.bm.a \(56\) \(1.557\) None None \(0\) \(0\) \(-8\) \(0\)
195.3.d.a \(32\) \(5.313\) None None \(0\) \(8\) \(0\) \(0\)
195.3.e.a \(1\) \(5.313\) \(\Q\) \(\Q(\sqrt{-195}) \) None \(0\) \(-3\) \(-5\) \(1\) \(q-3q^{3}+4q^{4}-5q^{5}+q^{7}+9q^{9}+\cdots\)
195.3.e.b \(1\) \(5.313\) \(\Q\) \(\Q(\sqrt{-195}) \) None \(0\) \(-3\) \(5\) \(-1\) \(q-3q^{3}+4q^{4}+5q^{5}-q^{7}+9q^{9}+\cdots\)
195.3.e.c \(1\) \(5.313\) \(\Q\) \(\Q(\sqrt{-195}) \) None \(0\) \(3\) \(-5\) \(-1\) \(q+3q^{3}+4q^{4}-5q^{5}-q^{7}+9q^{9}+\cdots\)
195.3.e.d \(1\) \(5.313\) \(\Q\) \(\Q(\sqrt{-195}) \) None \(0\) \(3\) \(5\) \(1\) \(q+3q^{3}+4q^{4}+5q^{5}+q^{7}+9q^{9}+\cdots\)
195.3.e.e \(8\) \(5.313\) 8.0.\(\cdots\).2 \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{2}-3\beta _{1}q^{3}+(-4+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
195.3.e.f \(40\) \(5.313\) None None \(0\) \(0\) \(0\) \(0\)
195.3.f.a \(48\) \(5.313\) None None \(0\) \(0\) \(0\) \(0\)
195.3.g.a \(4\) \(5.313\) \(\Q(\sqrt{-2}, \sqrt{5})\) None None \(0\) \(-12\) \(0\) \(0\) \(q-\beta _{2}q^{2}-3q^{3}+q^{4}-\beta _{2}q^{5}+3\beta _{2}q^{6}+\cdots\)
195.3.g.b \(32\) \(5.313\) None None \(0\) \(12\) \(0\) \(0\)
195.3.j.a \(2\) \(5.313\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-6\) \(0\) \(0\) \(q+iq^{2}-3q^{3}+3q^{4}+5iq^{5}-3iq^{6}+\cdots\)
195.3.j.b \(2\) \(5.313\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-3iq^{3}+3q^{4}-5iq^{5}-3q^{6}+\cdots\)
195.3.j.c \(4\) \(5.313\) \(\Q(\zeta_{8})\) None None \(0\) \(8\) \(0\) \(0\) \(q+(2\zeta_{8}+2\zeta_{8}^{3})q^{2}+(2+2\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots\)
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