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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1122.2.a.a \(1\) \(8.959\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) \(-\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
1122.2.a.b \(1\) \(8.959\) \(\Q\) None \(-1\) \(-1\) \(2\) \(-2\) \(+\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots\)
1122.2.a.c \(1\) \(8.959\) \(\Q\) None \(-1\) \(-1\) \(2\) \(4\) \(-\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
1122.2.a.d \(1\) \(8.959\) \(\Q\) None \(-1\) \(1\) \(-2\) \(-2\) \(+\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
1122.2.a.e \(1\) \(8.959\) \(\Q\) None \(1\) \(-1\) \(-2\) \(0\) \(+\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
1122.2.a.f \(1\) \(8.959\) \(\Q\) None \(1\) \(-1\) \(-2\) \(0\) \(+\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
1122.2.a.g \(1\) \(8.959\) \(\Q\) None \(1\) \(-1\) \(2\) \(-2\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-2q^{7}+\cdots\)
1122.2.a.h \(1\) \(8.959\) \(\Q\) None \(1\) \(-1\) \(2\) \(4\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots\)
1122.2.a.i \(1\) \(8.959\) \(\Q\) None \(1\) \(1\) \(-2\) \(-4\) \(+\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots\)
1122.2.a.j \(1\) \(8.959\) \(\Q\) None \(1\) \(1\) \(0\) \(2\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
1122.2.a.k \(1\) \(8.959\) \(\Q\) None \(1\) \(1\) \(0\) \(2\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
1122.2.a.l \(1\) \(8.959\) \(\Q\) None \(1\) \(1\) \(2\) \(-2\) \(-\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots\)
1122.2.a.m \(1\) \(8.959\) \(\Q\) None \(1\) \(1\) \(2\) \(4\) \(-\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
1122.2.a.n \(1\) \(8.959\) \(\Q\) None \(1\) \(1\) \(4\) \(-2\) \(-\) \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}-2q^{7}+\cdots\)
1122.2.a.o \(2\) \(8.959\) \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(-2\) \(6\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
1122.2.a.p \(2\) \(8.959\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(-4\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-2+\beta )q^{7}+\cdots\)
1122.2.a.q \(2\) \(8.959\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(0\) \(-4\) \(+\) \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots\)
1122.2.a.r \(2\) \(8.959\) \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(2\) \(-2\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
1122.2.a.s \(3\) \(8.959\) 3.3.148.1 None \(3\) \(-3\) \(0\) \(2\) \(-\) \(q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots\)
1122.2.b.a \(16\) \(8.959\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-16\) \(1\) \(0\) \(0\) \(q-q^{2}-\beta _{9}q^{3}+q^{4}+\beta _{13}q^{5}+\beta _{9}q^{6}+\cdots\)
1122.2.b.b \(16\) \(8.959\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-16\) \(1\) \(0\) \(0\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)
1122.2.b.c \(16\) \(8.959\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(16\) \(1\) \(0\) \(0\) \(q+q^{2}-\beta _{9}q^{3}+q^{4}+\beta _{13}q^{5}-\beta _{9}q^{6}+\cdots\)
1122.2.b.d \(16\) \(8.959\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(1\) \(0\) \(0\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)
1122.2.c.a \(2\) \(8.959\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}-iq^{3}+q^{4}+4iq^{5}+iq^{6}+\cdots\)
1122.2.c.b \(2\) \(8.959\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+iq^{3}+q^{4}-iq^{6}-q^{8}-q^{9}+\cdots\)
1122.2.c.c \(2\) \(8.959\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}-iq^{3}+q^{4}+2iq^{5}-iq^{6}+\cdots\)
1122.2.c.d \(2\) \(8.959\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}-iq^{3}+q^{4}+2iq^{5}-iq^{6}+\cdots\)
1122.2.c.e \(4\) \(8.959\) \(\Q(i, \sqrt{13})\) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1122.2.c.f \(4\) \(8.959\) \(\Q(\zeta_{8})\) None \(4\) \(0\) \(0\) \(0\) \(q+q^{2}+\zeta_{8}q^{3}+q^{4}+(2\zeta_{8}-\zeta_{8}^{2})q^{5}+\cdots\)
1122.2.c.g \(6\) \(8.959\) 6.0.419904.1 None \(6\) \(0\) \(0\) \(0\) \(q+q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{1}q^{5}+\beta _{2}q^{6}+\cdots\)
1122.2.c.h \(10\) \(8.959\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-10\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-\beta _{1}+\beta _{7})q^{5}+\cdots\)
1122.2.h.a \(2\) \(8.959\) \(\Q(\sqrt{-2}) \) None \(-2\) \(-2\) \(0\) \(4\) \(q-q^{2}+(-1-\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots\)
1122.2.h.b \(2\) \(8.959\) \(\Q(\sqrt{-2}) \) None \(-2\) \(2\) \(0\) \(-4\) \(q-q^{2}+(1-\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
1122.2.h.c \(2\) \(8.959\) \(\Q(\sqrt{-2}) \) None \(2\) \(-2\) \(0\) \(-4\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
1122.2.h.d \(2\) \(8.959\) \(\Q(\sqrt{-2}) \) None \(2\) \(2\) \(0\) \(4\) \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots\)
1122.2.h.e \(4\) \(8.959\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{2}q^{6}-2\beta _{2}q^{7}+\cdots\)
1122.2.h.f \(4\) \(8.959\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(4\) \(0\) \(0\) \(0\) \(q+q^{2}-\beta _{2}q^{3}+q^{4}-\beta _{2}q^{6}-2\beta _{2}q^{7}+\cdots\)
1122.2.h.g \(28\) \(8.959\) None \(-28\) \(0\) \(0\) \(0\)
1122.2.h.h \(28\) \(8.959\) None \(28\) \(0\) \(0\) \(0\)
1122.2.l.a \(4\) \(8.959\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(0\) \(q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+(-1+2\zeta_{8}+\cdots)q^{5}+\cdots\)
1122.2.l.b \(4\) \(8.959\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(0\) \(q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+(-1+2\zeta_{8}+\cdots)q^{5}+\cdots\)
1122.2.l.c \(4\) \(8.959\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+(1+2\zeta_{8}+\cdots)q^{5}+\cdots\)
1122.2.l.d \(4\) \(8.959\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(8\) \(0\) \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+(2+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
1122.2.l.e \(12\) \(8.959\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(-12\) \(0\) \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
1122.2.l.f \(16\) \(8.959\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(4\) \(0\) \(q-\beta _{10}q^{2}-\beta _{6}q^{3}-q^{4}+\beta _{15}q^{5}+\cdots\)
1122.2.l.g \(20\) \(8.959\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(-4\) \(0\) \(q-\beta _{8}q^{2}-\beta _{2}q^{3}-q^{4}+\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots\)
1122.3.d.a \(72\) \(30.572\) None \(0\) \(0\) \(0\) \(0\)
1122.3.f.a \(64\) \(30.572\) None \(0\) \(0\) \(0\) \(0\)
1122.4.a.a \(1\) \(66.200\) \(\Q\) None \(-2\) \(-3\) \(-18\) \(26\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}-18q^{5}+6q^{6}+\cdots\)
1122.4.a.b \(3\) \(66.200\) 3.3.2636.1 None \(6\) \(9\) \(-20\) \(-28\) \(-\) \(q+2q^{2}+3q^{3}+4q^{4}+(-6+\beta _{1}+2\beta _{2})q^{5}+\cdots\)
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