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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1155.1.e.a \(2\) \(0.576\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-231}) \) \(\Q(\sqrt{165}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+q^{4}-iq^{5}+iq^{7}-q^{9}-q^{11}+\cdots\)
1155.1.e.b \(2\) \(0.576\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-231}) \) \(\Q(\sqrt{165}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+q^{4}-iq^{5}-iq^{7}-q^{9}+q^{11}+\cdots\)
1155.1.e.c \(4\) \(0.576\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-231}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}^{2}+\zeta_{12}^{4})q^{2}+\zeta_{12}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)
1155.1.e.d \(4\) \(0.576\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-231}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{2}+\zeta_{12}^{3}q^{3}+\cdots\)
1155.1.ca.a \(8\) \(0.576\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{5}q^{3}+\zeta_{20}^{4}q^{4}-\zeta_{20}^{3}q^{5}+\cdots\)
1155.1.ca.b \(8\) \(0.576\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{7}q^{3}+\zeta_{20}^{4}q^{4}-\zeta_{20}^{3}q^{5}+\cdots\)
1155.2.a.a \(1\) \(9.223\) \(\Q\) None None \(-2\) \(-1\) \(1\) \(1\) \(+\) \(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}+q^{7}+\cdots\)
1155.2.a.b \(1\) \(9.223\) \(\Q\) None None \(-2\) \(1\) \(-1\) \(-1\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}-q^{7}+\cdots\)
1155.2.a.c \(1\) \(9.223\) \(\Q\) None None \(-2\) \(1\) \(1\) \(1\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
1155.2.a.d \(1\) \(9.223\) \(\Q\) None None \(-1\) \(-1\) \(-1\) \(-1\) \(+\) \(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
1155.2.a.e \(1\) \(9.223\) \(\Q\) None None \(-1\) \(-1\) \(1\) \(-1\) \(+\) \(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
1155.2.a.f \(1\) \(9.223\) \(\Q\) None None \(-1\) \(1\) \(1\) \(1\) \(-\) \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
1155.2.a.g \(1\) \(9.223\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(1\) \(+\) \(q-q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}+q^{11}+\cdots\)
1155.2.a.h \(1\) \(9.223\) \(\Q\) None None \(0\) \(1\) \(-1\) \(1\) \(+\) \(q+q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}-q^{11}+\cdots\)
1155.2.a.i \(1\) \(9.223\) \(\Q\) None None \(0\) \(1\) \(1\) \(-1\) \(+\) \(q+q^{3}-2q^{4}+q^{5}-q^{7}+q^{9}-q^{11}+\cdots\)
1155.2.a.j \(1\) \(9.223\) \(\Q\) None None \(1\) \(-1\) \(-1\) \(1\) \(-\) \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
1155.2.a.k \(1\) \(9.223\) \(\Q\) None None \(1\) \(-1\) \(1\) \(1\) \(+\) \(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
1155.2.a.l \(1\) \(9.223\) \(\Q\) None None \(1\) \(1\) \(-1\) \(-1\) \(+\) \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
1155.2.a.m \(1\) \(9.223\) \(\Q\) None None \(1\) \(1\) \(1\) \(1\) \(-\) \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
1155.2.a.n \(1\) \(9.223\) \(\Q\) None None \(2\) \(-1\) \(-1\) \(-1\) \(+\) \(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}-q^{7}+\cdots\)
1155.2.a.o \(2\) \(9.223\) \(\Q(\sqrt{17}) \) None None \(-1\) \(-2\) \(2\) \(-2\) \(+\) \(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
1155.2.a.p \(2\) \(9.223\) \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(-2\) \(-2\) \(-\) \(q+\beta q^{2}-q^{3}-q^{5}-\beta q^{6}-q^{7}-2\beta q^{8}+\cdots\)
1155.2.a.q \(2\) \(9.223\) \(\Q(\sqrt{6}) \) None None \(0\) \(2\) \(2\) \(2\) \(-\) \(q+\beta q^{2}+q^{3}+4q^{4}+q^{5}+\beta q^{6}+q^{7}+\cdots\)
1155.2.a.r \(2\) \(9.223\) \(\Q(\sqrt{3}) \) None None \(2\) \(-2\) \(-2\) \(2\) \(-\) \(q+(1+\beta )q^{2}-q^{3}+(2+2\beta )q^{4}-q^{5}+\cdots\)
1155.2.a.s \(3\) \(9.223\) 3.3.316.1 None None \(1\) \(-3\) \(3\) \(-3\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
1155.2.a.t \(3\) \(9.223\) 3.3.316.1 None None \(1\) \(3\) \(3\) \(-3\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
1155.2.a.u \(4\) \(9.223\) 4.4.13448.1 None None \(0\) \(4\) \(-4\) \(-4\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
1155.2.a.v \(4\) \(9.223\) 4.4.7232.1 None None \(2\) \(-4\) \(4\) \(4\) \(-\) \(q-\beta _{2}q^{2}-q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+q^{5}+\cdots\)
1155.2.a.w \(5\) \(9.223\) 5.5.352076.1 None None \(1\) \(5\) \(-5\) \(5\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
1155.2.c.a \(2\) \(9.223\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{2}+iq^{3}+q^{4}+(-2+i)q^{5}+\cdots\)
1155.2.c.b \(2\) \(9.223\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{2}+iq^{3}+q^{4}+(-2-i)q^{5}+\cdots\)
1155.2.c.c \(6\) \(9.223\) 6.0.350464.1 None None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{5}q^{2}-\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
1155.2.c.d \(6\) \(9.223\) 6.0.350464.1 None None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{5}q^{2}-\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
1155.2.c.e \(20\) \(9.223\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{1}q^{2}+\beta _{13}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
1155.2.c.f \(20\) \(9.223\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{1}q^{2}-\beta _{11}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
1155.2.i.a \(8\) \(9.223\) 8.0.303595776.1 None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{5})q^{2}+\beta _{4}q^{3}+(-2-\beta _{7})q^{4}+\cdots\)
1155.2.i.b \(8\) \(9.223\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}^{4}-\zeta_{24}^{5})q^{2}-\zeta_{24}^{3}q^{3}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
1155.2.i.c \(16\) \(9.223\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{8}q^{2}+\beta _{9}q^{3}+(-2-\beta _{3})q^{4}-\beta _{9}q^{5}+\cdots\)
1155.2.i.d \(32\) \(9.223\) None None \(0\) \(0\) \(0\) \(0\)
1155.2.k.a \(48\) \(9.223\) None None \(0\) \(-48\) \(4\) \(0\)
1155.2.k.b \(48\) \(9.223\) None None \(0\) \(48\) \(-4\) \(0\)
1155.2.l.a \(4\) \(9.223\) \(\Q(\zeta_{8})\) None None \(-4\) \(4\) \(0\) \(0\) \(q+(-1-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}^{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
1155.2.l.b \(4\) \(9.223\) \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}+(1-\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(-2\zeta_{8}+\cdots)q^{6}+\cdots\)
1155.2.l.c \(4\) \(9.223\) \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}+(1-\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+(-2\zeta_{8}+\cdots)q^{6}+\cdots\)
1155.2.l.d \(4\) \(9.223\) \(\Q(\zeta_{8})\) None None \(4\) \(4\) \(0\) \(0\) \(q+(1-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}^{2})q^{3}+(1-2\zeta_{8}^{3})q^{4}+\cdots\)
1155.2.l.e \(40\) \(9.223\) None None \(-4\) \(-4\) \(0\) \(0\)
1155.2.l.f \(40\) \(9.223\) None None \(4\) \(-4\) \(0\) \(0\)
1155.3.b.a \(96\) \(31.471\) None None \(0\) \(0\) \(0\) \(0\)
1155.4.a.a \(1\) \(68.147\) \(\Q\) None None \(-3\) \(-3\) \(-5\) \(7\) \(-\) \(q-3q^{2}-3q^{3}+q^{4}-5q^{5}+9q^{6}+\cdots\)
1155.4.a.b \(1\) \(68.147\) \(\Q\) None None \(-3\) \(-3\) \(-5\) \(7\) \(-\) \(q-3q^{2}-3q^{3}+q^{4}-5q^{5}+9q^{6}+\cdots\)
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