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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1176.1.e.a \(8\) \(0.587\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{4}q^{2}-\zeta_{16}q^{3}-q^{4}+\zeta_{16}^{5}q^{6}+\cdots\)
1176.1.n.a \(1\) \(0.587\) \(\Q\) \(\Q(\sqrt{-6}) \) None \(-1\) \(-1\) \(1\) \(0\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
1176.1.n.b \(1\) \(0.587\) \(\Q\) \(\Q(\sqrt{-6}) \) None \(-1\) \(1\) \(-1\) \(0\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
1176.1.n.c \(1\) \(0.587\) \(\Q\) \(\Q(\sqrt{-6}) \) None \(1\) \(-1\) \(1\) \(0\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
1176.1.n.d \(1\) \(0.587\) \(\Q\) \(\Q(\sqrt{-6}) \) None \(1\) \(1\) \(-1\) \(0\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
1176.1.n.e \(4\) \(0.587\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+(\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{5}+\cdots\)
1176.1.s.a \(2\) \(0.587\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-6}) \) None \(-1\) \(1\) \(-1\) \(0\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\cdots\)
1176.1.s.b \(2\) \(0.587\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-6}) \) None \(1\) \(-1\) \(1\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots\)
1176.1.s.c \(8\) \(0.587\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{8}q^{4}+\cdots\)
1176.1.be.a \(16\) \(0.587\) \(\Q(\zeta_{48})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{48}^{4}q^{2}+\zeta_{48}^{5}q^{3}+\zeta_{48}^{8}q^{4}+\cdots\)
1176.1.bj.a \(6\) \(0.587\) \(\Q(\zeta_{14})\) \(\Q(\sqrt{-6}) \) None \(-1\) \(-1\) \(-2\) \(-1\) \(q-\zeta_{14}^{3}q^{2}+\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}+\cdots\)
1176.1.bj.b \(6\) \(0.587\) \(\Q(\zeta_{14})\) \(\Q(\sqrt{-6}) \) None \(1\) \(1\) \(2\) \(-1\) \(q+\zeta_{14}^{3}q^{2}-\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}+\cdots\)
1176.1.ck.a \(12\) \(0.587\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-6}) \) None \(-1\) \(-1\) \(1\) \(1\) \(q+\zeta_{42}^{13}q^{2}+\zeta_{42}^{11}q^{3}-\zeta_{42}^{5}q^{4}+\cdots\)
1176.1.ck.b \(12\) \(0.587\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-6}) \) None \(1\) \(1\) \(-1\) \(1\) \(q-\zeta_{42}^{13}q^{2}-\zeta_{42}^{11}q^{3}-\zeta_{42}^{5}q^{4}+\cdots\)
1176.2.a.a \(1\) \(9.390\) \(\Q\) None None \(0\) \(-1\) \(-2\) \(0\) \(-\) \(q-q^{3}-2q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots\)
1176.2.a.b \(1\) \(9.390\) \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) \(+\) \(q-q^{3}+q^{9}-4q^{13}-4q^{17}+4q^{19}+\cdots\)
1176.2.a.c \(1\) \(9.390\) \(\Q\) None None \(0\) \(-1\) \(1\) \(0\) \(-\) \(q-q^{3}+q^{5}+q^{9}+3q^{11}-4q^{13}+\cdots\)
1176.2.a.d \(1\) \(9.390\) \(\Q\) None None \(0\) \(-1\) \(2\) \(0\) \(+\) \(q-q^{3}+2q^{5}+q^{9}-6q^{11}-3q^{13}+\cdots\)
1176.2.a.e \(1\) \(9.390\) \(\Q\) None None \(0\) \(1\) \(-2\) \(0\) \(+\) \(q+q^{3}-2q^{5}+q^{9}-6q^{11}+3q^{13}+\cdots\)
1176.2.a.f \(1\) \(9.390\) \(\Q\) None None \(0\) \(1\) \(-2\) \(0\) \(+\) \(q+q^{3}-2q^{5}+q^{9}-6q^{13}-2q^{15}+\cdots\)
1176.2.a.g \(1\) \(9.390\) \(\Q\) None None \(0\) \(1\) \(-1\) \(0\) \(-\) \(q+q^{3}-q^{5}+q^{9}+3q^{11}+4q^{13}+\cdots\)
1176.2.a.h \(1\) \(9.390\) \(\Q\) None None \(0\) \(1\) \(0\) \(0\) \(-\) \(q+q^{3}+q^{9}+4q^{13}+4q^{17}-4q^{19}+\cdots\)
1176.2.a.i \(1\) \(9.390\) \(\Q\) None None \(0\) \(1\) \(2\) \(0\) \(-\) \(q+q^{3}+2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
1176.2.a.j \(2\) \(9.390\) \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(-4\) \(0\) \(+\) \(q-q^{3}+(-2+\beta )q^{5}+q^{9}+(2-2\beta )q^{11}+\cdots\)
1176.2.a.k \(2\) \(9.390\) \(\Q(\sqrt{57}) \) None None \(0\) \(-2\) \(-1\) \(0\) \(-\) \(q-q^{3}-\beta q^{5}+q^{9}-\beta q^{11}+(3-\beta )q^{13}+\cdots\)
1176.2.a.l \(2\) \(9.390\) \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(4\) \(0\) \(-\) \(q-q^{3}+(2+\beta )q^{5}+q^{9}+(-2+2\beta )q^{11}+\cdots\)
1176.2.a.m \(2\) \(9.390\) \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(-4\) \(0\) \(+\) \(q+q^{3}+(-2+\beta )q^{5}+q^{9}+(-2-2\beta )q^{11}+\cdots\)
1176.2.a.n \(2\) \(9.390\) \(\Q(\sqrt{57}) \) None None \(0\) \(2\) \(1\) \(0\) \(-\) \(q+q^{3}+\beta q^{5}+q^{9}-\beta q^{11}+(-3+\beta )q^{13}+\cdots\)
1176.2.a.o \(2\) \(9.390\) \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(4\) \(0\) \(-\) \(q+q^{3}+(2+\beta )q^{5}+q^{9}+(2+2\beta )q^{11}+\cdots\)
1176.2.c.a \(2\) \(9.390\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(0\) \(0\) \(q+(-1+i)q^{2}-iq^{3}-2iq^{4}+2iq^{5}+\cdots\)
1176.2.c.b \(4\) \(9.390\) \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(0\) \(0\) \(q+(1+\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1176.2.c.c \(8\) \(9.390\) 8.0.386672896.3 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-\beta _{4}q^{3}+\beta _{2}q^{4}+(\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
1176.2.c.d \(12\) \(9.390\) 12.0.\(\cdots\).1 None None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{2}+\beta _{7}q^{3}-\beta _{11}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
1176.2.c.e \(16\) \(9.390\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(-2\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+\beta _{5}q^{3}-\beta _{2}q^{4}-\beta _{4}q^{5}+\cdots\)
1176.2.c.f \(16\) \(9.390\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(-2\) \(0\) \(0\) \(0\) \(q-\beta _{10}q^{2}+\beta _{4}q^{3}-\beta _{3}q^{4}-\beta _{2}q^{5}+\cdots\)
1176.2.c.g \(24\) \(9.390\) None None \(4\) \(0\) \(0\) \(0\)
1176.2.k.a \(16\) \(9.390\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+\beta _{8}q^{5}+\beta _{5}q^{9}-\beta _{6}q^{11}+\cdots\)
1176.2.k.b \(24\) \(9.390\) None None \(0\) \(0\) \(0\) \(0\)
1176.2.p.a \(32\) \(9.390\) None None \(4\) \(0\) \(0\) \(0\)
1176.2.p.b \(48\) \(9.390\) None None \(-8\) \(0\) \(0\) \(0\)
1176.2.q.a \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(0\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
1176.2.q.b \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(0\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
1176.2.q.c \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(0\) \(0\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}+4q^{13}+(-4+\cdots)q^{17}+\cdots\)
1176.2.q.d \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
1176.2.q.e \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
1176.2.q.f \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+6q^{13}+\cdots\)
1176.2.q.g \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-1\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots\)
1176.2.q.h \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(0\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}-4q^{13}+(4-4\zeta_{6})q^{17}+\cdots\)
1176.2.q.i \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(2\) \(0\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots\)
1176.2.q.j \(2\) \(9.390\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(2\) \(0\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+2q^{13}+\cdots\)
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