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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1680.1.bb.a \(1\) \(0.838\) \(\Q\) \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-105}) \) \(\Q(\sqrt{21}) \) \(0\) \(-1\) \(-1\) \(-1\) \(q-q^{3}-q^{5}-q^{7}+q^{9}+q^{15}+q^{21}+\cdots\)
1680.1.bb.b \(1\) \(0.838\) \(\Q\) \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-105}) \) \(\Q(\sqrt{21}) \) \(0\) \(-1\) \(1\) \(1\) \(q-q^{3}+q^{5}+q^{7}+q^{9}-q^{15}-q^{21}+\cdots\)
1680.1.bb.c \(1\) \(0.838\) \(\Q\) \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-105}) \) \(\Q(\sqrt{21}) \) \(0\) \(1\) \(-1\) \(1\) \(q+q^{3}-q^{5}+q^{7}+q^{9}-q^{15}+q^{21}+\cdots\)
1680.1.bb.d \(1\) \(0.838\) \(\Q\) \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-105}) \) \(\Q(\sqrt{21}) \) \(0\) \(1\) \(1\) \(-1\) \(q+q^{3}+q^{5}-q^{7}+q^{9}+q^{15}-q^{21}+\cdots\)
1680.1.bb.e \(2\) \(0.838\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-21}) \) \(\Q(\sqrt{15}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{5}-iq^{7}-q^{9}-q^{11}+\cdots\)
1680.1.bb.f \(2\) \(0.838\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-21}) \) \(\Q(\sqrt{15}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{5}+iq^{7}-q^{9}+q^{11}+\cdots\)
1680.1.bb.g \(4\) \(0.838\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
1680.1.bb.h \(4\) \(0.838\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+\zeta_{12}^{3}q^{5}+\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
1680.1.dp.a \(2\) \(0.838\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(-2\) \(-1\) \(-1\) \(q-q^{3}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+q^{9}+\zeta_{6}q^{15}+\cdots\)
1680.1.dp.b \(2\) \(0.838\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(-1\) \(1\) \(-1\) \(q-\zeta_{6}q^{3}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
1680.1.dp.c \(2\) \(0.838\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(1\) \(1\) \(1\) \(q+\zeta_{6}q^{3}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
1680.1.dp.d \(2\) \(0.838\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(2\) \(-1\) \(1\) \(q+q^{3}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+q^{9}-\zeta_{6}q^{15}+\cdots\)
1680.2.a.a \(1\) \(13.415\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(-1\) \(-\) \(q-q^{3}-q^{5}-q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
1680.2.a.b \(1\) \(13.415\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(-1\) \(-\) \(q-q^{3}-q^{5}-q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
1680.2.a.c \(1\) \(13.415\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(-1\) \(+\) \(q-q^{3}-q^{5}-q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
1680.2.a.d \(1\) \(13.415\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(1\) \(-\) \(q-q^{3}-q^{5}+q^{7}+q^{9}+6q^{13}+q^{15}+\cdots\)
1680.2.a.e \(1\) \(13.415\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(1\) \(-\) \(q-q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
1680.2.a.f \(1\) \(13.415\) \(\Q\) None None \(0\) \(-1\) \(1\) \(-1\) \(+\) \(q-q^{3}+q^{5}-q^{7}+q^{9}-6q^{13}-q^{15}+\cdots\)
1680.2.a.g \(1\) \(13.415\) \(\Q\) None None \(0\) \(-1\) \(1\) \(-1\) \(+\) \(q-q^{3}+q^{5}-q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
1680.2.a.h \(1\) \(13.415\) \(\Q\) None None \(0\) \(-1\) \(1\) \(1\) \(+\) \(q-q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
1680.2.a.i \(1\) \(13.415\) \(\Q\) None None \(0\) \(-1\) \(1\) \(1\) \(-\) \(q-q^{3}+q^{5}+q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots\)
1680.2.a.j \(1\) \(13.415\) \(\Q\) None None \(0\) \(-1\) \(1\) \(1\) \(-\) \(q-q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
1680.2.a.k \(1\) \(13.415\) \(\Q\) None None \(0\) \(1\) \(-1\) \(-1\) \(-\) \(q+q^{3}-q^{5}-q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
1680.2.a.l \(1\) \(13.415\) \(\Q\) None None \(0\) \(1\) \(-1\) \(-1\) \(-\) \(q+q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
1680.2.a.m \(1\) \(13.415\) \(\Q\) None None \(0\) \(1\) \(-1\) \(1\) \(+\) \(q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
1680.2.a.n \(1\) \(13.415\) \(\Q\) None None \(0\) \(1\) \(-1\) \(1\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots\)
1680.2.a.o \(1\) \(13.415\) \(\Q\) None None \(0\) \(1\) \(-1\) \(1\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
1680.2.a.p \(1\) \(13.415\) \(\Q\) None None \(0\) \(1\) \(1\) \(-1\) \(+\) \(q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
1680.2.a.q \(1\) \(13.415\) \(\Q\) None None \(0\) \(1\) \(1\) \(-1\) \(-\) \(q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
1680.2.a.r \(1\) \(13.415\) \(\Q\) None None \(0\) \(1\) \(1\) \(-1\) \(-\) \(q+q^{3}+q^{5}-q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots\)
1680.2.a.s \(1\) \(13.415\) \(\Q\) None None \(0\) \(1\) \(1\) \(1\) \(-\) \(q+q^{3}+q^{5}+q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
1680.2.a.t \(1\) \(13.415\) \(\Q\) None None \(0\) \(1\) \(1\) \(1\) \(-\) \(q+q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
1680.2.a.u \(2\) \(13.415\) \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(2\) \(-2\) \(-\) \(q-q^{3}+q^{5}-q^{7}+q^{9}+\beta q^{11}+2q^{13}+\cdots\)
1680.2.a.v \(2\) \(13.415\) \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(-2\) \(-2\) \(+\) \(q+q^{3}-q^{5}-q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
1680.2.d.a \(4\) \(13.415\) \(\Q(i, \sqrt{6})\) None None \(0\) \(-4\) \(0\) \(0\) \(q-q^{3}+\beta _{1}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+q^{9}+\cdots\)
1680.2.d.b \(4\) \(13.415\) \(\Q(i, \sqrt{6})\) None None \(0\) \(4\) \(0\) \(0\) \(q+q^{3}-\beta _{1}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+q^{9}+\cdots\)
1680.2.d.c \(12\) \(13.415\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-12\) \(0\) \(4\) \(q-q^{3}-\beta _{1}q^{5}-\beta _{9}q^{7}+q^{9}-\beta _{7}q^{11}+\cdots\)
1680.2.d.d \(12\) \(13.415\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(12\) \(0\) \(-4\) \(q+q^{3}+\beta _{1}q^{5}+\beta _{8}q^{7}+q^{9}-\beta _{7}q^{11}+\cdots\)
1680.2.f.a \(2\) \(13.415\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(2\) \(-4\) \(q+(-2+\zeta_{6})q^{3}+q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
1680.2.f.b \(2\) \(13.415\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-2\) \(-4\) \(q+\zeta_{6}q^{3}-q^{5}+(-2-\zeta_{6})q^{7}-3q^{9}+\cdots\)
1680.2.f.c \(2\) \(13.415\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(2\) \(-4\) \(q-\zeta_{6}q^{3}+q^{5}+(-2+\zeta_{6})q^{7}-3q^{9}+\cdots\)
1680.2.f.d \(2\) \(13.415\) \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(-2\) \(-4\) \(q+(2-\zeta_{6})q^{3}-q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
1680.2.f.e \(4\) \(13.415\) \(\Q(i, \sqrt{5})\) None None \(0\) \(-2\) \(-4\) \(-6\) \(q+(\beta _{1}+\beta _{2})q^{3}-q^{5}+(-1+\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
1680.2.f.f \(4\) \(13.415\) \(\Q(i, \sqrt{5})\) None None \(0\) \(-2\) \(-4\) \(6\) \(q+(-1-\beta _{1})q^{3}-q^{5}+(1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1680.2.f.g \(4\) \(13.415\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(-1\) \(4\) \(8\) \(q-\beta _{1}q^{3}+q^{5}+(2+\beta _{2})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
1680.2.f.h \(4\) \(13.415\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(1\) \(-4\) \(8\) \(q+\beta _{1}q^{3}-q^{5}+(2-\beta _{2})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
1680.2.f.i \(4\) \(13.415\) \(\Q(i, \sqrt{5})\) None None \(0\) \(2\) \(4\) \(-6\) \(q+(-\beta _{1}-\beta _{2})q^{3}+q^{5}+(-1-2\beta _{2}+\cdots)q^{7}+\cdots\)
1680.2.f.j \(4\) \(13.415\) \(\Q(i, \sqrt{5})\) None None \(0\) \(2\) \(4\) \(6\) \(q+(1+\beta _{1})q^{3}+q^{5}+(1+\beta _{2}+\beta _{3})q^{7}+\cdots\)
1680.2.f.k \(16\) \(13.415\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(-16\) \(-2\) \(q+\beta _{3}q^{3}-q^{5}-\beta _{9}q^{7}+\beta _{7}q^{9}+\beta _{8}q^{11}+\cdots\)
1680.2.f.l \(16\) \(13.415\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(16\) \(-2\) \(q-\beta _{3}q^{3}+q^{5}-\beta _{4}q^{7}+\beta _{7}q^{9}+\beta _{8}q^{11}+\cdots\)
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