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Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7 23
7728.2.a.a \(1\) \(61.708\) \(\Q\) None \(0\) \(-1\) \(-3\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-3q^{5}-q^{7}+q^{9}+5q^{13}+3q^{15}+\cdots\)
7728.2.a.b \(1\) \(61.708\) \(\Q\) None \(0\) \(-1\) \(-2\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}-2q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
7728.2.a.c \(1\) \(61.708\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots\)
7728.2.a.d \(1\) \(61.708\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{7}+q^{9}-3q^{11}+2q^{13}+\cdots\)
7728.2.a.e \(1\) \(61.708\) \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{7}+q^{9}-q^{11}+2q^{13}+4q^{17}+\cdots\)
7728.2.a.f \(1\) \(61.708\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{7}+q^{9}-q^{11}-6q^{13}-7q^{19}+\cdots\)
7728.2.a.g \(1\) \(61.708\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
7728.2.a.h \(1\) \(61.708\) \(\Q\) None \(0\) \(-1\) \(2\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}+2q^{5}-q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots\)
7728.2.a.i \(1\) \(61.708\) \(\Q\) None \(0\) \(-1\) \(2\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}+2q^{5}-q^{7}+q^{9}+6q^{13}-2q^{15}+\cdots\)
7728.2.a.j \(1\) \(61.708\) \(\Q\) None \(0\) \(-1\) \(3\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+3q^{5}+q^{7}+q^{9}-4q^{11}-3q^{13}+\cdots\)
7728.2.a.k \(1\) \(61.708\) \(\Q\) None \(0\) \(-1\) \(4\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}+4q^{5}-q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots\)
7728.2.a.l \(1\) \(61.708\) \(\Q\) None \(0\) \(-1\) \(4\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+4q^{5}+q^{7}+q^{9}+5q^{11}-2q^{13}+\cdots\)
7728.2.a.m \(1\) \(61.708\) \(\Q\) None \(0\) \(1\) \(-4\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-4q^{5}-q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
7728.2.a.n \(1\) \(61.708\) \(\Q\) None \(0\) \(1\) \(-3\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}-3q^{5}+q^{7}+q^{9}-q^{13}-3q^{15}+\cdots\)
7728.2.a.o \(1\) \(61.708\) \(\Q\) None \(0\) \(1\) \(-2\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
7728.2.a.p \(1\) \(61.708\) \(\Q\) None \(0\) \(1\) \(-2\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}-2q^{5}+q^{7}+q^{9}+4q^{13}-2q^{15}+\cdots\)
7728.2.a.q \(1\) \(61.708\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
7728.2.a.r \(1\) \(61.708\) \(\Q\) None \(0\) \(1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{7}+q^{9}+5q^{11}-6q^{13}+\cdots\)
7728.2.a.s \(1\) \(61.708\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}+q^{5}-q^{7}+q^{9}-q^{13}+q^{15}+\cdots\)
7728.2.a.t \(1\) \(61.708\) \(\Q\) None \(0\) \(1\) \(2\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots\)
7728.2.a.u \(1\) \(61.708\) \(\Q\) None \(0\) \(1\) \(3\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}+3q^{5}-q^{7}+q^{9}-4q^{11}+3q^{13}+\cdots\)
7728.2.a.v \(2\) \(61.708\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-5\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}+(-2-\beta )q^{5}-q^{7}+q^{9}+(3+\cdots)q^{11}+\cdots\)
7728.2.a.w \(2\) \(61.708\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-5\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}+(-2-\beta )q^{5}-q^{7}+q^{9}+q^{11}+\cdots\)
7728.2.a.x \(2\) \(61.708\) \(\Q(\sqrt{13}) \) None \(0\) \(-2\) \(-5\) \(2\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+(-2-\beta )q^{5}+q^{7}+q^{9}+5q^{11}+\cdots\)
7728.2.a.y \(2\) \(61.708\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-1\) \(-2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-\beta q^{5}-q^{7}+q^{9}+(3-2\beta )q^{11}+\cdots\)
7728.2.a.z \(2\) \(61.708\) \(\Q(\sqrt{41}) \) None \(0\) \(-2\) \(-1\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}-\beta q^{5}+q^{7}+q^{9}+(2+\beta )q^{13}+\cdots\)
7728.2.a.ba \(2\) \(61.708\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-1\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}-\beta q^{5}+q^{7}+q^{9}+3q^{11}+(-1+\cdots)q^{13}+\cdots\)
7728.2.a.bb \(2\) \(61.708\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(1\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}+(-1+3\beta )q^{5}-q^{7}+q^{9}-3q^{11}+\cdots\)
7728.2.a.bc \(2\) \(61.708\) \(\Q(\sqrt{41}) \) None \(0\) \(-2\) \(1\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}+\beta q^{5}-q^{7}+q^{9}+4q^{11}+(2+\cdots)q^{13}+\cdots\)
7728.2.a.bd \(2\) \(61.708\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(4\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}+2q^{5}-q^{7}+q^{9}-\beta q^{13}-2q^{15}+\cdots\)
7728.2.a.be \(2\) \(61.708\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(5\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}+(3-\beta )q^{5}-q^{7}+q^{9}-q^{11}+\cdots\)
7728.2.a.bf \(2\) \(61.708\) \(\Q(\sqrt{13}) \) None \(0\) \(2\) \(-5\) \(2\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+(-2-\beta )q^{5}+q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
7728.2.a.bg \(2\) \(61.708\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-3\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
7728.2.a.bh \(2\) \(61.708\) \(\Q(\sqrt{33}) \) None \(0\) \(2\) \(-3\) \(2\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}-4q^{11}+\cdots\)
7728.2.a.bi \(2\) \(61.708\) \(\Q(\sqrt{41}) \) None \(0\) \(2\) \(0\) \(-2\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{7}+q^{9}+\beta q^{11}+2q^{13}+\cdots\)
7728.2.a.bj \(2\) \(61.708\) \(\Q(\sqrt{33}) \) None \(0\) \(2\) \(1\) \(-2\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}+\beta q^{5}-q^{7}+q^{9}+(-1+\beta )q^{11}+\cdots\)
7728.2.a.bk \(2\) \(61.708\) \(\Q(\sqrt{13}) \) None \(0\) \(2\) \(1\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}+\beta q^{5}-q^{7}+q^{9}+(-1+2\beta )q^{11}+\cdots\)
7728.2.a.bl \(2\) \(61.708\) \(\Q(\sqrt{29}) \) None \(0\) \(2\) \(1\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+\beta q^{5}+q^{7}+q^{9}-5q^{11}+(1+\cdots)q^{13}+\cdots\)
7728.2.a.bm \(2\) \(61.708\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(1\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(-2+2\beta )q^{11}+\cdots\)
7728.2.a.bn \(2\) \(61.708\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(1\) \(2\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(-1+2\beta )q^{11}+\cdots\)
7728.2.a.bo \(2\) \(61.708\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(1\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(1+2\beta )q^{11}+\cdots\)
7728.2.a.bp \(3\) \(61.708\) 3.3.229.1 None \(0\) \(-3\) \(-3\) \(-3\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}+(-1+\beta _{1})q^{5}-q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
7728.2.a.bq \(3\) \(61.708\) 3.3.733.1 None \(0\) \(-3\) \(-3\) \(3\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+(-1-\beta _{2})q^{5}+q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
7728.2.a.br \(3\) \(61.708\) 3.3.1101.1 None \(0\) \(-3\) \(1\) \(3\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+\beta _{1}q^{5}+q^{7}+q^{9}-q^{11}+(-1+\cdots)q^{13}+\cdots\)
7728.2.a.bs \(3\) \(61.708\) 3.3.229.1 None \(0\) \(-3\) \(1\) \(3\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}-\beta _{2}q^{5}+q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
7728.2.a.bt \(3\) \(61.708\) 3.3.837.1 None \(0\) \(-3\) \(3\) \(3\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+(1-\beta _{1})q^{5}+q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
7728.2.a.bu \(3\) \(61.708\) 3.3.621.1 None \(0\) \(3\) \(-3\) \(-3\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}-q^{7}+q^{9}+\cdots\)
7728.2.a.bv \(3\) \(61.708\) 3.3.1509.1 None \(0\) \(3\) \(-1\) \(-3\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-\beta _{1}q^{5}-q^{7}+q^{9}+(-1+2\beta _{1}+\cdots)q^{11}+\cdots\)
7728.2.a.bw \(3\) \(61.708\) 3.3.229.1 None \(0\) \(3\) \(-1\) \(3\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+\beta _{2}q^{5}+q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
7728.2.a.bx \(3\) \(61.708\) 3.3.837.1 None \(0\) \(3\) \(0\) \(-3\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}+\beta _{1}q^{5}-q^{7}+q^{9}+(-2+\beta _{1}+\cdots)q^{11}+\cdots\)
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