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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
6840.2.a.a \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) \(-\) \(q-q^{5}-2q^{7}-2q^{11}+6q^{17}-q^{19}+\cdots\)
6840.2.a.b \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) \(+\) \(q-q^{5}-2q^{7}+2q^{11}-4q^{13}+2q^{17}+\cdots\)
6840.2.a.c \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(+\) \(q-q^{5}-q^{7}-4q^{11}+q^{13}+7q^{17}+\cdots\)
6840.2.a.d \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(q-q^{5}-4q^{11}-2q^{13}-2q^{17}-q^{19}+\cdots\)
6840.2.a.e \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(q-q^{5}-4q^{11}+2q^{13}-6q^{17}-q^{19}+\cdots\)
6840.2.a.f \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(+\) \(q-q^{5}-2q^{11}-q^{19}+4q^{23}+q^{25}+\cdots\)
6840.2.a.g \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(q-q^{5}-2q^{13}+6q^{17}+q^{19}-4q^{23}+\cdots\)
6840.2.a.h \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(q-q^{5}+4q^{11}-6q^{13}+6q^{17}-q^{19}+\cdots\)
6840.2.a.i \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(-1\) \(0\) \(-\) \(q-q^{5}+4q^{11}+4q^{13}+2q^{17}+q^{19}+\cdots\)
6840.2.a.j \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(-1\) \(2\) \(+\) \(q-q^{5}+2q^{7}-6q^{11}+4q^{13}+2q^{17}+\cdots\)
6840.2.a.k \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(-1\) \(2\) \(+\) \(q-q^{5}+2q^{7}-2q^{13}-4q^{17}+q^{19}+\cdots\)
6840.2.a.l \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(-1\) \(4\) \(+\) \(q-q^{5}+4q^{7}-4q^{11}-4q^{13}+2q^{17}+\cdots\)
6840.2.a.m \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(-1\) \(4\) \(-\) \(q-q^{5}+4q^{7}+2q^{13}-2q^{17}-q^{19}+\cdots\)
6840.2.a.n \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(-1\) \(4\) \(-\) \(q-q^{5}+4q^{7}+2q^{11}-4q^{13}-4q^{17}+\cdots\)
6840.2.a.o \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(-1\) \(4\) \(+\) \(q-q^{5}+4q^{7}+4q^{11}-6q^{17}-q^{19}+\cdots\)
6840.2.a.p \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(-1\) \(4\) \(-\) \(q-q^{5}+4q^{7}+4q^{11}+2q^{13}+6q^{17}+\cdots\)
6840.2.a.q \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(-\) \(q+q^{5}-2q^{7}+2q^{11}-6q^{17}-q^{19}+\cdots\)
6840.2.a.r \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(-\) \(q+q^{5}-2q^{7}+4q^{11}-2q^{13}+q^{19}+\cdots\)
6840.2.a.s \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(+\) \(q+q^{5}+2q^{11}-q^{19}-4q^{23}+q^{25}+\cdots\)
6840.2.a.t \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(+\) \(q+q^{5}+4q^{11}-2q^{13}+2q^{17}+q^{19}+\cdots\)
6840.2.a.u \(1\) \(54.618\) \(\Q\) None \(0\) \(0\) \(1\) \(4\) \(-\) \(q+q^{5}+4q^{7}-2q^{11}-4q^{13}+4q^{17}+\cdots\)
6840.2.a.v \(2\) \(54.618\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(-6\) \(+\) \(q-q^{5}+(-3+\beta )q^{7}+(1+3\beta )q^{11}+\cdots\)
6840.2.a.w \(2\) \(54.618\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(-2\) \(-2\) \(+\) \(q-q^{5}+(-1+\beta )q^{7}+(3-\beta )q^{11}+(1+\cdots)q^{13}+\cdots\)
6840.2.a.x \(2\) \(54.618\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(-4\) \(+\) \(q+q^{5}+(-2+\beta )q^{7}-\beta q^{11}-3\beta q^{13}+\cdots\)
6840.2.a.y \(2\) \(54.618\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(0\) \(+\) \(q+q^{5}-2q^{11}+(1+\beta )q^{13}+(-4+2\beta )q^{17}+\cdots\)
6840.2.a.z \(2\) \(54.618\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) \(+\) \(q+q^{5}+2\beta q^{7}+(-2-2\beta )q^{11}+(2+\cdots)q^{13}+\cdots\)
6840.2.a.ba \(2\) \(54.618\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) \(+\) \(q+q^{5}+\beta q^{7}+\beta q^{11}+(-2-\beta )q^{13}+\cdots\)
6840.2.a.bb \(2\) \(54.618\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) \(-\) \(q+q^{5}+\beta q^{7}+(2-\beta )q^{11}+(2-\beta )q^{13}+\cdots\)
6840.2.a.bc \(2\) \(54.618\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(2\) \(-\) \(q+q^{5}+(1+\beta )q^{7}+(1+\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
6840.2.a.bd \(2\) \(54.618\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(6\) \(-\) \(q+q^{5}+(3+\beta )q^{7}+(-1+\beta )q^{11}+(3+\cdots)q^{13}+\cdots\)
6840.2.a.be \(3\) \(54.618\) 3.3.148.1 None \(0\) \(0\) \(-3\) \(-2\) \(+\) \(q-q^{5}+(-2\beta _{1}-\beta _{2})q^{7}+(1-\beta _{1})q^{11}+\cdots\)
6840.2.a.bf \(3\) \(54.618\) 3.3.316.1 None \(0\) \(0\) \(-3\) \(-2\) \(-\) \(q-q^{5}+(-1+\beta _{1})q^{7}+(1+\beta _{2})q^{11}+\cdots\)
6840.2.a.bg \(3\) \(54.618\) 3.3.229.1 None \(0\) \(0\) \(-3\) \(-1\) \(+\) \(q-q^{5}+\beta _{1}q^{7}+(2+\beta _{2})q^{13}+(-2+\cdots)q^{17}+\cdots\)
6840.2.a.bh \(3\) \(54.618\) 3.3.1772.1 None \(0\) \(0\) \(-3\) \(0\) \(-\) \(q-q^{5}+\beta _{2}q^{7}+(-2-\beta _{2})q^{11}+(1+\cdots)q^{13}+\cdots\)
6840.2.a.bi \(3\) \(54.618\) 3.3.2804.1 None \(0\) \(0\) \(-3\) \(2\) \(-\) \(q-q^{5}+(1-\beta _{1})q^{7}+(-2-\beta _{2})q^{11}+\cdots\)
6840.2.a.bj \(3\) \(54.618\) 3.3.568.1 None \(0\) \(0\) \(3\) \(-5\) \(-\) \(q+q^{5}+(-2-\beta _{2})q^{7}+(2-2\beta _{1})q^{11}+\cdots\)
6840.2.a.bk \(3\) \(54.618\) 3.3.568.1 None \(0\) \(0\) \(3\) \(-2\) \(+\) \(q+q^{5}+(-1-\beta _{2})q^{7}+(-1+\beta _{2})q^{11}+\cdots\)
6840.2.a.bl \(3\) \(54.618\) 3.3.148.1 None \(0\) \(0\) \(3\) \(-2\) \(+\) \(q+q^{5}+(-2\beta _{1}-\beta _{2})q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
6840.2.a.bm \(3\) \(54.618\) 3.3.316.1 None \(0\) \(0\) \(3\) \(-1\) \(-\) \(q+q^{5}+(-1+2\beta _{1}-\beta _{2})q^{7}-2\beta _{2}q^{11}+\cdots\)
6840.2.a.bn \(3\) \(54.618\) 3.3.1016.1 None \(0\) \(0\) \(3\) \(0\) \(-\) \(q+q^{5}+\beta _{2}q^{7}+(-1+\beta _{1}+\beta _{2})q^{11}+\cdots\)
6840.2.a.bo \(3\) \(54.618\) 3.3.2804.1 None \(0\) \(0\) \(3\) \(2\) \(-\) \(q+q^{5}+(1-\beta _{1})q^{7}+(2+\beta _{2})q^{11}+(3+\cdots)q^{13}+\cdots\)
6840.2.a.bp \(4\) \(54.618\) 4.4.20308.1 None \(0\) \(0\) \(-4\) \(-4\) \(+\) \(q-q^{5}+(-1+\beta _{1})q^{7}+(1-\beta _{1}-\beta _{3})q^{11}+\cdots\)
6840.2.a.bq \(4\) \(54.618\) 4.4.20308.1 None \(0\) \(0\) \(4\) \(-4\) \(+\) \(q+q^{5}+(-1+\beta _{1})q^{7}+(-1+\beta _{1}+\beta _{3})q^{11}+\cdots\)
6840.2.a.br \(5\) \(54.618\) 5.5.4636128.1 None \(0\) \(0\) \(-5\) \(2\) \(-\) \(q-q^{5}+\beta _{4}q^{7}-\beta _{3}q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
6840.2.a.bs \(5\) \(54.618\) 5.5.4636128.1 None \(0\) \(0\) \(5\) \(2\) \(-\) \(q+q^{5}+\beta _{4}q^{7}+\beta _{3}q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
6840.2.r.a \(40\) \(54.618\) None \(0\) \(0\) \(0\) \(-8\)
6840.2.r.b \(40\) \(54.618\) None \(0\) \(0\) \(0\) \(-8\)
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