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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1840.1.g.a \(1\) \(0.918\) \(\Q\) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(-1\) \(-1\) \(q-q^{5}-q^{7}+q^{9}+q^{17}+q^{23}+q^{25}+\cdots\)
1840.1.g.b \(1\) \(0.918\) \(\Q\) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(1\) \(1\) \(q+q^{5}+q^{7}+q^{9}-q^{17}-q^{23}+q^{25}+\cdots\)
1840.1.bq.a \(20\) \(0.918\) \(\Q(\zeta_{44})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(-\zeta_{44}^{7}-\zeta_{44}^{9})q^{3}+\zeta_{44}^{6}q^{5}+\cdots\)
1840.2.a.a \(1\) \(14.692\) \(\Q\) None None \(0\) \(-3\) \(-1\) \(-2\) \(+\) \(q-3q^{3}-q^{5}-2q^{7}+6q^{9}-3q^{13}+\cdots\)
1840.2.a.b \(1\) \(14.692\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(2\) \(+\) \(q-q^{3}-q^{5}+2q^{7}-2q^{9}+q^{13}+q^{15}+\cdots\)
1840.2.a.c \(1\) \(14.692\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(4\) \(-\) \(q-q^{3}-q^{5}+4q^{7}-2q^{9}+6q^{11}+\cdots\)
1840.2.a.d \(1\) \(14.692\) \(\Q\) None None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(q-q^{5}-q^{7}-3q^{9}-2q^{11}-2q^{13}+\cdots\)
1840.2.a.e \(1\) \(14.692\) \(\Q\) None None \(0\) \(0\) \(-1\) \(1\) \(+\) \(q-q^{5}+q^{7}-3q^{9}-6q^{11}+6q^{13}+\cdots\)
1840.2.a.f \(1\) \(14.692\) \(\Q\) None None \(0\) \(0\) \(1\) \(-1\) \(-\) \(q+q^{5}-q^{7}-3q^{9}+6q^{11}-2q^{13}+\cdots\)
1840.2.a.g \(1\) \(14.692\) \(\Q\) None None \(0\) \(1\) \(1\) \(0\) \(+\) \(q+q^{3}+q^{5}-2q^{9}-2q^{11}-5q^{13}+\cdots\)
1840.2.a.h \(1\) \(14.692\) \(\Q\) None None \(0\) \(1\) \(1\) \(2\) \(-\) \(q+q^{3}+q^{5}+2q^{7}-2q^{9}+4q^{11}+\cdots\)
1840.2.a.i \(1\) \(14.692\) \(\Q\) None None \(0\) \(3\) \(1\) \(2\) \(-\) \(q+3q^{3}+q^{5}+2q^{7}+6q^{9}+q^{13}+\cdots\)
1840.2.a.j \(2\) \(14.692\) \(\Q(\sqrt{13}) \) None None \(0\) \(-3\) \(2\) \(-3\) \(-\) \(q+(-1-\beta )q^{3}+q^{5}+(-2+\beta )q^{7}+\cdots\)
1840.2.a.k \(2\) \(14.692\) \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(2\) \(-2\) \(-\) \(q-\beta q^{3}+q^{5}-2\beta q^{7}+(1+\beta )q^{9}+4q^{11}+\cdots\)
1840.2.a.l \(2\) \(14.692\) \(\Q(\sqrt{5}) \) None None \(0\) \(-1\) \(2\) \(-1\) \(+\) \(q-\beta q^{3}+q^{5}+(-1+\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
1840.2.a.m \(2\) \(14.692\) \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(2\) \(-1\) \(+\) \(q-\beta q^{3}+q^{5}+(-1+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
1840.2.a.n \(2\) \(14.692\) \(\Q(\sqrt{21}) \) None None \(0\) \(1\) \(-2\) \(-1\) \(-\) \(q+\beta q^{3}-q^{5}+(-1+\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
1840.2.a.o \(2\) \(14.692\) \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(-2\) \(1\) \(-\) \(q+\beta q^{3}-q^{5}+(1-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
1840.2.a.p \(2\) \(14.692\) \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(-2\) \(2\) \(+\) \(q+q^{3}-q^{5}+(1+\beta )q^{7}-2q^{9}+(1-\beta )q^{11}+\cdots\)
1840.2.a.q \(3\) \(14.692\) 3.3.229.1 None None \(0\) \(-2\) \(3\) \(-7\) \(+\) \(q+(-1-\beta _{2})q^{3}+q^{5}+(-2+\beta _{2})q^{7}+\cdots\)
1840.2.a.r \(3\) \(14.692\) 3.3.1101.1 None None \(0\) \(-1\) \(-3\) \(-3\) \(+\) \(q-\beta _{1}q^{3}-q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
1840.2.a.s \(3\) \(14.692\) 3.3.2597.1 None None \(0\) \(-1\) \(3\) \(-2\) \(-\) \(q-\beta _{1}q^{3}+q^{5}+(-1+\beta _{1})q^{7}+(3+\beta _{2})q^{9}+\cdots\)
1840.2.a.t \(3\) \(14.692\) 3.3.621.1 None None \(0\) \(0\) \(-3\) \(-3\) \(+\) \(q-\beta _{1}q^{3}-q^{5}+(-1-\beta _{1})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
1840.2.a.u \(4\) \(14.692\) 4.4.15317.1 None None \(0\) \(2\) \(4\) \(3\) \(-\) \(q+(1+\beta _{2})q^{3}+q^{5}+(1+\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots\)
1840.2.a.v \(5\) \(14.692\) 5.5.13955077.1 None None \(0\) \(0\) \(-5\) \(2\) \(-\) \(q-\beta _{1}q^{3}-q^{5}+(\beta _{3}+\beta _{4})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
1840.2.e.a \(2\) \(14.692\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) \(q+2iq^{3}+(2+i)q^{5}-3iq^{7}-q^{9}+\cdots\)
1840.2.e.b \(2\) \(14.692\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) \(q+2iq^{3}+(2+i)q^{5}-iq^{7}-q^{9}-2iq^{13}+\cdots\)
1840.2.e.c \(4\) \(14.692\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(1+2\beta _{2})q^{5}+(3\beta _{1}+3\beta _{3})q^{7}+\cdots\)
1840.2.e.d \(8\) \(14.692\) 8.0.527896576.2 None None \(0\) \(0\) \(-6\) \(0\) \(q+(-\beta _{1}+\beta _{2}+\beta _{4})q^{3}+(-1-\beta _{6}+\cdots)q^{5}+\cdots\)
1840.2.e.e \(8\) \(14.692\) 8.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{2}-\beta _{5})q^{3}+(\beta _{3}+\beta _{6})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1840.2.e.f \(12\) \(14.692\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{5}+\beta _{6})q^{3}-\beta _{8}q^{5}+(-\beta _{1}-\beta _{6}+\cdots)q^{7}+\cdots\)
1840.2.e.g \(14\) \(14.692\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{8}q^{3}-\beta _{5}q^{5}+(\beta _{7}-\beta _{13})q^{7}+(1+\cdots)q^{9}+\cdots\)
1840.2.e.h \(16\) \(14.692\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(-2\) \(0\) \(q-\beta _{5}q^{3}-\beta _{10}q^{5}+(-\beta _{2}+\beta _{13})q^{7}+\cdots\)
1840.2.i.a \(16\) \(14.692\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{8}q^{5}+(\beta _{3}-\beta _{10})q^{7}+(-2+\cdots)q^{9}+\cdots\)
1840.2.i.b \(16\) \(14.692\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{3}+\beta _{2}q^{5}+\beta _{13}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots\)
1840.2.i.c \(16\) \(14.692\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+\beta _{5}q^{5}+(-\beta _{10}+\beta _{14})q^{7}+\cdots\)
1840.2.m.a \(4\) \(14.692\) \(\Q(\sqrt{6}, \sqrt{-14})\) None None \(0\) \(-4\) \(0\) \(0\) \(q-q^{3}-\beta _{2}q^{5}-2q^{9}+(2\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots\)
1840.2.m.b \(4\) \(14.692\) \(\Q(\sqrt{5}, \sqrt{-23})\) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}-\beta _{2}q^{7}-3q^{9}+3\beta _{1}q^{17}+\cdots\)
1840.2.m.c \(4\) \(14.692\) \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(2\beta _{1}-\beta _{2})q^{3}+\beta _{3}q^{5}+3\beta _{2}q^{7}+\cdots\)
1840.2.m.d \(4\) \(14.692\) \(\Q(\sqrt{6}, \sqrt{-14})\) None None \(0\) \(4\) \(0\) \(0\) \(q+q^{3}+\beta _{2}q^{5}-2q^{9}+(2\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots\)
1840.2.m.e \(8\) \(14.692\) 8.0.\(\cdots\).1 \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}+\beta _{7}q^{7}-3q^{9}+(-\beta _{1}+\beta _{4}+\cdots)q^{17}+\cdots\)
1840.2.m.f \(8\) \(14.692\) 8.0.40960000.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+\beta _{6}q^{5}+2\beta _{5}q^{7}+2q^{9}+\cdots\)
1840.2.m.g \(40\) \(14.692\) None None \(0\) \(0\) \(0\) \(0\)
1840.3.c.a \(32\) \(50.136\) None None \(0\) \(0\) \(0\) \(0\)
1840.3.c.b \(56\) \(50.136\) None None \(0\) \(0\) \(0\) \(0\)
1840.3.k.a \(6\) \(50.136\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(-2\) \(0\) \(0\) \(q-\beta _{4}q^{3}-\beta _{3}q^{5}+(\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots\)
1840.3.k.b \(10\) \(50.136\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(2\) \(0\) \(0\) \(q-\beta _{5}q^{3}-\beta _{3}q^{5}+(\beta _{2}+\beta _{3})q^{7}+(-2+\cdots)q^{9}+\cdots\)
1840.3.k.c \(16\) \(50.136\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}-\beta _{4}q^{5}-\beta _{7}q^{7}+(4+\beta _{2}+\cdots)q^{9}+\cdots\)
1840.3.k.d \(16\) \(50.136\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{5})q^{7}+(5+\cdots)q^{9}+\cdots\)
1840.3.k.e \(48\) \(50.136\) None None \(0\) \(0\) \(0\) \(0\)
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