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Results (displaying all 40 matches)

Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1175.1.b.a \(2\) \(0.586\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-47}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}+q^{6}-iq^{7}-iq^{8}+\cdots\)
1175.1.b.b \(4\) \(0.586\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-47}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
1175.1.b.c \(8\) \(0.586\) 8.0.324000000.1 \(\Q(\sqrt{-47}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{3}+\beta _{7})q^{2}+(\beta _{3}+\beta _{4})q^{3}+\cdots\)
1175.1.d.a \(1\) \(0.586\) \(\Q\) \(\Q(\sqrt{-47}) \) None \(-1\) \(-1\) \(0\) \(-1\) \(q-q^{2}-q^{3}+q^{6}-q^{7}+q^{8}+q^{14}+\cdots\)
1175.1.d.b \(1\) \(0.586\) \(\Q\) \(\Q(\sqrt{-47}) \) None \(1\) \(1\) \(0\) \(1\) \(q+q^{2}+q^{3}+q^{6}+q^{7}-q^{8}+q^{14}+\cdots\)
1175.1.d.c \(2\) \(0.586\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-47}) \) None \(1\) \(1\) \(0\) \(1\) \(q+(1-\beta )q^{2}+\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots\)
1175.1.d.d \(4\) \(0.586\) \(\Q(\zeta_{15})^+\) \(\Q(\sqrt{-47}) \) None \(-1\) \(-1\) \(0\) \(-1\) \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1+\beta _{3})q^{4}+\cdots\)
1175.1.d.e \(4\) \(0.586\) \(\Q(\zeta_{15})^+\) \(\Q(\sqrt{-47}) \) None \(1\) \(1\) \(0\) \(1\) \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{3})q^{4}+\cdots\)
1175.2.a.a \(1\) \(9.382\) \(\Q\) None None \(-2\) \(-2\) \(0\) \(2\) \(+\) \(q-2q^{2}-2q^{3}+2q^{4}+4q^{6}+2q^{7}+\cdots\)
1175.2.a.b \(1\) \(9.382\) \(\Q\) None None \(1\) \(1\) \(0\) \(-1\) \(+\) \(q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots\)
1175.2.a.c \(1\) \(9.382\) \(\Q\) None None \(1\) \(1\) \(0\) \(-1\) \(+\) \(q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots\)
1175.2.a.d \(3\) \(9.382\) \(\Q(\zeta_{18})^+\) None None \(0\) \(0\) \(0\) \(0\) \(+\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(-1-\beta _{1}+\cdots)q^{6}+\cdots\)
1175.2.a.e \(3\) \(9.382\) \(\Q(\zeta_{18})^+\) None None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(-1-\beta _{1}+\cdots)q^{6}+\cdots\)
1175.2.a.f \(4\) \(9.382\) 4.4.1957.1 None None \(-1\) \(0\) \(0\) \(-4\) \(+\) \(q-\beta _{3}q^{2}+(\beta _{2}+\beta _{3})q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1175.2.a.g \(5\) \(9.382\) 5.5.106069.1 None None \(4\) \(5\) \(0\) \(5\) \(-\) \(q+(1+\beta _{2})q^{2}+(1-\beta _{3})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
1175.2.a.h \(7\) \(9.382\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(-1\) \(-1\) \(0\) \(3\) \(-\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{4})q^{4}-\beta _{5}q^{6}+\cdots\)
1175.2.a.i \(11\) \(9.382\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(-4\) \(-4\) \(0\) \(-12\) \(+\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{1}+\beta _{6})q^{4}+\cdots\)
1175.2.a.j \(11\) \(9.382\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(4\) \(4\) \(0\) \(12\) \(-\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{1}+\beta _{6})q^{4}+\cdots\)
1175.2.a.k \(13\) \(9.382\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(2+\beta _{3})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
1175.2.a.l \(13\) \(9.382\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(2+\beta _{3})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
1175.2.c.a \(2\) \(9.382\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-2iq^{3}-2q^{4}+4q^{6}-2iq^{7}+\cdots\)
1175.2.c.b \(2\) \(9.382\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}+q^{4}+q^{6}-iq^{7}+3iq^{8}+\cdots\)
1175.2.c.c \(2\) \(9.382\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}+q^{4}+q^{6}-iq^{7}+3iq^{8}+\cdots\)
1175.2.c.d \(6\) \(9.382\) 6.0.419904.1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{5})q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots\)
1175.2.c.e \(8\) \(9.382\) 8.0.980441344.2 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+(\beta _{3}-\beta _{7})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
1175.2.c.f \(10\) \(9.382\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+(37+1129\beta _{1}-405\beta _{2}+204\beta _{3}+\cdots)q^{2}+\cdots\)
1175.2.c.g \(14\) \(9.382\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(33747-2353\beta _{1}-19985\beta _{2}+\cdots)q^{3}+\cdots\)
1175.2.c.h \(26\) \(9.382\) None None \(0\) \(0\) \(0\) \(0\)
1175.4.a.a \(3\) \(69.327\) 3.3.1101.1 None None \(5\) \(5\) \(0\) \(45\) \(+\) \(q+(2+\beta _{2})q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+(2+\cdots)q^{4}+\cdots\)
1175.4.a.b \(8\) \(69.327\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-3\) \(-7\) \(0\) \(-39\) \(-\) \(q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(5-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
1175.4.a.c \(8\) \(69.327\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(3\) \(10\) \(0\) \(15\) \(-\) \(q+\beta _{1}q^{2}+(2-\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
1175.4.a.d \(10\) \(69.327\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(-7\) \(-8\) \(0\) \(-9\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{2})q^{3}+(4+\cdots)q^{4}+\cdots\)
1175.4.a.e \(13\) \(69.327\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(3\) \(10\) \(0\) \(19\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(4+\beta _{5})q^{4}+\cdots\)
1175.4.a.f \(15\) \(69.327\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None None \(-7\) \(-8\) \(0\) \(-13\) \(+\) \(q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(5+\beta _{3})q^{4}+\cdots\)
1175.4.a.g \(18\) \(69.327\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-1\) \(-7\) \(0\) \(-6\) \(-\) \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(3+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1175.4.a.h \(18\) \(69.327\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(1\) \(7\) \(0\) \(6\) \(-\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(3+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1175.4.a.i \(28\) \(69.327\) None None \(-1\) \(-7\) \(0\) \(-6\) \(+\)
1175.4.a.j \(28\) \(69.327\) None None \(1\) \(7\) \(0\) \(6\) \(+\)
1175.4.a.k \(35\) \(69.327\) None None \(-8\) \(-12\) \(0\) \(-84\) \(-\)
1175.4.a.l \(35\) \(69.327\) None None \(8\) \(12\) \(0\) \(84\) \(+\)


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