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Results (displaying all 46 matches)

Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1001.1.r.a \(4\) \(0.500\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-\zeta_{12}^{3}q^{8}+\cdots\)
1001.1.y.a \(2\) \(0.500\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-143}) \) None \(-1\) \(1\) \(0\) \(1\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-q^{6}+\zeta_{6}q^{7}-q^{8}+\cdots\)
1001.1.y.b \(2\) \(0.500\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-143}) \) None \(1\) \(1\) \(0\) \(-1\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}+q^{6}-\zeta_{6}q^{7}+q^{8}+\cdots\)
1001.1.y.c \(8\) \(0.500\) \(\Q(\zeta_{15})\) \(\Q(\sqrt{-143}) \) None \(-1\) \(-1\) \(0\) \(1\) \(q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots\)
1001.1.y.d \(8\) \(0.500\) \(\Q(\zeta_{15})\) \(\Q(\sqrt{-143}) \) None \(1\) \(-1\) \(0\) \(-1\) \(q+(-\zeta_{30}^{4}-\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots\)
1001.1.bo.a \(4\) \(0.500\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
1001.2.a.a \(1\) \(7.993\) \(\Q\) None None \(-2\) \(-3\) \(-3\) \(-1\) \(-\) \(q-2q^{2}-3q^{3}+2q^{4}-3q^{5}+6q^{6}+\cdots\)
1001.2.a.b \(1\) \(7.993\) \(\Q\) None None \(-1\) \(0\) \(-2\) \(-1\) \(-\) \(q-q^{2}-q^{4}-2q^{5}-q^{7}+3q^{8}-3q^{9}+\cdots\)
1001.2.a.c \(1\) \(7.993\) \(\Q\) None None \(0\) \(2\) \(-1\) \(-1\) \(+\) \(q+2q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}-q^{11}+\cdots\)
1001.2.a.d \(2\) \(7.993\) \(\Q(\sqrt{5}) \) None None \(0\) \(3\) \(3\) \(2\) \(-\) \(q+(1-2\beta )q^{2}+(2-\beta )q^{3}+3q^{4}+(1+\cdots)q^{5}+\cdots\)
1001.2.a.e \(2\) \(7.993\) \(\Q(\sqrt{21}) \) None None \(2\) \(1\) \(-1\) \(2\) \(-\) \(q+q^{2}+(1-\beta )q^{3}-q^{4}-\beta q^{5}+(1-\beta )q^{6}+\cdots\)
1001.2.a.f \(3\) \(7.993\) 3.3.1101.1 None None \(3\) \(-1\) \(1\) \(-3\) \(-\) \(q+q^{2}-\beta _{1}q^{3}-q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
1001.2.a.g \(4\) \(7.993\) 4.4.23301.1 None None \(-2\) \(-1\) \(-5\) \(4\) \(-\) \(q+(-1+\beta _{3})q^{2}-\beta _{1}q^{3}+(2-\beta _{2})q^{4}+\cdots\)
1001.2.a.h \(4\) \(7.993\) 4.4.1957.1 None None \(0\) \(-1\) \(5\) \(-4\) \(+\) \(q+(-\beta _{1}-\beta _{2}-\beta _{3})q^{2}+(\beta _{1}+\beta _{2})q^{3}+\cdots\)
1001.2.a.i \(5\) \(7.993\) 5.5.106069.1 None None \(-2\) \(-3\) \(0\) \(5\) \(+\) \(q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1001.2.a.j \(5\) \(7.993\) 5.5.216637.1 None None \(-2\) \(0\) \(-4\) \(-5\) \(+\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1001.2.a.k \(5\) \(7.993\) 5.5.81509.1 None None \(0\) \(-4\) \(-6\) \(5\) \(+\) \(q+\beta _{4}q^{2}+(-1+\beta _{2})q^{3}+(1-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
1001.2.a.l \(7\) \(7.993\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(0\) \(6\) \(9\) \(-7\) \(-\) \(q+\beta _{5}q^{2}+(1-\beta _{1})q^{3}+(4+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
1001.2.a.m \(8\) \(7.993\) 8.8.3212905625.1 None None \(2\) \(-1\) \(-5\) \(-8\) \(-\) \(q+\beta _{7}q^{2}-\beta _{2}q^{3}+(2-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1001.2.a.n \(11\) \(7.993\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(-1\) \(2\) \(7\) \(11\) \(-\) \(q-\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots\)
1001.2.b.a \(48\) \(7.993\) None None \(0\) \(0\) \(0\) \(4\)
1001.2.b.b \(48\) \(7.993\) None None \(0\) \(0\) \(0\) \(-4\)
1001.2.d.a \(2\) \(7.993\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(0\) \(0\) \(q+iq^{2}-2q^{3}+q^{4}-2iq^{5}-2iq^{6}+\cdots\)
1001.2.d.b \(30\) \(7.993\) None None \(0\) \(-8\) \(0\) \(0\)
1001.2.d.c \(40\) \(7.993\) None None \(0\) \(12\) \(0\) \(0\)
1001.2.i.a \(8\) \(7.993\) 8.0.447703281.1 None None \(-2\) \(-1\) \(1\) \(-16\) \(q-\beta _{3}q^{2}+(-\beta _{5}+\beta _{6})q^{3}+(-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
1001.2.i.b \(22\) \(7.993\) None None \(2\) \(-1\) \(0\) \(15\)
1001.2.i.c \(30\) \(7.993\) None None \(6\) \(2\) \(3\) \(1\)
1001.2.i.d \(50\) \(7.993\) None None \(-6\) \(2\) \(1\) \(1\)
1001.2.i.e \(50\) \(7.993\) None None \(0\) \(-2\) \(3\) \(-1\)
1001.4.a.a \(18\) \(59.061\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-4\) \(-12\) \(-34\) \(126\) \(-\) \(q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
1001.4.a.b \(18\) \(59.061\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(0\) \(-14\) \(-126\) \(-\) \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1001.4.a.c \(22\) \(59.061\) None None \(-4\) \(-2\) \(16\) \(-154\) \(-\)
1001.4.a.d \(22\) \(59.061\) None None \(0\) \(-14\) \(0\) \(154\) \(-\)
1001.4.a.e \(25\) \(59.061\) None None \(0\) \(-8\) \(-42\) \(-175\) \(+\)
1001.4.a.f \(25\) \(59.061\) None None \(0\) \(18\) \(48\) \(175\) \(+\)
1001.4.a.g \(25\) \(59.061\) None None \(4\) \(4\) \(-2\) \(175\) \(+\)
1001.4.a.h \(25\) \(59.061\) None None \(4\) \(6\) \(44\) \(-175\) \(+\)
1001.6.a.a \(35\) \(160.544\) None None \(-8\) \(-42\) \(-2\) \(1715\) \(+\)
1001.6.a.b \(35\) \(160.544\) None None \(-8\) \(7\) \(-178\) \(-1715\) \(+\)
1001.6.a.c \(35\) \(160.544\) None None \(0\) \(-29\) \(-258\) \(1715\) \(+\)
1001.6.a.d \(35\) \(160.544\) None None \(0\) \(-6\) \(180\) \(-1715\) \(+\)
1001.6.a.e \(38\) \(160.544\) None None \(0\) \(12\) \(-51\) \(1862\) \(-\)
1001.6.a.f \(38\) \(160.544\) None None \(8\) \(-24\) \(-71\) \(-1862\) \(-\)
1001.6.a.g \(42\) \(160.544\) None None \(0\) \(25\) \(73\) \(-2058\) \(-\)
1001.6.a.h \(42\) \(160.544\) None None \(8\) \(61\) \(191\) \(2058\) \(-\)


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