Learn more about

Refine search

Results (displaying matches 1-50 of 208) Next

Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1764.1.d.a \(2\) \(0.880\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{13}+(\zeta_{6}+\zeta_{6}^{2})q^{19}+\cdots\)
1764.1.g.a \(1\) \(0.880\) \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{7}) \) \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{16}-q^{25}+2q^{29}+\cdots\)
1764.1.g.b \(2\) \(0.880\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-\beta q^{5}-q^{8}+\beta q^{10}-\beta q^{13}+\cdots\)
1764.1.g.c \(2\) \(0.880\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-21}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}+iq^{11}+q^{16}+\cdots\)
1764.1.g.d \(2\) \(0.880\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-\beta q^{5}+q^{8}-\beta q^{10}+\beta q^{13}+\cdots\)
1764.1.h.a \(8\) \(0.880\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{4}q^{2}-q^{4}+(\zeta_{16}^{3}-\zeta_{16}^{5})q^{5}+\cdots\)
1764.1.q.a \(8\) \(0.880\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{9}q^{8}+\cdots\)
1764.1.q.b \(16\) \(0.880\) \(\Q(\zeta_{48})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{48}^{20}q^{2}-\zeta_{48}^{16}q^{4}+(-\zeta_{48}^{5}+\cdots)q^{5}+\cdots\)
1764.1.y.a \(2\) \(0.880\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{7}) \) \(-1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{8}-\zeta_{6}q^{16}+\cdots\)
1764.1.y.b \(4\) \(0.880\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
1764.1.y.c \(4\) \(0.880\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-21}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{5}q^{11}+\cdots\)
1764.1.y.d \(4\) \(0.880\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
1764.1.z.a \(2\) \(0.880\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(1+\zeta_{6})q^{19}+\cdots\)
1764.1.co.a \(12\) \(0.880\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-\zeta_{42}^{16}q^{7}+(-\zeta_{42}^{8}+\zeta_{42}^{10})q^{13}+\cdots\)
1764.2.a.a \(1\) \(14.086\) \(\Q\) None None \(0\) \(0\) \(-3\) \(0\) \(+\) \(q-3q^{5}+3q^{11}+2q^{13}-3q^{17}-q^{19}+\cdots\)
1764.2.a.b \(1\) \(14.086\) \(\Q\) None None \(0\) \(0\) \(-2\) \(0\) \(-\) \(q-2q^{5}-2q^{11}-4q^{13}-6q^{17}+8q^{19}+\cdots\)
1764.2.a.c \(1\) \(14.086\) \(\Q\) None None \(0\) \(0\) \(-2\) \(0\) \(-\) \(q-2q^{5}-2q^{11}+3q^{13}+8q^{17}+q^{19}+\cdots\)
1764.2.a.d \(1\) \(14.086\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(q-5q^{13}+q^{19}-5q^{25}-11q^{31}+\cdots\)
1764.2.a.e \(1\) \(14.086\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(q-2q^{13}-8q^{19}-5q^{25}+4q^{31}+\cdots\)
1764.2.a.f \(1\) \(14.086\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+5q^{13}-q^{19}-5q^{25}+11q^{31}+\cdots\)
1764.2.a.g \(1\) \(14.086\) \(\Q\) None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+6q^{11}-2q^{13}+4q^{19}+6q^{23}+\cdots\)
1764.2.a.h \(1\) \(14.086\) \(\Q\) None None \(0\) \(0\) \(2\) \(0\) \(+\) \(q+2q^{5}-2q^{11}-3q^{13}-8q^{17}-q^{19}+\cdots\)
1764.2.a.i \(1\) \(14.086\) \(\Q\) None None \(0\) \(0\) \(2\) \(0\) \(-\) \(q+2q^{5}-2q^{11}+4q^{13}+6q^{17}-8q^{19}+\cdots\)
1764.2.a.j \(1\) \(14.086\) \(\Q\) None None \(0\) \(0\) \(3\) \(0\) \(-\) \(q+3q^{5}+3q^{11}-2q^{13}+3q^{17}+q^{19}+\cdots\)
1764.2.a.k \(1\) \(14.086\) \(\Q\) None None \(0\) \(0\) \(4\) \(0\) \(-\) \(q+4q^{5}-2q^{11}+6q^{13}-4q^{17}+4q^{19}+\cdots\)
1764.2.a.l \(2\) \(14.086\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta q^{5}-4q^{11}-3\beta q^{13}+\beta q^{17}+\cdots\)
1764.2.a.m \(4\) \(14.086\) \(\Q(\sqrt{2}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta _{2}q^{5}-\beta _{3}q^{11}-3\beta _{1}q^{13}+\beta _{2}q^{17}+\cdots\)
1764.2.b.a \(4\) \(14.086\) \(\Q(\zeta_{12})\) None None \(-4\) \(0\) \(0\) \(0\) \(q+(-1+\zeta_{12})q^{2}-2\zeta_{12}q^{4}-\zeta_{12}^{2}q^{5}+\cdots\)
1764.2.b.b \(4\) \(14.086\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None None \(-2\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-2-\beta _{2})q^{4}+\beta _{3}q^{5}+(2+\cdots)q^{8}+\cdots\)
1764.2.b.c \(4\) \(14.086\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
1764.2.b.d \(4\) \(14.086\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
1764.2.b.e \(4\) \(14.086\) 4.0.2048.2 \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+2q^{4}+(\beta _{1}+2\beta _{3})q^{5}+2\beta _{2}q^{8}+\cdots\)
1764.2.b.f \(4\) \(14.086\) 4.0.2048.2 \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+2q^{4}+\beta _{1}q^{5}+2\beta _{2}q^{8}+\cdots\)
1764.2.b.g \(4\) \(14.086\) 4.0.2048.2 \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+2q^{4}+(\beta _{1}+2\beta _{3})q^{5}-2\beta _{2}q^{8}+\cdots\)
1764.2.b.h \(4\) \(14.086\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(-2-\beta _{2})q^{4}+\beta _{3}q^{5}+(-2+\cdots)q^{8}+\cdots\)
1764.2.b.i \(8\) \(14.086\) 8.0.562828176.1 None None \(2\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{5}+(\beta _{3}+\cdots)q^{8}+\cdots\)
1764.2.b.j \(8\) \(14.086\) 8.0.562828176.1 None None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+\beta _{6}q^{4}+(\beta _{2}-\beta _{6})q^{5}+(-1+\cdots)q^{8}+\cdots\)
1764.2.b.k \(8\) \(14.086\) 8.0.\(\cdots\).10 None None \(4\) \(0\) \(0\) \(0\) \(q+(1+\beta _{3})q^{2}+(1+\beta _{3}+\beta _{5}-\beta _{6})q^{4}+\cdots\)
1764.2.b.l \(12\) \(14.086\) 12.0.\(\cdots\).1 None None \(-4\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(\beta _{5}+\beta _{6})q^{4}+(1-\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots\)
1764.2.b.m \(12\) \(14.086\) 12.0.\(\cdots\).1 None None \(-4\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}+(-\beta _{2}-\beta _{11})q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots\)
1764.2.b.n \(16\) \(14.086\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{2}+(-1+\beta _{1}-\beta _{10})q^{4}+\beta _{12}q^{5}+\cdots\)
1764.2.e.a \(2\) \(14.086\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{2}-2q^{4}+3\beta q^{5}-2\beta q^{8}-6q^{10}+\cdots\)
1764.2.e.b \(2\) \(14.086\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{2}-2q^{4}+\beta q^{5}-2\beta q^{8}-2q^{10}+\cdots\)
1764.2.e.c \(2\) \(14.086\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}-2q^{4}+3\beta q^{5}+2\beta q^{8}+6q^{10}+\cdots\)
1764.2.e.d \(4\) \(14.086\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}-2q^{4}+2\zeta_{8}q^{5}+2\zeta_{8}^{2}q^{8}+\cdots\)
1764.2.e.e \(4\) \(14.086\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-2q^{4}-\zeta_{8}q^{5}-2\zeta_{8}^{2}q^{8}+\cdots\)
1764.2.e.f \(8\) \(14.086\) 8.0.157351936.1 \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}-\beta _{1}q^{4}-\beta _{5}q^{8}+(\beta _{5}+\beta _{6}+\cdots)q^{11}+\cdots\)
1764.2.e.g \(12\) \(14.086\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+(1+\beta _{10})q^{4}-\beta _{4}q^{5}+(\beta _{6}+\cdots)q^{8}+\cdots\)
1764.2.e.h \(16\) \(14.086\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{5}q^{5}+(\beta _{3}-\beta _{5}+\cdots)q^{8}+\cdots\)
1764.2.e.i \(16\) \(14.086\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{5}q^{5}+(-\beta _{3}+\beta _{5}+\cdots)q^{8}+\cdots\)
Next

Download all search results for