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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
256.1.c.a \(1\) \(0.128\) \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{9}-2q^{17}-q^{25}-2q^{41}+q^{49}+\cdots\)
256.2.a.a \(1\) \(2.044\) \(\Q\) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) \(+\) \(q-2q^{3}+q^{9}-6q^{11}-6q^{17}-2q^{19}+\cdots\)
256.2.a.b \(1\) \(2.044\) \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(+\) \(q-4q^{5}-3q^{9}-4q^{13}-2q^{17}+11q^{25}+\cdots\)
256.2.a.c \(1\) \(2.044\) \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(-\) \(q+4q^{5}-3q^{9}+4q^{13}-2q^{17}+11q^{25}+\cdots\)
256.2.a.d \(1\) \(2.044\) \(\Q\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(-\) \(q+2q^{3}+q^{9}+6q^{11}-6q^{17}+2q^{19}+\cdots\)
256.2.a.e \(2\) \(2.044\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta q^{3}+5q^{9}-\beta q^{11}+6q^{17}-3\beta q^{19}+\cdots\)
256.2.b.a \(2\) \(2.044\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-8\) \(q+iq^{3}+iq^{5}-4q^{7}-q^{9}+iq^{11}+\cdots\)
256.2.b.b \(2\) \(2.044\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{5}+3q^{9}+3iq^{13}+2q^{17}+q^{25}+\cdots\)
256.2.b.c \(2\) \(2.044\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(8\) \(q+iq^{3}-iq^{5}+4q^{7}-q^{9}+iq^{11}+\cdots\)
256.2.e.a \(8\) \(2.044\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{2}q^{3}-\zeta_{24}^{7}q^{5}+(\zeta_{24}^{2}-\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
256.2.e.b \(8\) \(2.044\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{2}q^{3}+\zeta_{24}^{7}q^{5}+(-\zeta_{24}^{2}+\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
256.2.g.a \(4\) \(2.044\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(4\) \(-4\) \(q+(\zeta_{8}+\zeta_{8}^{2})q^{3}+(1+\zeta_{8}+2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{5}+\cdots\)
256.2.g.b \(4\) \(2.044\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(4\) \(4\) \(q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(1+\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
256.2.g.c \(8\) \(2.044\) 8.0.18939904.2 None None \(0\) \(-4\) \(0\) \(8\) \(q+(-1+\beta _{1}+\beta _{6}-\beta _{7})q^{3}+(\beta _{4}-\beta _{7})q^{5}+\cdots\)
256.2.g.d \(8\) \(2.044\) 8.0.18939904.2 None None \(0\) \(4\) \(0\) \(-8\) \(q+(\beta _{2}+\beta _{6}-\beta _{7})q^{3}+(\beta _{6}+\beta _{7})q^{5}+\cdots\)
256.2.i.a \(56\) \(2.044\) None None \(0\) \(8\) \(-8\) \(8\)
256.2.m.a \(992\) \(2.044\) None None \(-32\) \(-32\) \(-32\) \(-32\)
256.3.c.a \(1\) \(6.975\) \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-8\) \(0\) \(q-8q^{5}+9q^{9}+24q^{13}+30q^{17}+\cdots\)
256.3.c.b \(1\) \(6.975\) \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(8\) \(0\) \(q+8q^{5}+9q^{9}-24q^{13}+30q^{17}+\cdots\)
256.3.c.c \(2\) \(6.975\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(-8\) \(0\) \(q+\beta q^{3}-4q^{5}+4\beta q^{7}+q^{9}-5\beta q^{11}+\cdots\)
256.3.c.d \(2\) \(6.975\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{3}-23q^{9}+3\beta q^{11}-2q^{17}+\cdots\)
256.3.c.e \(2\) \(6.975\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+5q^{9}+7iq^{11}+2q^{17}+17iq^{19}+\cdots\)
256.3.c.f \(2\) \(6.975\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(8\) \(0\) \(q+\beta q^{3}+4q^{5}-4\beta q^{7}+q^{9}-5\beta q^{11}+\cdots\)
256.3.c.g \(4\) \(6.975\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{7}-3q^{9}+\cdots\)
256.3.d.a \(2\) \(6.975\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-8\) \(0\) \(0\) \(q-4q^{3}+iq^{5}-4iq^{7}+7q^{9}-4q^{11}+\cdots\)
256.3.d.b \(2\) \(6.975\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{5}-9q^{9}+5iq^{13}-30q^{17}+\cdots\)
256.3.d.c \(2\) \(6.975\) \(\Q(\sqrt{-1}) \) None None \(0\) \(8\) \(0\) \(0\) \(q+4q^{3}+iq^{5}+4iq^{7}+7q^{9}+4q^{11}+\cdots\)
256.3.d.d \(4\) \(6.975\) \(\Q(\zeta_{8})\) None None \(0\) \(-8\) \(0\) \(0\) \(q+(-2-\zeta_{8}^{2})q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
256.3.d.e \(4\) \(6.975\) \(\Q(\zeta_{8})\) None None \(0\) \(8\) \(0\) \(0\) \(q+(2-\zeta_{8}^{2})q^{3}+(\zeta_{8}-\zeta_{8}^{3})q^{5}+(2\zeta_{8}+\cdots)q^{7}+\cdots\)
256.3.f.a \(8\) \(6.975\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(-16\) \(0\) \(q+\zeta_{24}^{2}q^{3}+(-2-2\zeta_{24}+\zeta_{24}^{4}+\cdots)q^{5}+\cdots\)
256.3.f.b \(8\) \(6.975\) 8.0.8540717056.1 None None \(0\) \(0\) \(-16\) \(0\) \(q+\beta _{2}q^{3}+(-2-2\beta _{1}-\beta _{6})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
256.3.f.c \(8\) \(6.975\) 8.0.8540717056.1 None None \(0\) \(0\) \(16\) \(0\) \(q+\beta _{2}q^{3}+(2+2\beta _{1}+\beta _{6})q^{5}+(\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
256.3.f.d \(8\) \(6.975\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(16\) \(0\) \(q+\zeta_{24}^{2}q^{3}+(2+2\zeta_{24}-\zeta_{24}^{4})q^{5}+\cdots\)
256.3.h.a \(28\) \(6.975\) None None \(0\) \(-4\) \(4\) \(4\)
256.3.h.b \(28\) \(6.975\) None None \(0\) \(4\) \(4\) \(-4\)
256.3.j.a \(120\) \(6.975\) None None \(0\) \(8\) \(-8\) \(8\)
256.3.n.a \(2016\) \(6.975\) None None \(-32\) \(-32\) \(-32\) \(-32\)
256.4.a.a \(1\) \(15.104\) \(\Q\) \(\Q(\sqrt{-2}) \) None \(0\) \(-10\) \(0\) \(0\) \(-\) \(q-10q^{3}+73q^{9}+18q^{11}+90q^{17}+\cdots\)
256.4.a.b \(1\) \(15.104\) \(\Q\) None None \(0\) \(-8\) \(-12\) \(32\) \(-\) \(q-8q^{3}-12q^{5}+2^{5}q^{7}+37q^{9}+8q^{11}+\cdots\)
256.4.a.c \(1\) \(15.104\) \(\Q\) None None \(0\) \(-8\) \(12\) \(-32\) \(+\) \(q-8q^{3}+12q^{5}-2^{5}q^{7}+37q^{9}+8q^{11}+\cdots\)
256.4.a.d \(1\) \(15.104\) \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(+\) \(q-4q^{5}-3^{3}q^{9}+92q^{13}+94q^{17}+\cdots\)
256.4.a.e \(1\) \(15.104\) \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(-\) \(q+4q^{5}-3^{3}q^{9}-92q^{13}+94q^{17}+\cdots\)
256.4.a.f \(1\) \(15.104\) \(\Q\) None None \(0\) \(8\) \(-12\) \(-32\) \(-\) \(q+8q^{3}-12q^{5}-2^{5}q^{7}+37q^{9}-8q^{11}+\cdots\)
256.4.a.g \(1\) \(15.104\) \(\Q\) None None \(0\) \(8\) \(12\) \(32\) \(+\) \(q+8q^{3}+12q^{5}+2^{5}q^{7}+37q^{9}-8q^{11}+\cdots\)
256.4.a.h \(1\) \(15.104\) \(\Q\) \(\Q(\sqrt{-2}) \) None \(0\) \(10\) \(0\) \(0\) \(+\) \(q+10q^{3}+73q^{9}-18q^{11}+90q^{17}+\cdots\)
256.4.a.i \(2\) \(15.104\) \(\Q(\sqrt{3}) \) None None \(0\) \(-4\) \(0\) \(0\) \(+\) \(q-2q^{3}-\beta q^{5}-2\beta q^{7}-23q^{9}+42q^{11}+\cdots\)
256.4.a.j \(2\) \(15.104\) \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(0\) \(-16\) \(-\) \(q+\beta q^{3}-2\beta q^{5}-8q^{7}+q^{9}+3\beta q^{11}+\cdots\)
256.4.a.k \(2\) \(15.104\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta q^{3}-19q^{9}-5^{2}\beta q^{11}-90q^{17}+\cdots\)
256.4.a.l \(2\) \(15.104\) \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(0\) \(16\) \(+\) \(q+\beta q^{3}+2\beta q^{5}+8q^{7}+q^{9}+3\beta q^{11}+\cdots\)
256.4.a.m \(2\) \(15.104\) \(\Q(\sqrt{3}) \) None None \(0\) \(4\) \(0\) \(0\) \(-\) \(q+2q^{3}-\beta q^{5}+2\beta q^{7}-23q^{9}-42q^{11}+\cdots\)
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