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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
6300.2.a.a \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(q-q^{7}-6q^{11}+4q^{13}+6q^{17}+2q^{19}+\cdots\)
6300.2.a.b \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(q-q^{7}-4q^{11}-2q^{13}+2q^{17}-2q^{19}+\cdots\)
6300.2.a.c \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(q-q^{7}-3q^{11}-q^{13}-5q^{17}-8q^{19}+\cdots\)
6300.2.a.d \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(q-q^{7}-3q^{11}+q^{13}-3q^{17}+2q^{19}+\cdots\)
6300.2.a.e \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(q-q^{7}-3q^{11}+4q^{13}+2q^{19}-3q^{23}+\cdots\)
6300.2.a.f \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(q-q^{7}-q^{11}-4q^{13}+2q^{17}-4q^{19}+\cdots\)
6300.2.a.g \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(q-q^{7}-4q^{13}+4q^{17}+4q^{19}+8q^{23}+\cdots\)
6300.2.a.h \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(q-q^{7}+4q^{13}-6q^{17}+2q^{19}-6q^{23}+\cdots\)
6300.2.a.i \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(q-q^{7}+4q^{13}+6q^{17}+2q^{19}+6q^{23}+\cdots\)
6300.2.a.j \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(q-q^{7}+q^{11}-2q^{13}-8q^{17}-2q^{19}+\cdots\)
6300.2.a.k \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(q-q^{7}+q^{11}-2q^{13}+6q^{19}-q^{23}+\cdots\)
6300.2.a.l \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(q-q^{7}+2q^{11}-4q^{13}+2q^{17}+2q^{19}+\cdots\)
6300.2.a.m \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(q-q^{7}+3q^{11}+4q^{13}-6q^{17}-4q^{19}+\cdots\)
6300.2.a.n \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(q-q^{7}+4q^{11}+6q^{13}+2q^{17}+6q^{19}+\cdots\)
6300.2.a.o \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(q-q^{7}+5q^{11}+6q^{13}+4q^{17}-6q^{19}+\cdots\)
6300.2.a.p \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(q-q^{7}+6q^{11}-2q^{13}-4q^{19}-6q^{23}+\cdots\)
6300.2.a.q \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(+\) \(q+q^{7}-4q^{11}+2q^{17}-6q^{19}+6q^{23}+\cdots\)
6300.2.a.r \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(+\) \(q+q^{7}-4q^{11}+2q^{13}-2q^{17}-2q^{19}+\cdots\)
6300.2.a.s \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(+\) \(q+q^{7}-3q^{11}-4q^{13}+2q^{19}+3q^{23}+\cdots\)
6300.2.a.t \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(+\) \(q+q^{7}-3q^{11}+q^{13}+5q^{17}-8q^{19}+\cdots\)
6300.2.a.u \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(q+q^{7}-2q^{11}-4q^{13}+2q^{17}-2q^{19}+\cdots\)
6300.2.a.v \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(q+q^{7}-2q^{11}-4q^{13}+6q^{17}+6q^{19}+\cdots\)
6300.2.a.w \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(q+q^{7}-2q^{11}+6q^{13}-4q^{17}-4q^{19}+\cdots\)
6300.2.a.x \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(+\) \(q+q^{7}-q^{11}+4q^{13}-2q^{17}-4q^{19}+\cdots\)
6300.2.a.y \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(+\) \(q+q^{7}+4q^{13}-4q^{17}+4q^{19}-8q^{23}+\cdots\)
6300.2.a.z \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(q+q^{7}+q^{11}+2q^{13}+6q^{19}+q^{23}+\cdots\)
6300.2.a.ba \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(q+q^{7}+q^{11}+2q^{13}+8q^{17}-2q^{19}+\cdots\)
6300.2.a.bb \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(+\) \(q+q^{7}+3q^{11}-4q^{13}+6q^{17}-4q^{19}+\cdots\)
6300.2.a.bc \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(+\) \(q+q^{7}+4q^{11}-6q^{13}-2q^{17}+6q^{19}+\cdots\)
6300.2.a.bd \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(+\) \(q+q^{7}+4q^{11}-2q^{17}-6q^{19}-6q^{23}+\cdots\)
6300.2.a.be \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(q+q^{7}+5q^{11}-6q^{13}-4q^{17}-6q^{19}+\cdots\)
6300.2.a.bf \(1\) \(50.306\) \(\Q\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(q+q^{7}+5q^{11}+3q^{13}-q^{17}+6q^{19}+\cdots\)
6300.2.a.bg \(2\) \(50.306\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(q-q^{7}+\beta q^{11}-2q^{13}+2q^{19}-\beta q^{23}+\cdots\)
6300.2.a.bh \(2\) \(50.306\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(q-q^{7}+\beta q^{11}+2\beta q^{17}-3\beta q^{23}+\cdots\)
6300.2.a.bi \(2\) \(50.306\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(2\) \(+\) \(q+q^{7}+\beta q^{11}-2\beta q^{17}+3\beta q^{23}+\cdots\)
6300.2.a.bj \(2\) \(50.306\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(q+q^{7}+\beta q^{11}+2q^{13}+2q^{19}+\beta q^{23}+\cdots\)
6300.2.a.bk \(4\) \(50.306\) \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(-4\) \(+\) \(q-q^{7}+(-\beta _{1}-\beta _{3})q^{11}+(-1+\beta _{2}+\cdots)q^{13}+\cdots\)
6300.2.a.bl \(4\) \(50.306\) \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(4\) \(-\) \(q+q^{7}+(-\beta _{1}-\beta _{3})q^{11}+(1-\beta _{2})q^{13}+\cdots\)
6300.2.d.a \(4\) \(50.306\) \(\Q(\sqrt{-2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{3})q^{7}-\beta _{1}q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
6300.2.d.b \(4\) \(50.306\) \(\Q(\sqrt{-2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{3})q^{7}+\beta _{1}q^{11}+(\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots\)
6300.2.d.c \(4\) \(50.306\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(4\) \(q+(1+\beta _{1})q^{7}+\beta _{2}q^{11}+2\beta _{1}q^{13}+\cdots\)
6300.2.d.d \(12\) \(50.306\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(-2\) \(q+\beta _{5}q^{7}-\beta _{9}q^{11}+\beta _{8}q^{13}+\beta _{1}q^{17}+\cdots\)
6300.2.d.e \(12\) \(50.306\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(2\) \(q-\beta _{5}q^{7}-\beta _{9}q^{11}-\beta _{8}q^{13}-\beta _{1}q^{17}+\cdots\)
6300.2.d.f \(16\) \(50.306\) 16.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{7}-\beta _{1}q^{11}+\beta _{2}q^{13}-\beta _{4}q^{17}+\cdots\)
6300.2.f.a \(8\) \(50.306\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{2}+\beta _{3})q^{7}-\beta _{4}q^{11}+(\beta _{3}+\beta _{7})q^{13}+\cdots\)
6300.2.f.b \(8\) \(50.306\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{3}q^{7}+\zeta_{24}^{5}q^{11}+(-\zeta_{24}-2\zeta_{24}^{3}+\cdots)q^{13}+\cdots\)
6300.2.f.c \(8\) \(50.306\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{2}+\beta _{3})q^{7}-\beta _{4}q^{11}+(\beta _{3}+\beta _{7})q^{13}+\cdots\)
6300.2.f.d \(24\) \(50.306\) None \(0\) \(0\) \(0\) \(0\)
6300.2.k.a \(2\) \(50.306\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{7}-6q^{11}-4iq^{13}+6iq^{17}+\cdots\)
6300.2.k.b \(2\) \(50.306\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-4q^{11}+2iq^{17}+6q^{19}+\cdots\)
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