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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2475.1.b.a \(1\) \(1.235\) \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{4}+q^{11}+q^{16}-2q^{31}+q^{44}+\cdots\)
2475.1.b.b \(2\) \(1.235\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{2}-q^{4}-\beta q^{7}-q^{11}-\beta q^{13}+\cdots\)
2475.1.b.c \(2\) \(1.235\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}-q^{4}-\beta q^{7}+q^{11}-\beta q^{13}+\cdots\)
2475.1.m.a \(8\) \(1.235\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{16}+\zeta_{16}^{3})q^{2}+(\zeta_{16}^{2}-\zeta_{16}^{4}+\cdots)q^{4}+\cdots\)
2475.1.m.b \(8\) \(1.235\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{16}-\zeta_{16}^{3})q^{2}+(\zeta_{16}^{2}-\zeta_{16}^{4}+\cdots)q^{4}+\cdots\)
2475.1.t.a \(4\) \(1.235\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{2}q^{11}+\cdots\)
2475.1.y.a \(2\) \(1.235\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(0\) \(0\) \(q+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{11}+\cdots\)
2475.1.y.b \(4\) \(1.235\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{2}q^{11}+\cdots\)
2475.1.bs.a \(4\) \(1.235\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{10}^{4}q^{4}+q^{5}+\zeta_{10}^{2}q^{11}-\zeta_{10}^{3}q^{16}+\cdots\)
2475.1.bu.a \(4\) \(1.235\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{10}^{4}q^{4}-q^{5}-\zeta_{10}^{2}q^{11}-\zeta_{10}^{3}q^{16}+\cdots\)
2475.1.cr.a \(4\) \(1.235\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+\zeta_{12}^{4}q^{3}-\zeta_{12}q^{4}-\zeta_{12}^{2}q^{9}+\zeta_{12}^{5}q^{11}+\cdots\)
2475.1.cr.b \(4\) \(1.235\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-\zeta_{12}q^{4}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{5}q^{11}+\cdots\)
2475.1.eu.a \(8\) \(1.235\) \(\Q(\zeta_{15})\) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(-4\) \(0\) \(q+\zeta_{30}^{2}q^{3}+\zeta_{30}^{8}q^{4}+\zeta_{30}^{10}q^{5}+\cdots\)
2475.1.eu.b \(8\) \(1.235\) \(\Q(\zeta_{15})\) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(8\) \(0\) \(q+\zeta_{30}^{14}q^{3}+\zeta_{30}^{8}q^{4}+q^{5}-\zeta_{30}^{13}q^{9}+\cdots\)
2475.1.ev.a \(8\) \(1.235\) \(\Q(\zeta_{15})\) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(-8\) \(0\) \(q+\zeta_{30}^{7}q^{3}-\zeta_{30}^{4}q^{4}-q^{5}+\zeta_{30}^{14}q^{9}+\cdots\)
2475.1.ev.b \(8\) \(1.235\) \(\Q(\zeta_{15})\) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(4\) \(0\) \(q-\zeta_{30}q^{3}-\zeta_{30}^{4}q^{4}+\zeta_{30}^{5}q^{5}+\zeta_{30}^{2}q^{9}+\cdots\)
2475.1.fy.a \(16\) \(1.235\) \(\Q(\zeta_{60})\) \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-\zeta_{60}^{8}q^{3}-\zeta_{60}^{17}q^{4}-\zeta_{60}^{25}q^{5}+\cdots\)
2475.1.fy.b \(16\) \(1.235\) \(\Q(\zeta_{60})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{60}^{11}q^{3}-\zeta_{60}^{17}q^{4}-\zeta_{60}^{15}q^{5}+\cdots\)
2475.2.a.a \(1\) \(19.763\) \(\Q\) None None \(-2\) \(0\) \(0\) \(2\) \(-\) \(q-2q^{2}+2q^{4}+2q^{7}-q^{11}-4q^{13}+\cdots\)
2475.2.a.b \(1\) \(19.763\) \(\Q\) None None \(-1\) \(0\) \(0\) \(-3\) \(+\) \(q-q^{2}-q^{4}-3q^{7}+3q^{8}+q^{11}+2q^{13}+\cdots\)
2475.2.a.c \(1\) \(19.763\) \(\Q\) None None \(-1\) \(0\) \(0\) \(2\) \(-\) \(q-q^{2}-q^{4}+2q^{7}+3q^{8}+q^{11}+2q^{13}+\cdots\)
2475.2.a.d \(1\) \(19.763\) \(\Q\) None None \(-1\) \(0\) \(0\) \(3\) \(+\) \(q-q^{2}-q^{4}+3q^{7}+3q^{8}-q^{11}-2q^{13}+\cdots\)
2475.2.a.e \(1\) \(19.763\) \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) \(-\) \(q-2q^{4}-q^{7}+q^{11}-q^{13}+4q^{16}+\cdots\)
2475.2.a.f \(1\) \(19.763\) \(\Q\) None None \(0\) \(0\) \(0\) \(1\) \(+\) \(q-2q^{4}+q^{7}+q^{11}+q^{13}+4q^{16}+\cdots\)
2475.2.a.g \(1\) \(19.763\) \(\Q\) None None \(1\) \(0\) \(0\) \(-4\) \(-\) \(q+q^{2}-q^{4}-4q^{7}-3q^{8}-q^{11}+2q^{13}+\cdots\)
2475.2.a.h \(1\) \(19.763\) \(\Q\) None None \(1\) \(0\) \(0\) \(-3\) \(-\) \(q+q^{2}-q^{4}-3q^{7}-3q^{8}-q^{11}+2q^{13}+\cdots\)
2475.2.a.i \(1\) \(19.763\) \(\Q\) None None \(1\) \(0\) \(0\) \(0\) \(+\) \(q+q^{2}-q^{4}-3q^{8}+q^{11}-2q^{13}+\cdots\)
2475.2.a.j \(1\) \(19.763\) \(\Q\) None None \(1\) \(0\) \(0\) \(2\) \(+\) \(q+q^{2}-q^{4}+2q^{7}-3q^{8}-q^{11}+2q^{13}+\cdots\)
2475.2.a.k \(1\) \(19.763\) \(\Q\) None None \(1\) \(0\) \(0\) \(3\) \(-\) \(q+q^{2}-q^{4}+3q^{7}-3q^{8}+q^{11}-2q^{13}+\cdots\)
2475.2.a.l \(2\) \(19.763\) \(\Q(\sqrt{2}) \) None None \(-2\) \(0\) \(0\) \(-2\) \(+\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(-1-\beta )q^{7}+\cdots\)
2475.2.a.m \(2\) \(19.763\) \(\Q(\sqrt{2}) \) None None \(-2\) \(0\) \(0\) \(4\) \(+\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(2+2\beta )q^{7}+\cdots\)
2475.2.a.n \(2\) \(19.763\) \(\Q(\sqrt{5}) \) None None \(-1\) \(0\) \(0\) \(1\) \(-\) \(q-\beta q^{2}+(-1+\beta )q^{4}+(2-3\beta )q^{7}+\cdots\)
2475.2.a.o \(2\) \(19.763\) \(\Q(\sqrt{13}) \) None None \(-1\) \(0\) \(0\) \(5\) \(-\) \(q-\beta q^{2}+(1+\beta )q^{4}+(2+\beta )q^{7}-3q^{8}+\cdots\)
2475.2.a.p \(2\) \(19.763\) \(\Q(\sqrt{17}) \) None None \(-1\) \(0\) \(0\) \(-2\) \(+\) \(q-\beta q^{2}+(2+\beta )q^{4}-q^{7}+(-4-\beta )q^{8}+\cdots\)
2475.2.a.q \(2\) \(19.763\) \(\Q(\sqrt{17}) \) None None \(-1\) \(0\) \(0\) \(2\) \(+\) \(q-\beta q^{2}+(2+\beta )q^{4}+q^{7}+(-4-\beta )q^{8}+\cdots\)
2475.2.a.r \(2\) \(19.763\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(-4\) \(+\) \(q+\beta q^{2}+q^{4}-2q^{7}-\beta q^{8}+q^{11}+\cdots\)
2475.2.a.s \(2\) \(19.763\) \(\Q(\sqrt{5}) \) None None \(1\) \(0\) \(0\) \(-1\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{4}+(-2+3\beta )q^{7}+\cdots\)
2475.2.a.t \(2\) \(19.763\) \(\Q(\sqrt{13}) \) None None \(1\) \(0\) \(0\) \(-5\) \(+\) \(q+\beta q^{2}+(1+\beta )q^{4}+(-2-\beta )q^{7}+3q^{8}+\cdots\)
2475.2.a.u \(2\) \(19.763\) \(\Q(\sqrt{17}) \) None None \(1\) \(0\) \(0\) \(-2\) \(-\) \(q+\beta q^{2}+(2+\beta )q^{4}-q^{7}+(4+\beta )q^{8}+\cdots\)
2475.2.a.v \(2\) \(19.763\) \(\Q(\sqrt{17}) \) None None \(1\) \(0\) \(0\) \(2\) \(-\) \(q+\beta q^{2}+(2+\beta )q^{4}+q^{7}+(4+\beta )q^{8}+\cdots\)
2475.2.a.w \(2\) \(19.763\) \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(0\) \(2\) \(-\) \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(1-\beta )q^{7}+\cdots\)
2475.2.a.x \(2\) \(19.763\) \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(0\) \(4\) \(-\) \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2q^{7}+(3+\cdots)q^{8}+\cdots\)
2475.2.a.y \(3\) \(19.763\) 3.3.148.1 None None \(-3\) \(0\) \(0\) \(8\) \(-\) \(q+(-1-\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2475.2.a.z \(3\) \(19.763\) 3.3.568.1 None None \(-2\) \(0\) \(0\) \(-3\) \(+\) \(q+(-1+\beta _{1})q^{2}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{7}+\cdots\)
2475.2.a.ba \(3\) \(19.763\) 3.3.148.1 None None \(-1\) \(0\) \(0\) \(4\) \(+\) \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
2475.2.a.bb \(3\) \(19.763\) 3.3.148.1 None None \(-1\) \(0\) \(0\) \(0\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
2475.2.a.bc \(3\) \(19.763\) 3.3.148.1 None None \(1\) \(0\) \(0\) \(-4\) \(+\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
2475.2.a.bd \(3\) \(19.763\) 3.3.568.1 None None \(2\) \(0\) \(0\) \(3\) \(-\) \(q+(1-\beta _{1})q^{2}+(3+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
2475.2.a.be \(3\) \(19.763\) 3.3.148.1 None None \(3\) \(0\) \(0\) \(-8\) \(-\) \(q+(1+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(-3+\cdots)q^{7}+\cdots\)
2475.2.a.bf \(4\) \(19.763\) 4.4.48704.2 None None \(-2\) \(0\) \(0\) \(-4\) \(+\) \(q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{7}+\cdots\)
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