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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2775.1.b.a $2$ $1.385$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-111}) \) \(\Q(\sqrt{37}) \) \(0\) \(0\) \(0\) \(0\) $-$ \(q-iq^{3}+q^{4}-iq^{7}-q^{9}-iq^{12}+\cdots\)
2775.1.b.b $4$ $1.385$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-111}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots\)
2775.1.h.a $1$ $1.385$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-111}) \) \(\Q(\sqrt{37}) \) \(0\) \(-1\) \(0\) \(2\) $-$ \(q-q^{3}-q^{4}+2q^{7}+q^{9}+q^{12}+q^{16}+\cdots\)
2775.1.h.b $2$ $1.385$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-111}) \) None \(0\) \(2\) \(0\) \(0\) $-$ \(q-\beta q^{2}+q^{3}+q^{4}-\beta q^{6}+q^{9}+q^{12}+\cdots\)
2775.1.h.c $4$ $1.385$ \(\Q(\zeta_{16})^+\) \(\Q(\sqrt{-111}) \) None \(0\) \(-4\) \(0\) \(0\) $-$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
2775.1.h.d $4$ $1.385$ \(\Q(\zeta_{16})^+\) \(\Q(\sqrt{-111}) \) None \(0\) \(4\) \(0\) \(0\) $-$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
2775.1.k.a $4$ $1.385$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{8}q^{3}+q^{4}+\zeta_{8}q^{7}+\zeta_{8}^{2}q^{9}-\zeta_{8}q^{12}+\cdots\)
2775.1.u.a $4$ $1.385$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{8}^{3}q^{3}-q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}^{2}q^{9}+\cdots\)
2775.1.w.a $2$ $1.385$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) $-$ \(q+\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
2775.1.x.a $4$ $1.385$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{7}+\cdots\)
2775.1.z.a $2$ $1.385$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-1\) $-$ \(q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots\)
2775.1.bb.a $4$ $1.385$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{2}q^{4}-\zeta_{12}^{5}q^{7}+\cdots\)
2775.1.bg.a $4$ $1.385$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-111}) \) None \(-2\) \(-1\) \(-1\) \(8\) $-$ \(q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}-\zeta_{10}q^{3}+(-\zeta_{10}+\cdots)q^{4}+\cdots\)
2775.1.bg.b $4$ $1.385$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-111}) \) None \(2\) \(-1\) \(1\) \(8\) $-$ \(q+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{2}-\zeta_{10}q^{3}+(-\zeta_{10}+\cdots)q^{4}+\cdots\)
2775.1.bg.c $8$ $1.385$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-111}) \) None \(0\) \(-2\) \(0\) \(-16\) $-$ \(q+(-\zeta_{20}^{3}-\zeta_{20}^{9})q^{2}-\zeta_{20}^{2}q^{3}+\cdots\)
2775.1.bg.d $16$ $1.385$ \(\Q(\zeta_{40})\) \(\Q(\sqrt{-111}) \) None \(0\) \(4\) \(0\) \(0\) $-$ \(q+(\zeta_{40}+\zeta_{40}^{7})q^{2}-\zeta_{40}^{8}q^{3}+(\zeta_{40}^{2}+\cdots)q^{4}+\cdots\)
2775.1.bi.a $32$ $1.385$ \(\Q(\zeta_{80})\) \(\Q(\sqrt{-111}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+(\zeta_{80}^{17}-\zeta_{80}^{31})q^{2}+\zeta_{80}^{28}q^{3}+\cdots\)
2775.1.bm.a $8$ $1.385$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{24}q^{3}+\zeta_{24}^{4}q^{4}+\zeta_{24}q^{7}+\zeta_{24}^{2}q^{9}+\cdots\)
2775.1.bw.a $8$ $1.385$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{24}^{7}q^{3}-\zeta_{24}^{4}q^{4}-\zeta_{24}^{7}q^{7}+\cdots\)
2775.1.bz.a $6$ $1.385$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-3\) $-$ \(q+\zeta_{18}^{5}q^{3}-\zeta_{18}^{8}q^{4}+(\zeta_{18}^{6}-\zeta_{18}^{7}+\cdots)q^{7}+\cdots\)
2775.1.bz.b $6$ $1.385$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(3\) $-$ \(q-\zeta_{18}^{5}q^{3}-\zeta_{18}^{8}q^{4}+(-\zeta_{18}^{6}+\zeta_{18}^{7}+\cdots)q^{7}+\cdots\)
2775.1.ca.a $12$ $1.385$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{36}^{7}q^{3}-\zeta_{36}^{4}q^{4}+(\zeta_{36}^{3}-\zeta_{36}^{17}+\cdots)q^{7}+\cdots\)
2775.1.cd.a $12$ $1.385$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{36}^{7}q^{3}+\zeta_{36}^{4}q^{4}+(-\zeta_{36}^{3}+\zeta_{36}^{17}+\cdots)q^{7}+\cdots\)
2775.1.ce.a $6$ $1.385$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-3\) $-$ \(q-\zeta_{18}^{5}q^{3}+\zeta_{18}^{8}q^{4}+(\zeta_{18}^{6}-\zeta_{18}^{7}+\cdots)q^{7}+\cdots\)
2775.1.ce.b $6$ $1.385$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(3\) $-$ \(q+\zeta_{18}^{5}q^{3}+\zeta_{18}^{8}q^{4}+(-\zeta_{18}^{6}+\zeta_{18}^{7}+\cdots)q^{7}+\cdots\)
2775.1.cy.a $24$ $1.385$ \(\Q(\zeta_{72})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{72}^{31}q^{3}+\zeta_{72}^{28}q^{4}+(-\zeta_{72}^{3}+\cdots)q^{7}+\cdots\)
2775.1.di.a $24$ $1.385$ \(\Q(\zeta_{72})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\zeta_{72}^{35}q^{3}-\zeta_{72}^{20}q^{4}+(-\zeta_{72}^{15}+\cdots)q^{7}+\cdots\)
2775.2.a.a $1$ $22.158$ \(\Q\) None None \(-2\) \(1\) \(0\) \(0\) $+$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}+q^{9}-2q^{11}+\cdots\)
2775.2.a.b $1$ $22.158$ \(\Q\) None None \(-2\) \(1\) \(0\) \(1\) $+$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}+q^{7}+q^{9}+\cdots\)
2775.2.a.c $1$ $22.158$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-3\) $+$ \(q-q^{3}-2q^{4}-3q^{7}+q^{9}+4q^{11}+\cdots\)
2775.2.a.d $1$ $22.158$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) $+$ \(q-q^{3}-2q^{4}-2q^{7}+q^{9}+2q^{12}+\cdots\)
2775.2.a.e $1$ $22.158$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-1\) $-$ \(q-q^{3}-2q^{4}-q^{7}+q^{9}-2q^{11}+2q^{12}+\cdots\)
2775.2.a.f $1$ $22.158$ \(\Q\) None None \(0\) \(-1\) \(0\) \(2\) $-$ \(q-q^{3}-2q^{4}+2q^{7}+q^{9}+4q^{11}+\cdots\)
2775.2.a.g $1$ $22.158$ \(\Q\) None None \(0\) \(1\) \(0\) \(1\) $+$ \(q+q^{3}-2q^{4}+q^{7}+q^{9}-2q^{11}-2q^{12}+\cdots\)
2775.2.a.h $1$ $22.158$ \(\Q\) None None \(0\) \(1\) \(0\) \(3\) $-$ \(q+q^{3}-2q^{4}+3q^{7}+q^{9}+4q^{11}+\cdots\)
2775.2.a.i $1$ $22.158$ \(\Q\) None None \(2\) \(-1\) \(0\) \(-1\) $-$ \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-q^{7}+q^{9}+\cdots\)
2775.2.a.j $1$ $22.158$ \(\Q\) None None \(2\) \(-1\) \(0\) \(0\) $+$ \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}+q^{9}-2q^{11}+\cdots\)
2775.2.a.k $2$ $22.158$ \(\Q(\sqrt{2}) \) None None \(-2\) \(-2\) \(0\) \(-4\) $+$ \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+(1+\cdots)q^{6}+\cdots\)
2775.2.a.l $2$ $22.158$ \(\Q(\sqrt{13}) \) None None \(-1\) \(-2\) \(0\) \(-2\) $-$ \(q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+\beta q^{6}-q^{7}+\cdots\)
2775.2.a.m $2$ $22.158$ \(\Q(\sqrt{5}) \) None None \(-1\) \(2\) \(0\) \(0\) $+$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
2775.2.a.n $2$ $22.158$ \(\Q(\sqrt{5}) \) None None \(1\) \(-2\) \(0\) \(2\) $+$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
2775.2.a.o $2$ $22.158$ \(\Q(\sqrt{13}) \) None None \(1\) \(2\) \(0\) \(6\) $-$ \(q+\beta q^{2}+q^{3}+(1+\beta )q^{4}+\beta q^{6}+3q^{7}+\cdots\)
2775.2.a.p $2$ $22.158$ \(\Q(\sqrt{2}) \) None None \(2\) \(2\) \(0\) \(4\) $-$ \(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+(1+\beta )q^{6}+\cdots\)
2775.2.a.q $2$ $22.158$ \(\Q(\sqrt{5}) \) None None \(3\) \(-2\) \(0\) \(4\) $-$ \(q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+(-1-\beta )q^{6}+\cdots\)
2775.2.a.r $3$ $22.158$ 3.3.148.1 None None \(-3\) \(3\) \(0\) \(4\) $-$ \(q+(-1-\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2775.2.a.s $3$ $22.158$ 3.3.229.1 None None \(-2\) \(-3\) \(0\) \(4\) $+$ \(q+(-1-\beta _{2})q^{2}-q^{3}+(2+\beta _{1})q^{4}+\cdots\)
2775.2.a.t $3$ $22.158$ 3.3.469.1 None None \(-1\) \(3\) \(0\) \(-4\) $+$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
2775.2.a.u $3$ $22.158$ 3.3.257.1 None None \(0\) \(-3\) \(0\) \(6\) $-$ \(q-\beta _{2}q^{2}-q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\)
2775.2.a.v $3$ $22.158$ 3.3.257.1 None None \(0\) \(3\) \(0\) \(-6\) $+$ \(q+\beta _{2}q^{2}+q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\)
2775.2.a.w $4$ $22.158$ 4.4.4400.1 None None \(-2\) \(-4\) \(0\) \(8\) $+$ \(q+(-1-\beta _{2})q^{2}-q^{3}+\beta _{2}q^{4}+(1+\beta _{2}+\cdots)q^{6}+\cdots\)
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