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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2700.1.b.a 2700.b 15.d $2$ $1.347$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{7}-iq^{13}-q^{19}-q^{31}+iq^{37}+\cdots\)
2700.1.b.b 2700.b 15.d $2$ $1.347$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{7}+iq^{13}+q^{19}+q^{31}-iq^{37}+\cdots\)
2700.1.c.a 2700.c 4.b $2$ $1.347$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-15}) \) None \(-1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}+\zeta_{6}^{2}q^{16}+\cdots\)
2700.1.c.b 2700.c 4.b $2$ $1.347$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-15}) \) None \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+\zeta_{6}^{2}q^{16}+\cdots\)
2700.1.g.a 2700.g 3.b $1$ $1.347$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-2q^{7}+q^{13}+2q^{19}-q^{31}+q^{37}+\cdots\)
2700.1.g.b 2700.g 3.b $1$ $1.347$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+q^{7}+q^{13}-q^{19}+2q^{31}+q^{37}+\cdots\)
2700.1.g.c 2700.g 3.b $1$ $1.347$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q+2q^{7}-q^{13}+2q^{19}-q^{31}-q^{37}+\cdots\)
2700.1.l.a 2700.l 5.c $4$ $1.347$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{7}+\beta _{3}q^{13}-\beta _{2}q^{19}-2q^{31}+\cdots\)
2700.1.l.b 2700.l 5.c $4$ $1.347$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{13}+2\beta _{2}q^{19}+q^{31}-\beta _{1}q^{37}+\cdots\)
2700.1.m.a 2700.m 60.l $8$ $1.347$ \(\Q(\zeta_{24})\) None \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{9}q^{2}-\zeta_{24}^{6}q^{4}-\zeta_{24}^{3}q^{8}+\cdots\)
2700.1.m.b 2700.m 60.l $8$ $1.347$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{3}q^{8}+\zeta_{24}^{4}q^{16}+\cdots\)
2700.1.t.a 2700.t 36.f $4$ $1.347$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{7}-\zeta_{12}^{3}q^{8}+\cdots\)
2700.1.bb.a 2700.bb 75.j $8$ $1.347$ \(\Q(\zeta_{20})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{3}q^{5}+(-\zeta_{20}+\zeta_{20}^{7})q^{11}+\cdots\)
2700.1.be.a 2700.be 180.v $8$ $1.347$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(\zeta_{24}^{3}-\zeta_{24}^{11}+\cdots)q^{7}+\cdots\)
2700.1.bj.a 2700.bj 108.j $12$ $1.347$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{36}^{11}q^{2}+\zeta_{36}q^{3}-\zeta_{36}^{4}q^{4}+\cdots\)
2700.1.ca.a 2700.ca 540.ag $24$ $1.347$ \(\Q(\zeta_{72})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{72}^{29}q^{2}+\zeta_{72}^{19}q^{3}-\zeta_{72}^{22}q^{4}+\cdots\)
2700.2.a.a 2700.a 1.a $1$ $21.560$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-5\) $-$ $N(\mathrm{U}(1))$ \(q-5q^{7}-2q^{13}-q^{19}+11q^{31}-11q^{37}+\cdots\)
2700.2.a.b 2700.a 1.a $1$ $21.560$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-5\) $+$ $N(\mathrm{U}(1))$ \(q-5q^{7}+7q^{13}-q^{19}-4q^{31}+q^{37}+\cdots\)
2700.2.a.c 2700.a 1.a $1$ $21.560$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) $-$ $N(\mathrm{U}(1))$ \(q-4q^{7}-7q^{13}+8q^{19}-7q^{31}+11q^{37}+\cdots\)
2700.2.a.d 2700.a 1.a $1$ $21.560$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{11}+q^{13}+6q^{17}+2q^{19}+\cdots\)
2700.2.a.e 2700.a 1.a $1$ $21.560$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-2q^{11}+6q^{13}-q^{17}-3q^{19}+\cdots\)
2700.2.a.f 2700.a 1.a $1$ $21.560$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-2q^{13}-3q^{17}+5q^{19}+3q^{23}+\cdots\)
2700.2.a.g 2700.a 1.a $1$ $21.560$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{7}-2q^{13}+3q^{17}+5q^{19}-3q^{23}+\cdots\)
2700.2.a.h 2700.a 1.a $1$ $21.560$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{7}+2q^{11}+6q^{13}+q^{17}-3q^{19}+\cdots\)
2700.2.a.i 2700.a 1.a $1$ $21.560$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{7}+3q^{11}+q^{13}-6q^{17}+2q^{19}+\cdots\)
2700.2.a.j 2700.a 1.a $1$ $21.560$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) $+$ $N(\mathrm{U}(1))$ \(q-q^{7}+2q^{13}-7q^{19}-7q^{31}-q^{37}+\cdots\)
2700.2.a.k 2700.a 1.a $1$ $21.560$ \(\Q\) None None \(0\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}-6q^{11}+q^{13}-q^{19}+6q^{23}+\cdots\)
2700.2.a.l 2700.a 1.a $1$ $21.560$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) $+$ $N(\mathrm{U}(1))$ \(q+q^{7}-2q^{13}-7q^{19}-7q^{31}+q^{37}+\cdots\)
2700.2.a.m 2700.a 1.a $1$ $21.560$ \(\Q\) None None \(0\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}+6q^{11}+q^{13}-q^{19}-6q^{23}+\cdots\)
2700.2.a.n 2700.a 1.a $1$ $21.560$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{11}-q^{13}-6q^{17}+2q^{19}+\cdots\)
2700.2.a.o 2700.a 1.a $1$ $21.560$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{7}-2q^{11}-6q^{13}+q^{17}-3q^{19}+\cdots\)
2700.2.a.p 2700.a 1.a $1$ $21.560$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{7}+2q^{11}-6q^{13}-q^{17}-3q^{19}+\cdots\)
2700.2.a.q 2700.a 1.a $1$ $21.560$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{7}+3q^{11}-q^{13}+6q^{17}+2q^{19}+\cdots\)
2700.2.a.r 2700.a 1.a $1$ $21.560$ \(\Q\) None None \(0\) \(0\) \(0\) \(4\) $+$ $\mathrm{SU}(2)$ \(q+4q^{7}-6q^{11}+4q^{13}-3q^{17}-7q^{19}+\cdots\)
2700.2.a.s 2700.a 1.a $1$ $21.560$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(4\) $-$ $N(\mathrm{U}(1))$ \(q+4q^{7}+7q^{13}+8q^{19}-7q^{31}-11q^{37}+\cdots\)
2700.2.a.t 2700.a 1.a $1$ $21.560$ \(\Q\) None None \(0\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+4q^{7}+6q^{11}+4q^{13}+3q^{17}-7q^{19}+\cdots\)
2700.2.a.u 2700.a 1.a $1$ $21.560$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(5\) $-$ $N(\mathrm{U}(1))$ \(q+5q^{7}+2q^{13}-q^{19}+11q^{31}+11q^{37}+\cdots\)
2700.2.a.v 2700.a 1.a $2$ $21.560$ \(\Q(\sqrt{10}) \) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}-\beta q^{11}-3q^{13}+2\beta q^{17}+3q^{19}+\cdots\)
2700.2.a.w 2700.a 1.a $2$ $21.560$ \(\Q(\sqrt{10}) \) None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}-\beta q^{11}+3q^{13}-2\beta q^{17}+3q^{19}+\cdots\)
2700.2.d.a 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}-6q^{11}-iq^{13}+q^{19}-6iq^{23}+\cdots\)
2700.2.d.b 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4iq^{7}-6q^{11}-4iq^{13}-3iq^{17}+\cdots\)
2700.2.d.c 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}-3q^{11}+iq^{13}-6iq^{17}+\cdots\)
2700.2.d.d 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+4iq^{7}-7iq^{13}-8q^{19}-7q^{31}+\cdots\)
2700.2.d.e 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}-2iq^{13}+3iq^{17}-5q^{19}+\cdots\)
2700.2.d.f 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}-2iq^{13}-3iq^{17}-5q^{19}+\cdots\)
2700.2.d.g 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+5iq^{7}+7iq^{13}+q^{19}-4q^{31}+\cdots\)
2700.2.d.h 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+5iq^{7}-2iq^{13}+q^{19}+11q^{31}+\cdots\)
2700.2.d.i 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{7}+2iq^{13}+7q^{19}-7q^{31}+\cdots\)
2700.2.d.j 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}+3q^{11}+iq^{13}+6iq^{17}+\cdots\)
2700.2.d.k 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+6q^{11}-iq^{13}+q^{19}+6iq^{23}+\cdots\)
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