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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
6900.2.a.a 6900.a 1.a $1$ $55.097$ \(\Q\) None \(0\) \(-1\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{7}+q^{9}-5q^{11}-q^{13}+\cdots\)
6900.2.a.b 6900.a 1.a $1$ $55.097$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}+4q^{13}+3q^{17}+\cdots\)
6900.2.a.c 6900.a 1.a $1$ $55.097$ \(\Q\) None \(0\) \(-1\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
6900.2.a.d 6900.a 1.a $1$ $55.097$ \(\Q\) None \(0\) \(-1\) \(0\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{7}+q^{9}+q^{11}-q^{13}-5q^{19}+\cdots\)
6900.2.a.e 6900.a 1.a $1$ $55.097$ \(\Q\) None \(0\) \(-1\) \(0\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}+q^{9}-2q^{13}-6q^{17}+\cdots\)
6900.2.a.f 6900.a 1.a $1$ $55.097$ \(\Q\) None \(0\) \(1\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{7}+q^{9}+q^{11}+q^{13}-5q^{19}+\cdots\)
6900.2.a.g 6900.a 1.a $1$ $55.097$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}+6q^{13}-2q^{17}+6q^{19}+\cdots\)
6900.2.a.h 6900.a 1.a $1$ $55.097$ \(\Q\) None \(0\) \(1\) \(0\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{7}+q^{9}-5q^{11}+q^{13}+\cdots\)
6900.2.a.i 6900.a 1.a $1$ $55.097$ \(\Q\) None \(0\) \(1\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+5q^{7}+q^{9}-4q^{13}+3q^{17}+\cdots\)
6900.2.a.j 6900.a 1.a $2$ $55.097$ \(\Q(\sqrt{15}) \) None \(0\) \(-2\) \(0\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{7}+q^{9}+(1-\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
6900.2.a.k 6900.a 1.a $2$ $55.097$ \(\Q(\sqrt{13}) \) None \(0\) \(-2\) \(0\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-2-\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
6900.2.a.l 6900.a 1.a $2$ $55.097$ \(\Q(\sqrt{13}) \) None \(0\) \(-2\) \(0\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-2-\beta )q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
6900.2.a.m 6900.a 1.a $2$ $55.097$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{7}+q^{9}+4\beta q^{11}-4\beta q^{13}+\cdots\)
6900.2.a.n 6900.a 1.a $2$ $55.097$ \(\Q(\sqrt{73}) \) None \(0\) \(-2\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}+(-1+\beta )q^{11}+q^{13}+\cdots\)
6900.2.a.o 6900.a 1.a $2$ $55.097$ \(\Q(\sqrt{21}) \) None \(0\) \(-2\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{7}+q^{9}+(1-\beta )q^{11}+\cdots\)
6900.2.a.p 6900.a 1.a $2$ $55.097$ \(\Q(\sqrt{10}) \) None \(0\) \(2\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-2+\beta )q^{7}+q^{9}-4q^{13}+\cdots\)
6900.2.a.q 6900.a 1.a $2$ $55.097$ \(\Q(\sqrt{21}) \) None \(0\) \(2\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta )q^{7}+q^{9}+(1-\beta )q^{11}+\cdots\)
6900.2.a.r 6900.a 1.a $2$ $55.097$ \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}+q^{9}+(-2-\beta )q^{11}-\beta q^{13}+\cdots\)
6900.2.a.s 6900.a 1.a $2$ $55.097$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+2\beta )q^{7}+q^{9}+(-1+3\beta )q^{11}+\cdots\)
6900.2.a.t 6900.a 1.a $2$ $55.097$ \(\Q(\sqrt{73}) \) None \(0\) \(2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}+q^{9}+(-1+\beta )q^{11}-q^{13}+\cdots\)
6900.2.a.u 6900.a 1.a $2$ $55.097$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{7}+q^{9}+2\beta q^{11}-2q^{13}+\cdots\)
6900.2.a.v 6900.a 1.a $2$ $55.097$ \(\Q(\sqrt{13}) \) None \(0\) \(2\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(3-\beta )q^{7}+q^{9}+(1-\beta )q^{11}+\cdots\)
6900.2.a.w 6900.a 1.a $2$ $55.097$ \(\Q(\sqrt{13}) \) None \(0\) \(2\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(3-\beta )q^{7}+q^{9}+(3-\beta )q^{11}+\cdots\)
6900.2.a.x 6900.a 1.a $3$ $55.097$ 3.3.3144.1 None \(0\) \(-3\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(1+\beta _{2})q^{11}+\cdots\)
6900.2.a.y 6900.a 1.a $3$ $55.097$ 3.3.148.1 None \(0\) \(-3\) \(0\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}-\beta _{2}q^{11}+(1-\beta _{1}+\cdots)q^{13}+\cdots\)
6900.2.a.z 6900.a 1.a $3$ $55.097$ 3.3.148.1 None \(0\) \(3\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}+q^{9}-\beta _{2}q^{11}+(-1+\beta _{1}+\cdots)q^{13}+\cdots\)
6900.2.a.ba 6900.a 1.a $4$ $55.097$ 4.4.175557.1 None \(0\) \(-4\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-\beta _{1}-\beta _{3})q^{7}+q^{9}-\beta _{1}q^{11}+\cdots\)
6900.2.a.bb 6900.a 1.a $4$ $55.097$ 4.4.175557.1 None \(0\) \(4\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta _{1}+\beta _{3})q^{7}+q^{9}-\beta _{1}q^{11}+\cdots\)
6900.2.a.bc 6900.a 1.a $7$ $55.097$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-7\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta _{1}q^{7}+q^{9}+(\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{11}+\cdots\)
6900.2.a.bd 6900.a 1.a $7$ $55.097$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(7\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{1}q^{7}+q^{9}+(\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{11}+\cdots\)
6900.2.f.a 6900.f 5.b $2$ $55.097$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+3iq^{7}-q^{9}-5q^{11}-iq^{13}+\cdots\)
6900.2.f.b 6900.f 5.b $2$ $55.097$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+3iq^{7}-q^{9}-2q^{11}-2iq^{13}+\cdots\)
6900.2.f.c 6900.f 5.b $2$ $55.097$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-q^{9}+6iq^{13}+2iq^{17}-6q^{19}+\cdots\)
6900.2.f.d 6900.f 5.b $2$ $55.097$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+4iq^{7}-q^{9}+2iq^{13}-6iq^{17}+\cdots\)
6900.2.f.e 6900.f 5.b $2$ $55.097$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+iq^{7}-q^{9}-4iq^{13}+3iq^{17}+\cdots\)
6900.2.f.f 6900.f 5.b $2$ $55.097$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+5iq^{7}-q^{9}+4iq^{13}+3iq^{17}+\cdots\)
6900.2.f.g 6900.f 5.b $2$ $55.097$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+3iq^{7}-q^{9}+q^{11}+iq^{13}+\cdots\)
6900.2.f.h 6900.f 5.b $4$ $55.097$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-\beta _{1}q^{7}-q^{9}+(-2+\beta _{3})q^{11}+\cdots\)
6900.2.f.i 6900.f 5.b $4$ $55.097$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{3}+(\zeta_{12}-2\zeta_{12}^{2})q^{7}-q^{9}+\cdots\)
6900.2.f.j 6900.f 5.b $4$ $55.097$ \(\Q(i, \sqrt{73})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}-\beta _{2}q^{7}-q^{9}+(-1+\beta _{3})q^{11}+\cdots\)
6900.2.f.k 6900.f 5.b $4$ $55.097$ \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(2\beta _{1}-\beta _{2})q^{7}-q^{9}-4\beta _{1}q^{13}+\cdots\)
6900.2.f.l 6900.f 5.b $4$ $55.097$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{3}-\zeta_{8}^{2}q^{7}-q^{9}-4\zeta_{8}^{3}q^{11}+\cdots\)
6900.2.f.m 6900.f 5.b $4$ $55.097$ \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(\beta _{1}+3\beta _{2})q^{7}-q^{9}+\beta _{3}q^{11}+\cdots\)
6900.2.f.n 6900.f 5.b $4$ $55.097$ \(\Q(i, \sqrt{21})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{7}-q^{9}+\beta _{3}q^{11}+\cdots\)
6900.2.f.o 6900.f 5.b $4$ $55.097$ \(\Q(i, \sqrt{15})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+3\beta _{1}q^{7}-q^{9}+(1+\beta _{2})q^{11}+\cdots\)
6900.2.f.p 6900.f 5.b $4$ $55.097$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+\beta _{1}q^{7}-q^{9}+(2-2\beta _{3})q^{11}+\cdots\)
6900.2.f.q 6900.f 5.b $4$ $55.097$ \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(\beta _{1}+3\beta _{2})q^{7}-q^{9}+(2+\beta _{3})q^{11}+\cdots\)
6900.2.f.r 6900.f 5.b $6$ $55.097$ 6.0.158155776.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{5})q^{7}-q^{9}+(1+\cdots)q^{11}+\cdots\)
6900.2.f.s 6900.f 5.b $8$ $55.097$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{3}+(-\beta _{4}+\beta _{5})q^{7}-q^{9}+\beta _{2}q^{11}+\cdots\)
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