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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
6300.2.a.a 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}-6q^{11}+4q^{13}+6q^{17}+2q^{19}+\cdots\)
6300.2.a.b 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{7}-4q^{11}-2q^{13}+2q^{17}-2q^{19}+\cdots\)
6300.2.a.c 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{7}-3q^{11}-q^{13}-5q^{17}-8q^{19}+\cdots\)
6300.2.a.d 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}-3q^{11}+q^{13}-3q^{17}+2q^{19}+\cdots\)
6300.2.a.e 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}-3q^{11}+4q^{13}+2q^{19}-3q^{23}+\cdots\)
6300.2.a.f 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}-q^{11}-4q^{13}+2q^{17}-4q^{19}+\cdots\)
6300.2.a.g 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{7}-4q^{13}+4q^{17}+4q^{19}+8q^{23}+\cdots\)
6300.2.a.h 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{7}+4q^{13}-6q^{17}+2q^{19}-6q^{23}+\cdots\)
6300.2.a.i 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{7}+4q^{13}+6q^{17}+2q^{19}+6q^{23}+\cdots\)
6300.2.a.j 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{7}+q^{11}-2q^{13}-8q^{17}-2q^{19}+\cdots\)
6300.2.a.k 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{7}+q^{11}-2q^{13}+6q^{19}-q^{23}+\cdots\)
6300.2.a.l 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}+2q^{11}-4q^{13}+2q^{17}+2q^{19}+\cdots\)
6300.2.a.m 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}+3q^{11}+4q^{13}-6q^{17}-4q^{19}+\cdots\)
6300.2.a.n 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{7}+4q^{11}+6q^{13}+2q^{17}+6q^{19}+\cdots\)
6300.2.a.o 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{7}+5q^{11}+6q^{13}+4q^{17}-6q^{19}+\cdots\)
6300.2.a.p 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}+6q^{11}-2q^{13}-4q^{19}-6q^{23}+\cdots\)
6300.2.a.q 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}-4q^{11}+2q^{17}-6q^{19}+6q^{23}+\cdots\)
6300.2.a.r 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}-4q^{11}+2q^{13}-2q^{17}-2q^{19}+\cdots\)
6300.2.a.s 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}-3q^{11}-4q^{13}+2q^{19}+3q^{23}+\cdots\)
6300.2.a.t 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}-3q^{11}+q^{13}+5q^{17}-8q^{19}+\cdots\)
6300.2.a.u 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}-2q^{11}-4q^{13}+2q^{17}-2q^{19}+\cdots\)
6300.2.a.v 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}-2q^{11}-4q^{13}+6q^{17}+6q^{19}+\cdots\)
6300.2.a.w 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}-2q^{11}+6q^{13}-4q^{17}-4q^{19}+\cdots\)
6300.2.a.x 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}-q^{11}+4q^{13}-2q^{17}-4q^{19}+\cdots\)
6300.2.a.y 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}+4q^{13}-4q^{17}+4q^{19}-8q^{23}+\cdots\)
6300.2.a.z 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}+q^{11}+2q^{13}+6q^{19}+q^{23}+\cdots\)
6300.2.a.ba 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}+q^{11}+2q^{13}+8q^{17}-2q^{19}+\cdots\)
6300.2.a.bb 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}+3q^{11}-4q^{13}+6q^{17}-4q^{19}+\cdots\)
6300.2.a.bc 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}+4q^{11}-6q^{13}-2q^{17}+6q^{19}+\cdots\)
6300.2.a.bd 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}+4q^{11}-2q^{17}-6q^{19}-6q^{23}+\cdots\)
6300.2.a.be 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}+5q^{11}-6q^{13}-4q^{17}-6q^{19}+\cdots\)
6300.2.a.bf 6300.a 1.a $1$ $50.306$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}+5q^{11}+3q^{13}-q^{17}+6q^{19}+\cdots\)
6300.2.a.bg 6300.a 1.a $2$ $50.306$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{7}+\beta q^{11}-2q^{13}+2q^{19}-\beta q^{23}+\cdots\)
6300.2.a.bh 6300.a 1.a $2$ $50.306$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}+\beta q^{11}+2\beta q^{17}-3\beta q^{23}+\cdots\)
6300.2.a.bi 6300.a 1.a $2$ $50.306$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}+\beta q^{11}-2\beta q^{17}+3\beta q^{23}+\cdots\)
6300.2.a.bj 6300.a 1.a $2$ $50.306$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}+\beta q^{11}+2q^{13}+2q^{19}+\beta q^{23}+\cdots\)
6300.2.a.bk 6300.a 1.a $4$ $50.306$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}+(-\beta _{1}-\beta _{3})q^{11}+(-1+\beta _{2}+\cdots)q^{13}+\cdots\)
6300.2.a.bl 6300.a 1.a $4$ $50.306$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}+(-\beta _{1}-\beta _{3})q^{11}+(1-\beta _{2})q^{13}+\cdots\)
6300.2.d.a 6300.d 21.c $4$ $50.306$ \(\Q(\sqrt{-2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{3})q^{7}-\beta _{1}q^{11}+(\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
6300.2.d.b 6300.d 21.c $4$ $50.306$ \(\Q(\sqrt{-2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{3})q^{7}+\beta _{1}q^{11}+(\beta _{1}+\beta _{2}+\cdots)q^{13}+\cdots\)
6300.2.d.c 6300.d 21.c $4$ $50.306$ \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{1})q^{7}+\beta _{2}q^{11}+2\beta _{1}q^{13}+\cdots\)
6300.2.d.d 6300.d 21.c $12$ $50.306$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{7}-\beta _{9}q^{11}+\beta _{8}q^{13}+\beta _{1}q^{17}+\cdots\)
6300.2.d.e 6300.d 21.c $12$ $50.306$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{7}-\beta _{9}q^{11}-\beta _{8}q^{13}-\beta _{1}q^{17}+\cdots\)
6300.2.d.f 6300.d 21.c $16$ $50.306$ 16.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{7}q^{7}-\beta _{1}q^{11}+\beta _{2}q^{13}-\beta _{4}q^{17}+\cdots\)
6300.2.f.a 6300.f 105.g $8$ $50.306$ 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{2}+\beta _{3})q^{7}-\beta _{4}q^{11}+(\beta _{3}+\beta _{7})q^{13}+\cdots\)
6300.2.f.b 6300.f 105.g $8$ $50.306$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{24}^{3}q^{7}+\zeta_{24}^{5}q^{11}+(-\zeta_{24}-2\zeta_{24}^{3}+\cdots)q^{13}+\cdots\)
6300.2.f.c 6300.f 105.g $8$ $50.306$ 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{2}+\beta _{3})q^{7}-\beta _{4}q^{11}+(\beta _{3}+\beta _{7})q^{13}+\cdots\)
6300.2.f.d 6300.f 105.g $24$ $50.306$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
6300.2.k.a 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{7}-6q^{11}-4iq^{13}+6iq^{17}+\cdots\)
6300.2.k.b 6300.k 5.b $2$ $50.306$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}-4q^{11}+2iq^{17}+6q^{19}+\cdots\)
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