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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
48.2.a.a 48.a 1.a $1$ $0.383$ \(\Q\) None \(0\) \(1\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
48.2.c.a 48.c 12.b $2$ $0.383$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{3}+2\zeta_{6}q^{7}-3q^{9}-2q^{13}+\cdots\)
48.2.j.a 48.j 16.e $8$ $0.383$ 8.0.18939904.2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta _{4}+\beta _{5})q^{2}-\beta _{5}q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
48.2.k.a 48.k 48.k $12$ $0.383$ 12.0.\(\cdots\).2 None \(0\) \(-2\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{6}q^{2}-\beta _{10}q^{3}+(-\beta _{1}+\beta _{10}+\beta _{11})q^{4}+\cdots\)
48.3.e.a 48.e 3.b $1$ $1.308$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(-2\) $\mathrm{U}(1)[D_{2}]$ \(q+3q^{3}-2q^{7}+9q^{9}-22q^{13}-26q^{19}+\cdots\)
48.3.e.b 48.e 3.b $2$ $1.308$ \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta )q^{3}+2\beta q^{5}+6q^{7}+(-7+\cdots)q^{9}+\cdots\)
48.3.g.a 48.g 4.b $2$ $1.308$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}+6q^{5}-4\zeta_{6}q^{7}-3q^{9}+12\zeta_{6}q^{11}+\cdots\)
48.3.i.a 48.i 48.i $8$ $1.308$ 8.0.629407744.1 None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{4}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots\)
48.3.i.b 48.i 48.i $20$ $1.308$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{15}q^{2}+\beta _{4}q^{3}+(\beta _{1}+\beta _{8}-\beta _{12}+\cdots)q^{4}+\cdots\)
48.3.l.a 48.l 16.f $16$ $1.308$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{2}-\beta _{5}q^{3}+(1-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
48.4.a.a 48.a 1.a $1$ $2.832$ \(\Q\) None \(0\) \(-3\) \(-18\) \(-8\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-18q^{5}-8q^{7}+9q^{9}-6^{2}q^{11}+\cdots\)
48.4.a.b 48.a 1.a $1$ $2.832$ \(\Q\) None \(0\) \(-3\) \(14\) \(24\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+14q^{5}+24q^{7}+9q^{9}+28q^{11}+\cdots\)
48.4.a.c 48.a 1.a $1$ $2.832$ \(\Q\) None \(0\) \(3\) \(6\) \(16\) $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+6q^{5}+2^{4}q^{7}+9q^{9}-12q^{11}+\cdots\)
48.4.c.a 48.c 12.b $2$ $2.832$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{3}-6\zeta_{6}q^{7}-3^{3}q^{9}+70q^{13}+\cdots\)
48.4.c.b 48.c 12.b $4$ $2.832$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}-\beta _{3}q^{5}-5\beta _{1}q^{7}+(21-\beta _{3})q^{9}+\cdots\)
48.4.j.a 48.j 16.e $24$ $2.832$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
48.4.k.a 48.k 48.k $44$ $2.832$ None \(0\) \(-2\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$
48.5.e.a 48.e 3.b $1$ $4.962$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-9\) \(0\) \(94\) $\mathrm{U}(1)[D_{2}]$ \(q-9q^{3}+94q^{7}+3^{4}q^{9}+146q^{13}+\cdots\)
48.5.e.b 48.e 3.b $2$ $4.962$ \(\Q(\sqrt{-2}) \) None \(0\) \(6\) \(0\) \(-52\) $\mathrm{SU}(2)[C_{2}]$ \(q+(3+\beta )q^{3}+2\beta q^{5}-26q^{7}+(-63+\cdots)q^{9}+\cdots\)
48.5.e.c 48.e 3.b $4$ $4.962$ \(\Q(\sqrt{-2}, \sqrt{13})\) None \(0\) \(4\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\)
48.5.g.a 48.g 4.b $2$ $4.962$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-84\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\zeta_{6}q^{3}-42q^{5}+44\zeta_{6}q^{7}-3^{3}q^{9}+\cdots\)
48.5.g.b 48.g 4.b $2$ $4.962$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}+6q^{5}-12\zeta_{6}q^{7}-3^{3}q^{9}+\cdots\)
48.5.i.a 48.i 48.i $60$ $4.962$ None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
48.5.l.a 48.l 16.f $32$ $4.962$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
48.6.a.a 48.a 1.a $1$ $7.698$ \(\Q\) None \(0\) \(-9\) \(6\) \(40\) $-$ $\mathrm{SU}(2)$ \(q-9q^{3}+6q^{5}+40q^{7}+3^{4}q^{9}+564q^{11}+\cdots\)
48.6.a.b 48.a 1.a $1$ $7.698$ \(\Q\) None \(0\) \(-9\) \(38\) \(-120\) $+$ $\mathrm{SU}(2)$ \(q-9q^{3}+38q^{5}-120q^{7}+3^{4}q^{9}+\cdots\)
48.6.a.c 48.a 1.a $1$ $7.698$ \(\Q\) None \(0\) \(9\) \(-66\) \(-176\) $+$ $\mathrm{SU}(2)$ \(q+9q^{3}-66q^{5}-176q^{7}+3^{4}q^{9}+\cdots\)
48.6.a.d 48.a 1.a $1$ $7.698$ \(\Q\) None \(0\) \(9\) \(-34\) \(240\) $-$ $\mathrm{SU}(2)$ \(q+9q^{3}-34q^{5}+240q^{7}+3^{4}q^{9}+\cdots\)
48.6.a.e 48.a 1.a $1$ $7.698$ \(\Q\) None \(0\) \(9\) \(94\) \(-144\) $-$ $\mathrm{SU}(2)$ \(q+9q^{3}+94q^{5}-12^{2}q^{7}+3^{4}q^{9}+\cdots\)
48.6.c.a 48.c 12.b $2$ $7.698$ \(\Q(\sqrt{-11}) \) None \(0\) \(-24\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-12-\beta )q^{3}-8\beta q^{5}+18\beta q^{7}+\cdots\)
48.6.c.b 48.c 12.b $2$ $7.698$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-9\zeta_{6}q^{3}-62\zeta_{6}q^{7}-3^{5}q^{9}-1202q^{13}+\cdots\)
48.6.c.c 48.c 12.b $2$ $7.698$ \(\Q(\sqrt{-11}) \) None \(0\) \(24\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(12+\beta )q^{3}-8\beta q^{5}-18\beta q^{7}+(45+\cdots)q^{9}+\cdots\)
48.6.c.d 48.c 12.b $4$ $7.698$ \(\Q(\sqrt{-3}, \sqrt{-14})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2\beta _{1}-\beta _{2})q^{3}-\beta _{3}q^{5}+11\beta _{1}q^{7}+\cdots\)
48.6.j.a 48.j 16.e $40$ $7.698$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
48.6.k.a 48.k 48.k $76$ $7.698$ None \(0\) \(-2\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$
48.7.e.a 48.e 3.b $1$ $11.043$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(27\) \(0\) \(286\) $\mathrm{U}(1)[D_{2}]$ \(q+3^{3}q^{3}+286q^{7}+3^{6}q^{9}+506q^{13}+\cdots\)
48.7.e.b 48.e 3.b $2$ $11.043$ \(\Q(\sqrt{-2}) \) None \(0\) \(-42\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-21+\beta )q^{3}+10\beta q^{5}-2q^{7}+(153+\cdots)q^{9}+\cdots\)
48.7.e.c 48.e 3.b $2$ $11.043$ \(\Q(\sqrt{-5}) \) None \(0\) \(6\) \(0\) \(-484\) $\mathrm{SU}(2)[C_{2}]$ \(q+(3+\beta )q^{3}-6\beta q^{5}-242q^{7}+(-711+\cdots)q^{9}+\cdots\)
48.7.e.d 48.e 3.b $6$ $11.043$ 6.0.1173604352.2 None \(0\) \(10\) \(0\) \(-156\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2-\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-3^{3}+\cdots)q^{7}+\cdots\)
48.7.g.a 48.g 4.b $2$ $11.043$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-180\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}-90q^{5}+12\zeta_{6}q^{7}-3^{5}q^{9}+\cdots\)
48.7.g.b 48.g 4.b $2$ $11.043$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-9\zeta_{6}q^{3}+6q^{5}-116\zeta_{6}q^{7}-3^{5}q^{9}+\cdots\)
48.7.g.c 48.g 4.b $2$ $11.043$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(300\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-9\zeta_{6}q^{3}+150q^{5}+188\zeta_{6}q^{7}-3^{5}q^{9}+\cdots\)
48.7.i.a 48.i 48.i $92$ $11.043$ None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
48.7.l.a 48.l 16.f $48$ $11.043$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
48.8.a.a 48.a 1.a $1$ $14.994$ \(\Q\) None \(0\) \(-27\) \(-530\) \(-120\) $+$ $\mathrm{SU}(2)$ \(q-3^{3}q^{3}-530q^{5}-120q^{7}+3^{6}q^{9}+\cdots\)
48.8.a.b 48.a 1.a $1$ $14.994$ \(\Q\) None \(0\) \(-27\) \(-114\) \(1576\) $-$ $\mathrm{SU}(2)$ \(q-3^{3}q^{3}-114q^{5}+1576q^{7}+3^{6}q^{9}+\cdots\)
48.8.a.c 48.a 1.a $1$ $14.994$ \(\Q\) None \(0\) \(-27\) \(110\) \(-504\) $+$ $\mathrm{SU}(2)$ \(q-3^{3}q^{3}+110q^{5}-504q^{7}+3^{6}q^{9}+\cdots\)
48.8.a.d 48.a 1.a $1$ $14.994$ \(\Q\) None \(0\) \(-27\) \(270\) \(-1112\) $-$ $\mathrm{SU}(2)$ \(q-3^{3}q^{3}+270q^{5}-1112q^{7}+3^{6}q^{9}+\cdots\)
48.8.a.e 48.a 1.a $1$ $14.994$ \(\Q\) None \(0\) \(27\) \(-378\) \(832\) $+$ $\mathrm{SU}(2)$ \(q+3^{3}q^{3}-378q^{5}+832q^{7}+3^{6}q^{9}+\cdots\)
48.8.a.f 48.a 1.a $1$ $14.994$ \(\Q\) None \(0\) \(27\) \(-26\) \(-1056\) $-$ $\mathrm{SU}(2)$ \(q+3^{3}q^{3}-26q^{5}-1056q^{7}+3^{6}q^{9}+\cdots\)
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